Laurynas Sketeris

Alessandro Ratto

Oliver Allemann

Sarah Gaby

Magdalena Hugo

Manu Etienne David

Gadea A † Van

Cossard P Gillard-Bocquet

Van Assche

Assche D Van

J.-C And Baret

Keywords:

Development of droplet-based microfluidic tools for high-throughput screening

Key words: Droplet microfluidics -electric fields -high-throughput -coacervates Over the past two decades, droplet-based microfluidics has emerged as a technology in a range of high-throughput applications. As a primary application, it is utilized as a method for high-throughput screening of cells. A droplet may serve as a microcompartment to perform a biochemical assay for

the individual compartmentalization and analysis of a single cell. It is possible to produce millions of picoliter droplets, making it possible to perform millions of single cell biochemical assays with a small volume of reagents. Nevertheless, the controlled high-throughput manipulation of picoliter droplets is challenging and could benefit from the implementation of novel tools. This thesis presents experimental studies for the development of new tools, and the analysis and application of existing tools in droplet-based microfluidics.

In three of the presented studies, electric fields are utilized as an external means of control for three essential modules in high-throughput screening: (i) production; (ii) coalescence; (iii) sorting.

(i) Electric fields are implemented to provide a tool to increase the monodispersity of droplet production in hydrodynamic jets. (ii) A fundamental study of the coalescence of two droplets under the influence of electric fields is performed to address open questions on the influence of the electric properties of the system on the electrocoalescence mechanism. (iii) Electric fields are incorporated in a fully integrated microfluidic device for sorting of droplets, for directed evolution purposes of the enzyme glucose oxidase.

In study four, liquid-liquid phase separation in droplets is demonstrated as a tool to enhance the limit-of-detection in droplets. Moreover, this study involves the analysis of enzyme kinetics in phase separated systems with droplets, which could be of interest to shed light on the function of biomolecular condensates in cells. Au cours des deux dernières décennies, la microfluidique à base de gouttelettes est devenue une technologie dans une grande gamme d'applications à haut débit en particulier comme méthode de criblage à haut débit de cellules. Les gouttelettes servent de microcompartiments pour effectuer des tests biochimiques pour l'analyse d'une seule cellule. Il est possible de produire des millions de gouttelettes de quelques picolitres, ce qui permet d'effectuer des millions d'analyses biochimiques sur cellules uniques avec un petit volume de réactifs, et en parallèle. Néanmoins, la manipulation contrôlée à haut débit de gouttelettes de picolitres nécessite toujours de la mise en oeuvre de nouveaux outils.

Centre de Recherche

Cette thèse présente des études expérimentales pour le développement de nouveaux outils, ainsi que l'analyse et l'application d'outils existants en microfluidique à base de gouttelettes.

Dans trois des études présentées, les champs électriques sont utilisés comme moyen de contrôle externe pour trois modules essentiels dans le criblage à haut débit : (i) production ; (ii) coalescence ;

(iii) le tri. (i) Des champs électriques sont mis en oeuvre pour fournir un outil permettant d'augmenter la monodispersité de la production de gouttelettes dans les jets hydrodynamiques. (ii) Une étude fondamentale de la coalescence de deux gouttelettes sous l'influence de champs électriques est réalisée pour répondre aux questions ouvertes sur l'influence des propriétés électriques du système sur le mécanisme d'électrocoalescence. (iii) Des champs électriques sont incorporés dans un dispositif microfluidique entièrement intégré pour le tri des gouttelettes, à des fins d'évolution dirigée de l'enzyme glucose oxydase.

Dans la quatrième étude, la séparation de phase liquide-liquide dans les gouttelettes est démontrée comme un outil pour améliorer la limite de détection dans les gouttelettes. Cette étude est basée sure l'analyse de la cinétique enzymatique dans des systèmes à séparation de phase liquide-liquide avec des gouttelettes qui pourraient être ultérieurement utilisées pour mieux comprendre la fonction des condensats biomoléculaires dans les cellules.

Droplet-based microfluidics

Since the first microscopic studies of cells in the 17 th century, methods for cell analysis have continuously improved, which has led to many discoveries in biology and medicine [START_REF] Hook | Micrographia: Or some physiological descriptions of minute bodies made by magnifying glasses with observation and inquiries thereupon[END_REF]. However, there are still many open questions, such as what governs the regulation and metastasis of cancer. Traditionally cells are studied in Petri dishes or microwell plates. These systems have several shortcomings: they are limited in throughput, are expensive, and typically require several manual handling steps. Moreover, in these systems, a population of cells is studied and the response is an average measured over the whole population. Yet, individual cells within a population have shown a high level of heterogeneity. For example, cancer cells within the same tumor show phenotypic and functional differences [START_REF] Corbin | Tumour heterogeneity and cancer cell plasticity[END_REF]. Single cell studies are required to elucidate the origin of these heterogeneities which are hidden by populationaveraged measurements. With these studies the responses of individual cells are measured, which could shed light on the occurrence of therapy resistance to certain drugs or disease progression.

Over the past two decades, droplet microfluidics has emerged as a technology that could tackle some of the shortcomings of traditional methods. It is a technology where small droplets of one fluid (typically water) are manipulated in another immiscible fluid (typically oil). The technology is interesting for single cell studies because individual cells can be encapsulated in droplets, and the droplets serve as reaction vessels for analysis. It is possible to produce droplets in the range of picoliter volumes at a high rate which reduces reagent costs and increases throughput. However precise manipulation of picoliter volumes is not trivial. A variety of methods to produce and manipulate droplets are essential to meet the diverse requirements for different biochemical assays for single cell studies. The development of new and improved methods is required to advance the integration and automation of droplet microfluidics in the laboratory. In this chapter we introduce the general concept of droplet-based microfluidics. We introduce the necessary physical and chemical concepts and sketch the framework to use dropletbased microfluidics as a tool in life sciences. The chapter is finished with relevant examples of established workflows utilizing droplet microfluidics.

Basic concepts in microfluidics

Microfluidics is the field of study that deals with fluid flow at the microscale range. When moving to the microscale realm, physical phenomena which are usually negligible on the macroscale become more prominent. As illustrated in Equation 2.1, when decreasing in lengthscale L, surface effects (interfacial tension, viscosity, adhesion) gain importance over volume effects (gravity, momentum) [START_REF] Bruus | Theoretical Microfluidics[END_REF].

surface forces volume forces ∝ L 2 L 3 = L -1 ----→ L → 0 ∞ (2.1)
The Reynolds number (R) is a relevant illustration in microfluidics of the change in physics when decreasing to the microscale. The Reynolds number relates the inertial forces to the viscous forces (Equation 2.2) and it is used as a tool to predict the flow pattern in different situations.

R = ρ • u • L η (2.2)
Here ρ is the density, u the velocity and η the dynamic viscosity of the fluid, and L the typical length scale. When R < 2000 flow is laminar as opposed to turbulent flow when R > 3000.

Because L is low in microfluidics, in the range of micrometer scale, one works at low R in the laminar flow regime. Microfluidics has gained interest over the last decades due to this laminar flow regime as it allows for a predictable and controlled flow resulting in the possibility for so-called Lab-on-a-Chip (LOC) systems. These are microfluidic devices that can perform a miniaturized operation on a microfluidic chip. Due to the small dimensions of these LOC systems, only a low volume is required to perform a biochemical assay, reducing costs. However, several fundamental limitations have occurred when dealing with singlephase microfluidics: (i) cross-contamination of samples when using the same microfluidic channel for several assays; (ii) limited throughput, one assay needs one channel; (iii) rapid mixing of reagents is usually challenging as it is diffusion-limited.

Droplet-based microfluidics

Droplet-based microfluidics has emerged as a subfield of microfluidics in the past two decades [START_REF] Lee | Droplet Microfluidics[END_REF]. It deals with the flow of two immiscible fluids on the microscale. It emerged as it allows to omit some of the limitations of single-phase microfluidics: (i) by creating water-in-oil (w/o) droplets it is possible to compartmentalize a biochemical assay in one drop and in this way increase the throughput; (ii) the issue of surface contamination is omitted when the oil phase preferentially wets the channel surface; (iii) by the introduction of two immiscible fluids, one creates an interface which induces convective flow resolving the diffusion-limited mixing in single phase microfluidics.

Physics and chemistry of droplets

Introducing a second immiscible oil phase in a microfluidic system has advantages, but at the same time also creates a more complex and challenging system to understand and manipulate. In this section we will discuss the most important physical features and requirements that are essential for utilizing droplet microfluidics.

Interfacial tension

The main change droplets bring compared to single-phase microfluidics is the introduction of an interface and the adjoining interfacial tension. Interfacial tension, typically denoted by the Greek symbol γ, originates from the intermolecular attractions and the imbalance of those interactions at the interface compared to the bulk, resulting in excess energy at the surface. One can interpret the interfacial tension in two ways [START_REF] Baroud | Dynamics of microfluidic droplets[END_REF]: (i) it is expressed as a force per unit length (N/m). It can be seen as a force that pulls on the interface, any imbalance in this force along the interface will therefore create a flow from low to high interfacial tension. Flow induced by differences in surface tension is better known as the Marangoni effect. (ii) One can express the surface tension as energy per unit area (J/m 2 ). To reduce the free energy of the surface, the interfacial tension tries to minimize the surface area. This explains why the shape of a droplet is a sphere, as it is the minimum surface area for a given volume. Furthermore, it also explains the spontaneous coalescence of droplets in an emulsion, because the minimum energy in a mixture of two immiscible phases is a configuration where the liquids are separated in just two phases. To further clarify this we express the reduction in surface area when two droplets of the same volume V 1 fuse (Figure 2.1). One finds for a fused droplet with volume V 2 = 2V 1 the radius to be r 2 = 3 √ 2r 1 .

Expressing the surface area of the fused sphere one finds A 2 = 4π 3 √ 4r 2 1 < 2A 1 = 8πr 2 . Fusion of two droplets of the same volume results in a reduction of 21% in surface area.

In analogy with the definition of R which relates viscous and inertial stresses, the Capillary number (C) is a dimensionless number defined to compare the magnitude of the viscous stress and the interfacial stress to know which effect dominates (Equation 2.3).

C = η • u γ (2.3) A = 4πr 1 2 1 -4 3 V = πr 1 3 1 A 1 V 1 A 1 V 1 A = 4πr 2 2 2 -4 3 V = πr 2 3 2 A 2 V = 2V

Surfactant

It is thermodynamically favorable for drops to coalesce to minimize the energy in the system, which is detrimental to droplet microfluidics. Surfactants provide an energy barrier against coalescence. A surfactant molecule is an amphiphilic molecule, i.e. different parts of the molecule have an affinity for different immiscible phases. This specific property drives the surfactant molecule to the interface of the immiscible phases. The interfacial tension is decreased as a result of the adsorption of the surfactant at the interface. The relation between the surface tension and the local coverage of the surfactant molecule is described by the Gibbs adsorption isotherm for dilute solutions [START_REF] Cabane | Liquides. Solutions, dispersions, émulsions, gels: Solutions, dispersions, émulsions, gels[END_REF][START_REF] Baret | Fluorescenceactivated droplet sorting (fads): efficient microfluidic cell sorting based on enzymatic activity[END_REF]:

Γ = - c RT dγ dc (2.4)
with Γ the surface concentration, γ the surface tension, c the surfactant concentration in the bulk, T the temperature and R the gas constant. Any change in shape or curvature of the droplet will further lead to a local contraction or expansion of the interface resulting in an increase or decrease of the local surfactant concentration [START_REF] Baroud | Dynamics of microfluidic droplets[END_REF][START_REF] Brosseau | Microfluidic dynamic interfacial tensiometry (µdit)[END_REF]. Next to that, fluid flow also alters the local surfactant coverage of a droplet. As a result of non-uniform surfactant coverage due to fluid flow, it was observed that the interface of a rising bubble rigidifies due to the Marangoni effect (more surfactant at the rear and less at the front of the droplet) [START_REF] Ybert | Ascending air bubbles in protein solutions[END_REF].

The adsorption kinetics of the surfactant molecule is essential for rapid stabilization of the emulsion. It was found that 90% of the interface should be covered to prevent droplet coalescence [START_REF] Riechers | Surfactant adsorption kinetics in microfluidics[END_REF]. Surfactants work through several ways to prevent coalescence [START_REF] Baret | Surfactants in droplet-based microfluidics[END_REF]: (i) the overall energy in the system is reduced due to a reduced surface tension; (ii) steric repulsion of surfactant molecules at the droplet interface hinders the approach of droplets;

(iii) the drainage of the liquid film between two droplets induces surfactant gradients which generates a force working against this drainage due to the Marangoni effect [START_REF] Dai | The mechanism of surfactant effects on drop coalescence[END_REF].

There are three main requirements for surfactants for applications related to the high-throughput screening of cells: (i) the surfactant must ensure droplet stability; (ii) molecular exchange between droplets should be limited; (iii) the surfactant should be biocompatible and not interfere with chemical reactions in the droplet. Many applications nowadays rely on fluorinated oils and fluorosurfactants. The surfactant molecule is most often a tri-block copolymer consisting of two blocks of perfluorinated polyethers linked with polyethyleneglycol (PFPE-PEG-PFPE) (Figure 2.2) [START_REF] Holtze | Biocompatible surfactants for water-influorocarbon emulsions[END_REF].

Formulations and molecular transport

The physical chemistry in droplet-based microfluidics is highly dependent on the formulations which are used. For biotechnology applications, perfluorinated oils are preferred for the continuous phase of the emulsion because they have several advantages. First of all, perfluorocarbons are extremely nonpolar which results in weak intermolecular forces. There is an availability of interstitial space due to these weak intermolecular forces resulting in a high solubility of respiratory gasses [START_REF] Hamza | Solute-solvent interactions in perfluorocarbon solutions of oxygen. an nmr study[END_REF]. This gives the possibility to culture cells in aqueous droplets with perfluorinated oil as a continuous phase [START_REF] Clausell-Tormos | Droplet-based microfluidic platforms for the encapsulation and screening of mammalian cells and multicellular organisms[END_REF]. Secondly, fluorocarbons are compatible with PDMS because it does not swell PDMS as compared to hydrocarbons [START_REF] Ng | Solvent compatibility of poly (dimethylsiloxane)-based microfluidic devices[END_REF].

Thirdly, molecular transport between droplets is limited because perfluorocarbons are very nonpolar, i.e. the solubility of non-fluorous compounds is very low [START_REF] Bai | A double droplet trap system for studying mass transport across a droplet-droplet interface[END_REF].

Molecular transport in the emulsion homogenizes the concentration of molecules between droplets which is detrimental for screening applications. It was shown that the exchange of small molecules in water-in-fluorinated oil emulsions directly relates to the hydrophobicity of the molecule [START_REF] Woronoff | New generation of amino coumarin methyl sulfonate-based fluorogenic substrates for amidase assays in droplet-based microfluidic applications[END_REF] and for a first estimation one can look at the LogP value to estimate the compatibility of a molecule with these systems [START_REF] Woronoff | New generation of amino coumarin methyl sulfonate-based fluorogenic substrates for amidase assays in droplet-based microfluidic applications[END_REF][START_REF] Janiesch | Key factors for stable retention of fluorophores and labeled biomolecules in droplet-based microfluidics[END_REF]. Furthermore, the molecular transport is affected by the constituents of the aqueous phase. Addition of Bovine Serum Albumin (BSA) or sodium chloride has been shown to affect the exchange rate of fluorophores. BSA is suspected to bind to solutes and in this way increase the solubility of the component in the aqueous phase or decrease it in the continuous phase [START_REF] Skhiri | Dynamics of molecular transport by surfactants in emulsions[END_REF]. Sodium chloride was shown to work in the opposite way. By the addition of salts, more water molecules are involved in the solvation which leaves fewer water molecules available to hydrate the fluorophores. The solubility in the aqueous phase is therefore decreased with an increased salt concentration [START_REF] Gruner | Controlling molecular transport in minimal emulsions[END_REF].

A final essential parameter for stable molecular retention in droplets, apart from the properties of the aqueous and oil phase, is the properties of the surfactant. The physical properties of the surfactant, such as the geometry, molecular weight, and concentration can be tuned to increase molecular retention [START_REF] Janiesch | Key factors for stable retention of fluorophores and labeled biomolecules in droplet-based microfluidics[END_REF]. It was demonstrated that increased surfactant concentration increases the solubility of organic compounds in the continuous phase due to the formation of micelles, and in this way increases the exchange rate between droplets [START_REF] Skhiri | Dynamics of molecular transport by surfactants in emulsions[END_REF].

Increased molecular weight increases the thickness of the surfactant layer, which increases the energy barrier that molecules have to pass which reduces the exchange rate [START_REF] Janiesch | Key factors for stable retention of fluorophores and labeled biomolecules in droplet-based microfluidics[END_REF]. Furthermore, the structure of the surfactant affects the density of the layer at the water droplet interface. It was shown that a di-block polymer reduces the molecular transport as it can be more densely packed compared to a tri-block surfactant [START_REF] Janiesch | Key factors for stable retention of fluorophores and labeled biomolecules in droplet-based microfluidics[END_REF]. However, for droplet stability reasons a tri-block surfactant is preferred. In this regard, recently a novel dendronized surfactant was synthesized [START_REF] Mohammad Suman Chowdhury | Dendronized fluorosurfactant for highly stable water-in-fluorinated oil emulsions with minimal inter-droplet transfer of small molecules[END_REF]. This di-block surfactant has a fluorinated tail with a dendritic head group. Interactions between the dendrites of different surfactant molecules create a dense layer at the interface which limits molecular transport. Furthermore, there is an interest in the use of functionalized nanoparticles instead of surfactant molecules as they also tend to make a dense layer at the interface which limits molecular transport. However, the stability of droplets against coalescence remains challenging due to the slower adsorption kinetics of the nanoparticles [START_REF] Andreina | Rapid stabilization of droplets by particles in microfluidics: Role of droplet formation[END_REF].

Fluid flow within a droplet

The creation of a droplet implies a new set of physical boundary conditions at the interface: the velocity of the fluid at the interface should be equal. Due to the w/o interface friction, recirculating viscous streaming is generated inside the droplet when a droplet moves through the oil phase. This streaming is essential for rapid mixing of droplet content, which is usually challenging in single-phase microfluidics. This flow is symmetric when a droplet flows through a straight microchannel. When the microchannel is curved this symmetry disap-pears, and the resulting flow is a superposition of the internal flow and the circular flow field. The internal flow fields are visualized through microparticle imaging velocimetry in Figure 2.3 [START_REF] Malsch | upiv-analysis of taylor flow in micro channels[END_REF]. Therefore, to ensure rapid homogenization of the droplet content one can easily introduce a perturbation in the internal flow by introducing a short zigzag section in the microchannel [START_REF] Song | A microfluidic system for controlling reaction networks in time[END_REF]. To get a complete and correct picture of the generated flow field inside a droplet one needs to take into account the fluid properties, flow rates, and channel geometry.

A B

Droplets in external fields

The development of methods for droplet-based microfluidics has been essential for the application in high-throughput screening with biological assays. Overall we can distinguish two types of methods. On the one hand, passive methods use microfluidic structures to shape the local flow and work on all droplets without selectivity. On the other hand, active methods introduce external energy in the system which can be triggered to actively control the behavior of droplets. These external fields can be used to create more complex workflows and have a higher level of integration and automation of droplet microfluidics in a laboratory environment. Several external physical fields are used to provide external energy. In this regard, magnetic, pneumatic, and thermal control have been illustrated [START_REF] Joon | Magnetophoretic sorting of microdroplets with different microalgal cell densities for rapid isolation of fast growing strains[END_REF][START_REF] Choi | Designed pneumatic valve actuators for controlled droplet breakup and generation[END_REF][START_REF] Charles N Baroud | Thermocapillary valve for droplet production and sorting[END_REF]. However, the most commonly integrated external fields for droplet microfluidics are acoustic and electric fields. In this thesis, we focus on the use of electric fields, which will be introduced in

Droplets in external fields

the following section. Acoustic fields, although they are an interesting tool, are outside the scope of this thesis. We refer the reader to a recent review article by Zhang et al. for more information on the current state of acoustic fields in microfluidics [START_REF] Zhang | Acoustic microfluidics[END_REF].

Electric fields

Electric fields are integrated with microfluidics by the fabrication of electrodes close to the microfluidic channels. Originally, electrodes were patterned on a glass substrate whereafter the microfluidic channel in PDMS was bonded to the glass substrate [START_REF] Keunho Ahn | Electrocoalescence of drops synchronized by size-dependent flow in microfluidic channels[END_REF][START_REF] Priest | Controlled electrocoalescence in microfluidics: Targeting a single lamella[END_REF]. Nowadays, one usually produces the electrodes as separate channels which are not in contact with the fluidic channels. The electrode channels are filled with metal solder or a conducting salt solution which allows to locally generate an electric field.

The electrical properties of the fluids are essential to describe the effect of electric fields on droplets. The electric resistivity ρ e , expressed in Ω/m, relates to the transport of electric current. Secondly, the relative permittivity ε r , also called the dielectric constant, is a relative measure of the polarizability of the material when subjected to an electric field. Some examples of values of ε r and ρ e are given in Table 2.1.

Electrocapillarity

The electrocapillarity phenomenon, which is the interplay of electric fields and capillary forces, was first investigated by Lippmann [START_REF] Gabriel | Relation entre les phénomènes électriques et capillaires[END_REF]. He observed a capillary rise due to a change in surface tension under influence of an electric field. The change in surface tension is described by Equation 2.5.

-dγ = σ e dE (2.5)

Here dγ is the change in surface tension due to the electric field, σ e the electric stress on the interface, and dE the change in applied electric potential.

The electric stress originates from an accumulation of charges at the interface due to the electric field. The Coulombic repulsion of particles of the same charge works opposed to the surface tension and decreases the surface tension [START_REF] Chen | Electrohydrodynamic stability[END_REF].

Uniform fields

We consider now the effect of a uniform electric field on a water droplet in oil. The initial drop shape is spherical as this is the equilibrium shape with minimum surface energy (Figure 2.4A). When one considers the application of a homogeneous electric field across the droplet, an additional electrical stress at the interface is generated due to the difference in electrical properties between the two phases. The generated electrical stress σ e is given by Equation 2. [START_REF] Cabane | Liquides. Solutions, dispersions, émulsions, gels: Solutions, dispersions, émulsions, gels[END_REF].

σ e = ε 0 ε r E 2 (2.6)
With E the electric field strength, ε 0 the vacuum permittivity, and ε r the relative permittivity of the ambient oil. The force equilibrium between capillary pressure which wants to return to a spherical shape, and the electric stress which elongates the droplet along the direction of the electric field determines the deformation of the drop (Figure 2.4B). We again construct a dimensionless number, the electric bond number B e , by comparing the magnitude of two stresses to know which effect dominates. B e is defined as the ratio of the Maxwell stress σ e due to electric effects and the Laplace pressure γ/r due to interfacial effects (Equation 2.7).

B e = ε 0 ε r E 2 r γ (2.7)
The degree of deformation of a droplet in an electric field is determined by the electric bond number B e [START_REF] Muhammad Salman Abbasi | Mono-emulsion droplet stretching under direct current electric field[END_REF].

-----

+ + + + + ε r, oil ε r, drop Ε Ε Ε A B C + + + + + -- - - -

Nonuniform fields

Secondly, we consider the effect of a heterogeneous electric field across the droplet. In this case, the polarization of the droplet is not homogeneous because the electric field varies across the droplet. The gradient in electric field generates a net force on the droplet as now the electric stress is unbalanced. This results in a phenomenon called dielectrophoresis, which makes the droplet move towards the place of higher electric field intensity (Figure 2.4C).

In general, dielectrophoresis is defined as the motion of a particle induced by differences in polarization of the particle compared to the surrounding medium due to nonuniform electric fields [START_REF] Ackland | Some effects of nonuniform fields on dielectrics[END_REF]. The material with the highest dielectric constant will migrate to the place where the electric field intensity is the highest. It is important to understand for this phenomenon to take place the particle does not need to be charged. The two requirements for this are a nonuniform electric field and a relative difference in dielectric constant. Furthermore, reversing the electric field does not affect the direction of motion of the particle. The magnitude of the electric force on a spherical particle in a dielectric medium is given by Equation 2.8 [START_REF] Ackland | Some effects of nonuniform fields on dielectrics[END_REF].

F e = 2πa 3 ε 0 ε r,oil K∇E 2 (2.8)
Here a is the radius of the particle and the contrast factor K is given in Equation 2.9.

K = ε r,drop -ε r,oil ε r,drop + 2ε r,oil (2.9)
In summary, electric fields provide an actuation mechanism for droplets at the surface level that lead to body forces. It is therefore an interesting means to manipulate both bulk and interfaces. Furthermore, the response of droplets to electric fields is fast which makes it an ideal tool for the development and integration of high-throughput methods.

Droplet modules

In this section we describe the existing unit operations in droplet microfluidics required for life science applications. One can think of these unit operations as modules that could be assembled on demand to fit a required workflow.

Droplet formation

The first step in the microfluidic process is the production of a droplet. Droplets need to be produced in a regular and stable manner. Furthermore, the methods should allow scaling of the size of the droplets from femtoliter to nanoliter. In most cases droplet production is achieved by passive methods. The general strategy for these passive techniques is to design a flow field that deforms the w/o interface and promotes the natural growth of interfacial instabilities [START_REF] Baroud | Dynamics of microfluidic droplets[END_REF]. Three main approaches have emerged for the production of droplets: (i) T-junction [START_REF] Thorsen | Dynamic pattern formation in a vesicle-generating microfluidic device[END_REF]; (ii) flow focusing junction [START_REF] Anna | Formation of dispersions using "flow focusing" in microchannels[END_REF]; (iii) co-flow [START_REF] Cramer | Drop formation in a co-flowing ambient fluid[END_REF]. In all three cases the dispersed phase is flown into a channel where it encounters the immiscible continuous phase.

The local flow field deforms the interface which eventually leads to droplet pinch-off. The fluid properties together with the flow rates and the geometry of the junction determine the flow field. Droplet pinch-off is eventually a competition between the surface tension, which tries to limit the deformation of the interface, and the pressure due to the external flow and the viscous shear stress, which drive the deformation of the interface. Different breakup modes exist depending on which force is dominant. The different flow regimes will be discussed in detail in Chapter 3.

Step emulsification is an alternative method for droplet production which is less dependent on the flow rates. Generally speaking, a step emulsification device consists out of a shallow and a deep section. Initially, the aqueous phase flows through the shallow section.

When entering the deeper part of the channel, the Laplace pressure is abruptly decreased due to the sudden step in channel height. This pressure difference pushes the aqueous phase to the deeper channel and creates a droplet. It is a very parallelizable method because the droplet size is not influenced by small pressure variations, and many production nozzles can be produced next to each other [START_REF] Amstad | Robust scalable high throughput production of monodisperse drops[END_REF]. However, step emulsification does not allow tuning the drop size on demand because this is mainly determined by the dimensions of the channels and the wetting properties of the channel walls [START_REF] Eggersdorfer | Wetting controls of droplet formation in step emulsification[END_REF].

Droplet content

After the production of a droplet, the manipulation of its content is essential in a biochemical workflow. In this section the encapsulation process of single cells is discussed as well as the tools to alter the droplet content of surfactant-stabilized droplets after production.

Cell encapsulation

Droplets are an excellent tool for single cell analysis. Analyzing single cells individually instead of analyzing in bulk gives insights into the heterogeneity within a population. For this tool to be effective, one wants to ensure that a single cell and not multiple cells are encapsulated per droplet. Most often, for single cell encapsulation one uses a passive method.

When producing droplets the aqueous phase contains cells, the cells arrive randomly at the droplet production nozzle and are encapsulated in a drop. The encapsulation rate follows a probability function since the arrival of cells at the production nozzle is a random process.

By diluting the aqueous cell suspension sufficiently, the encapsulation rate is dictated by the Poisson distribution:

p(k, λ) = λ k e -λ k! (2.10)
with k the number of particles in a droplet and λ the average number of cells per droplet volume. The Poisson statistics remain valid as long as the spatial position of a cell is not affected by other cells. In other words, the sample is dilute and the particles flow independently from each other [START_REF] Collins | The poisson distribution and beyond: methods for microfluidic droplet production and single cell encapsulation[END_REF].

The factor λ is dependent on the volume fraction of particles pre-encapsulation φ s and that of a droplet containing one cell φ d , and can be expressed as λ = φ s /φ d [START_REF] Collins | The poisson distribution and beyond: methods for microfluidic droplet production and single cell encapsulation[END_REF]. In other words, λ can be tuned by the particle concentration in the suspension and by the droplet size. The number of droplets containing a single cell can be maximized by working at λ = 1, in this case the number of drops containing one cell is p(1, 1) = 1/e ≈ 37%. However, the amount of droplets containing two or more cells is p(k ≥ 2, 1) ≈ 26%, which can result in false positive hits in a screening process. To ensure a limited number of droplets containing two or more cells one typically works at λ ≈ 0.1. The probability to have a single cell per drop at λ = 0.1 is p(1, 0.1) ≈ 9%. This is much greater than the probability to have two or more cells encapsulated in a drop, p(k ≥ 2, 0.1) ≈ 0.46%. However, the number of empty droplets is high, p(0, 0.1) ≈ 90%. This decreases the effective throughput of single cell analysis in droplets as there is no straightforward way to remove the empty droplets from the emulsion.

One way to overcome this statistical limitation for single cell encapsulation is by organizing the cells prior to encapsulation by inertial ordering. At high flow velocities the interparticle interactions result in a hydrodynamic repulsing effect between particles, which organizes the particles to spatially organized equilibrium positions in the channel. This method has been demonstrated in straight and curved microchannels [START_REF] Edd | Controlled encapsulation of single-cells into monodisperse picolitre drops[END_REF][START_REF] Evelien | High-yield cell ordering and deterministic cellin-droplet encapsulation using dean flow in a curved microchannel[END_REF]. The encapsulation rate of single cells is increased close to the theoretical maximum when the oil flow is tuned in a way that the droplet production rate matches the arrival rate of the cells [START_REF] Rogier M Schoeman | High-throughput deterministic single-cell encapsulation and droplet pairing, fusion, and shrinkage in a single microfluidic device[END_REF]. However, the implementation of this method is challenging due to the high flow velocities required for inertial ordering, which limits the coupling of other microfluidic modules. Furthermore, inertial ordering is difficult for cell populations with heterogeneous characteristics as the hydrodynamic repulsing effect will vary within the population.

A second way to address this limitation is by the detection of cells and the subsequent on-demand drop production. Detection of the cell by electrical impedance or by optical methods was integrated with a trigger to produce a droplet [START_REF] Leibacher | Enhanced single-cell printing by acoustophoretic cell focusing[END_REF][START_REF] Schoendube | Single-cell printing based on impedance detection[END_REF][START_REF] Link | Active single cell encapsulation using saw overcoming the limitations of poisson distribution[END_REF]. However, these active methods are so far limited in throughput.

When encapsulating deformable gel particles it is possible to overcome the limit set by the Poisson distribution. Deformable particles order before droplet production when injected in a high volume fraction [START_REF] Adam R Abate | Beating poisson encapsulation statistics using close-packed ordering[END_REF]. The compliance of the hydrogel particle prevents it from clogging the channels. This method is used for single cell transcriptomic analysis where co-encapsulation of a gel bead and cell in one drop is maximized in this way [START_REF] Allon M Klein | Droplet barcoding for single-cell transcriptomics applied to embryonic stem cells[END_REF].

Addition

Once a droplet is produced, two methods exist to add reagent to a surfactant-stabilized droplet: (i) merging of two droplets with a different content (Figure 2.5A) [START_REF] Chabert | Droplet fusion by alternating current (ac) field electrocoalescence in microchannels[END_REF] or (ii) picoinjection of one fluid in an existing droplet (Figure 2.5B) [START_REF] Abate | High-throughput injection with microfluidics using picoinjectors[END_REF]. In both cases the liquid film between the two interfaces needs to be destabilized in a controlled way. One usually uses an external field for this to be able to trigger this on-demand. In this regard, electric fields are useful and widely adopted [START_REF] Keunho Ahn | Electrocoalescence of drops synchronized by size-dependent flow in microfluidic channels[END_REF][START_REF] Priest | Controlled electrocoalescence in microfluidics: Targeting a single lamella[END_REF][START_REF] Niu | Electro-coalescence of digitally controlled droplets[END_REF].

A B

Removal

Splitting of a droplet can be done passively by placing a pillar in the channel or by designing a narrow T-junction [START_REF] Link | Geometrically mediated breakup of drops in microfluidic devices[END_REF]. The splitting of a drop is controlled by the hydrodynamic resistance of the branches of the T-junction. Increasing the hydrodynamic resistance on one side results in an asymmetric breakup and results in two daughter droplets of different sizes.

Droplet incubation

Droplets may want to be stored or incubated during a biochemical workflow. First of all, droplets can be collected and incubated in a vial or syringe. Now the emulsion can be thermocycled to perform PCR in drops [START_REF] Didelot | Multiplex picoliter-droplet digital pcr for quantitative assessment of dna integrity in clinical samples[END_REF], one could place the emulsion in an incubator for cell proliferation [START_REF] Clausell-Tormos | Droplet-based microfluidic platforms for the encapsulation and screening of mammalian cells and multicellular organisms[END_REF], or one could incubate the cells to later check for the accumulation of cell metabolites [START_REF] Köster | Drop-based microfluidic devices for encapsulation of single cells[END_REF]. When cultivating cells in this way one needs to take into account the limited access to nutrients and oxygen. Although fluorinated oils have a high solubility of oxygen, the access to oxygen may not be homogeneous in the emulsion. A method was developed for the dynamic incubation of droplets [START_REF] Mahler | Enhanced and homogeneous oxygen availability during incubation of microfluidic droplets[END_REF]. A constant flow of oxygenated oil through the vial ensured a homogeneous availability of oxygen in the emulsion. This resulted in increased cell growth and metabolite secretion compared to normal static incubation where the oil was not refreshed.

Secondly, droplets are incubated in long incubation channels on a microfluidic chip. These incubation lines are long serpentine channels where the drops flow through slowly. This is practically possible for an incubation time below 1 hour. It is a useful tool to perform enzymatic assay with a shorter incubation time as it allows to maintain a good time resolution.

It was shown that two main characteristics are important for on-chip incubation [START_REF] Frenz | Reliable microfluidic on-chip incubation of droplets in delay-lines[END_REF]: (i) local constrictions ensure that the droplets have the same incubation time. The constriction redistributes the droplets and prevents a drop from staying in the same streamline for the whole incubation line. (ii) The incubation line has an increased depth compared with the rest of the chip which greatly reduces the hydrodynamic resistance of the device.

Droplet analysis

The next step in a biochemical workflow is the analysis of a droplet. Ideally, the analysis should be fast to be compatible with high-throughput measurements. Optical methods for droplet analysis are by far the most common. Herein, most assays rely on a laser-induced fluorescent measurement which allows for a highly sensitive readout to be performed on a sub-millisecond timescale [START_REF] Baret | Fluorescenceactivated droplet sorting (fads): efficient microfluidic cell sorting based on enzymatic activity[END_REF][START_REF] Agresti | Ultrahigh-throughput screening in drop-based microfluidics for directed evolution[END_REF]. Beyond the detection of fluorescent molecules, further developments have been made to extend the range of assays amenable to droplets.

Absorption-based readout has been developed by implementing optical fibers [START_REF] Gielen | Ultrahigh-throughput–directed enzyme evolution by absorbance-activated droplet sorting (aads)[END_REF]. This readout method is limited in sensitivity due to the reduced optical path length in droplet microfluidics. Recently a method named differential detection photothermal spectroscopy (DDPI) was developed. It relies on the phase shift of light due to the photothermal effect, which allowed for high-speed single-point absorption measurements at rates similar to those used in fluorescent-activated droplet sorting [START_REF] Maceiczyk | Differential detection photothermal spectroscopy: towards ultra-fast and sensitive label-free detection in picoliter & femtoliter droplets[END_REF]. Further, a method was developed to detect the scattering of light of a droplet with the use of an optical fiber and a laser. It was used to detect differences in cell proliferation within droplets [START_REF] Liu | High-throughput screening of antibioticresistant bacteria in picodroplets[END_REF]. Next to that, Raman scattering was measured in droplets [START_REF] Wang | Raman-activated droplet sorting (rads) for label-free high-throughput screening of microalgal single-cells[END_REF], and more recently also mass spectrometry has been implemented with droplet microfluidics [START_REF] Smith | Sensitive, high throughput detection of proteins in individual, surfactant-stabilized picoliter droplets using nanoelectrospray ionization mass spectrometry[END_REF][START_REF] Daniel | Mass activated droplet sorting (mads) enables high-throughput screening of enzymatic reactions at nanoliter scale[END_REF]. Further, also image processing was used to analyze droplets [START_REF] Girault | An on-chip imaging dropletsorting system: a real-time shape recognition method to screen target cells in droplets with single cell resolution[END_REF]. Finally, electrochemical measurements were implemented for droplets [START_REF] Goto | Microfluidic screening system based on boron-doped diamond electrodes and dielectrophoretic sorting for directed evolution of nad (p)-dependent oxidoreductases[END_REF]. The developed methods are summarized in Table 2.2.

Droplet sorting

A final module is the sorting of a droplet. This is an essential tool to enable droplet microfluidics as a technology for the high-throughput screening of cells. To sort a droplet one uses a bifurcation in a microchannel. The two sides of the junction have different hydrodynamic resistance. By default, droplets flow into the channel with lower hydrodynamic resistance, the negative outlet. The drop can be moved into the side with a higher hydrodynamic resistance, the positive outlet, by lateral deflection.

Passive methods for deflecting the drop make use of differences in rheology. Droplet sorting based on interfacial tension has been illustrated. A sorting rail in the microfluidic channel can deflect droplets with a different surface tension [START_REF] Pan | Sorting by interfacial tension (sift): label-free selection of live cells based on single-cell metabolism[END_REF]. Droplets are initially squeezed in the channel, while they take a spherical shape in the sorting rail which has a greater channel height. The droplets with high surface tension follow the sorting rail because the shear force working on the droplet is not sufficiently large to deform the drop to leave the sorting rail. The surface tension could be altered by the changes in pH inside the droplet which could be linked to a cellular metabolism. Secondly, passive droplet sorting has been shown based on a change in droplet viscosity. The intrinsic viscous and viscoelastic properties of the drop compared to the properties of the continuous oil phase cause lateral migration of the droplet towards low shear gradients at the center, or towards high shear gradients close to the channel wall [START_REF] Andrew C Hatch | Passive droplet sorting using viscoelastic flow focusing[END_REF]. Changes in viscoelasticity were induced by polymerization of the drop content.

Active methods deflect a droplet on demand by an external trigger. The main methods use acoustic or electric fields. Two alternative methods exist when using acoustic waves.

Standing acoustic waves, either bulk or surface acoustic waves [START_REF] Leibacher | Microfluidic droplet handling by bulk acoustic wave (baw) acoustophoresis[END_REF][START_REF] Ding | Standing surface acoustic wave (ssaw) based multichannel cell sorting[END_REF], generate a pressure field with nodes and anti-nodes. This pressure field generates an acoustic radiation force on the droplet pushing it either to the node or antinode of the pressure field and is in this way able to deflect the droplet. However, more often traveling surface acoustic waves are used.

Traveling surface acoustic waves generate local acoustic streaming in the microchannel when dissipating in the bulk fluid. This streaming drags and deflects the droplet sideways [START_REF] Franke | Surface acoustic wave (saw) directed droplet flow in microfluidics for pdms devices[END_REF].

Dielectrophoretic sorting

Droplet sorting based on electric fields uses dielectrophoresis to deflect droplets. In Figure 2.6 one can see the most notable advancements of the method. Sorting of droplets by the use of dielectrophoresis was first shown by Ahn et al. [START_REF] Keunho Ahn | Electrocoalescence of drops synchronized by size-dependent flow in microfluidic channels[END_REF]. Afterwards, droplet sorting was implemented in a high-throughput manner and linked with a fluorescent measurement, leading to a method called Fluorescent-Activated Droplet Sorting (FADS) which could sort droplets at a rate of 2 kHz [START_REF] Baret | Fluorescenceactivated droplet sorting (fads): efficient microfluidic cell sorting based on enzymatic activity[END_REF]. Subsequently, this method was used for the directed evolution of an enzyme [START_REF] Agresti | Ultrahigh-throughput screening in drop-based microfluidics for directed evolution[END_REF]. After the introduction of FADS, several designs were proposed by trialand-error to optimize the electric field gradient and maximize the deflection. Schutz et al.

have rationalized the electrode designs by a numerical study [START_REF] Schütz | Rational design of a high-throughput droplet sorter[END_REF]. They showed that the placement of ground electrodes is important to optimize the field gradient. Furthermore, they noticed that the field gradient in the height-direction is an important contributor to The evolution of dielectrophoretic droplet sorting. Adapted from [START_REF] Schütz | Rational design of a high-throughput droplet sorter[END_REF].

the displacement of the droplet. The numerical study of the electric field was also used to implement droplet sorting with five outlets [START_REF] Ouriel Caen | High-throughput multiplexed fluorescence-activated droplet sorting[END_REF].

The throughput of dielectrophoretic droplet sorting is limited by the magnitude of the electric field which can be applied without causing droplet breakup at the junction. Therefore, the microfluidic junction between positive and negative was optimized by Sciambi et al.. They proposed a multilayered channel which avoided the breakup of a droplet at the junction, and allowed sorting at a rate of 30 kHz, the highest reported throughput yet [START_REF] Sciambi | Accurate microfluidic sorting of droplets at 30 khz[END_REF].

Recently, an improvement was made to sort larger droplets at a high-throughput rate. An array of electrodes was developed which could be sequentially triggered [START_REF] Isozaki | Sequentially addressable dielectrophoretic array for high-throughput sorting of large-volume biological compartments[END_REF]. Each electrode in the array could deflect the droplet to result in a total deflection which is sufficient for sorting. They reached a volumetric throughput for sorting which is significantly higher than the previous methods.

Life science applications

Droplet microfluidics has several applications in life sciences. Here we introduce several important applications where the miniaturization and high-throughput capability of droplets have been applied and commercialized.

Polymerase chain reaction

Polymerase chain reaction (PCR) is a method which is used to make billions of copies a specific genetic sequence. It is a fundamental method essential to many procedures in genetic PCR has been combined with droplet microfluidics as it has certain advantages. Droplet digital PCR (ddPCR) differs from traditional PCR methods as instead of one biochemical bulk reaction, the sample is split over millions of droplets and thereby having millions of parallel reactions. Each droplet serves as a measurement that allows discrete quantification of the amplification without a standard curve. The high-throughput fluorescent analysis of these droplets allows for absolute quantification of the DNA copy number [START_REF] Benjamin J Hindson | High-throughput droplet digital pcr system for absolute quantitation of dna copy number[END_REF]. The method consists of droplet production, thermocycling, and fluorescent readout of the droplet. It has been made commercially available by Biorad, Stilla Technologies and QIAGEN.

Single cell transcriptomics

With single cell transcriptomics one examines the gene expression level of single cells by analyzing the mRNA. It allows to explore the heterogeneity within cell populations, to distinguish sub-populations within cell types, or to distinguish cell states. Two similar methods have been developed which make use of droplet microfluidics for single cell transcriptomic analysis: inDrop [START_REF] Allon M Klein | Droplet barcoding for single-cell transcriptomics applied to embryonic stem cells[END_REF] and Drop-seq [START_REF] Macosko | Highly parallel genome-wide expression profiling of individual cells using nanoliter droplets[END_REF]. Here we describe the inDrop method (Figure 2.7).

A single cell is encapsulated together with a hydrogel, lysis agent, and reverse transcription reagents. Due to the lysis agent, the mRNA of the cell is released in the droplet after encapsulation. The droplet serves as a compartment to attach a barcode to the intracellular material of each cell individually. Each hydrogel contains a unique oligonucleotide sequence which serves as a barcode. The end of the barcode consists of poly(T) which captures mRNA from the cell. The mRNA is captured and reverse transcribed in droplets. The emulsion is broken and linearly amplified, and the synthesized cDNA is sequenced with established methods [START_REF] Hashimshony | Cel-seq: single-cell rna-seq by multiplexed linear amplification[END_REF]. After sequencing the barcode allows to pool together the sequencing data from single cells. This method has been commercialized by 10x Genomics. Next to that, Mission Bio is another company that developed a platform for single cell transcriptomic analysis with the use of droplet microfluidics.

More recently this method is being combined with other single cell studies for multiparameter analysis of a single cell. This may give a better understanding in cellular processes.

Figure 2.7:

Workflow for single cell transcriptomics. Cells are co-encapsulated with a barcoded hydrogel, lysis buffer, and reverse transcription mix. After UV exposure the hydrogel is cleaved and reverse transcription is started in the droplet to yield the cDNA. The emulsion is broken and the material from all cells is linearly amplified and sequenced. Reprinted from [START_REF] Allon M Klein | Droplet barcoding for single-cell transcriptomics applied to embryonic stem cells[END_REF].

In Paper II: Frontiers in single cell analysis: multimodal technologies and their clinical perspectives an overview is presented of the recently developed microfluidic platforms for multimodal single cell analysis.

Directed evolution

The principle of natural Darwinian evolution relies on mutation and selection. In a particular environment, the organism which is best adapted and able to reproduce its genes remains.

In other words this has been summarized as survival of the fittest [START_REF] Spencer | The Principles of Biology[END_REF]. Directed evolution is a method that takes this principle into the lab environment. 2.9) [START_REF] Agresti | Ultrahigh-throughput screening in drop-based microfluidics for directed evolution[END_REF]. They achieved a 10-fold improvement in the catalytic rate of horseradish peroxidase.

The genetic library was transformed into a host cell which expressed the enzyme on the cell surface. The cells were co-encapsulated with a fluorogenic biochemical assay to test the enzyme functionality. The droplet served as a container that ensured genotype-phenotype linkage. Fluorescent readout of the droplet allowed to distinguish highly active variants from others. The highly fluorescent droplets were subsequently sorted and collected for further rounds of mutagenesis and selection. In total, they screened about 10 8 individual

Introduction

The production of a droplet is the first essential module in droplet microfluidics. Essential properties of the module are that the produced droplets are uniform in size and that the method is reproducible. Depending on the fluid properties and flow parameters different flow regimes exist. The two flow regimes which occur at moderate flow rates are dripping and jetting. In the next paragraph we will describe the difference between the flow regimes and the implications this has on the reliability of droplet production.

Dripping and jetting

Visually the dripping regime is characterized by a droplet pinch-off which happens close to the injection nozzle (Figure 3.1A) while the jetting regime on the other hand is characterized by droplet pinch-off which happens further downstream away from the nozzle (Figure 3.1B-C).

The dripping and jetting regime, and the transition between the flow regimes was studied by Intuitively one can understand this as follows: when the viscous stress on the interface is increased, the interface is pulled away from the nozzle and a long slender thinning jet is formed (Figure 3.1B). The jet is thinning because the outer fluid has a high flow velocity and accelerates the inner fluid when injected. Secondly, a jet is formed when the inertial force of the inner fluid is sufficient to push the interface further away from the nozzle (Figure 3.1C). In this case, the jet widens because the inner fluid initially has a high velocity but is decelerated by the outer fluid.

The dripping and jetting regime differ in terms of stability of liquid threads. In linear stability analysis of a liquid thread, the dripping regime has been described as an absolute instability: perturbations grow and propagate from a fixed location both upstream and downstream leading to monodisperse droplets produced at a rate that is intrinsic to the system [START_REF] Utada | Dripping to jetting transitions in coflowing liquid streams[END_REF][START_REF] Guillot | Stability of a jet in confined pressure-driven biphasic flows at low reynolds numbers[END_REF][START_REF] Guillot | Stability of a jet in confined pressuredriven biphasic flows at low reynolds number in various geometries[END_REF][START_REF] María | Quantitative analysis of the dripping and jetting regimes in co-flowing capillary jets[END_REF]. Absolutely unstable jets have been only rarely observed [START_REF] Utada | Absolute instability of a liquid jet in a coflowing stream[END_REF]. In contrast,

(B) A slender jet is formed when the outer flow is increased. (C)

A widening jet is formed when the inner flow is increased. Reprinted from [START_REF] Utada | Dripping to jetting transitions in coflowing liquid streams[END_REF].

the jetting regime is related to a convective instability: instabilities propagate solely downstream of the interface while they grow due to high flow velocities [START_REF] Utada | Dripping to jetting transitions in coflowing liquid streams[END_REF][START_REF] María | Quantitative analysis of the dripping and jetting regimes in co-flowing capillary jets[END_REF]. Random noise is amplified by the perturbations as they travel along the jet surface resulting in a less uniform droplet size. A liquid jet breaks up due to the Plateau-Rayleigh instability which implies that jets are unstable to perturbations with a wavelength greater than the circumference of the jet [START_REF] Plateau | experimental and theoretical researches on the figures of equilibrium of a liquid mass withdrawn from the action of gravity.-third series[END_REF][START_REF] Rayleigh | On the instability of jets[END_REF]. These perturbations are amplified on the jet surface which eventually results in breakup of the jet into droplets.

In a nutshell, when dripping occurs (C out , W in 1), droplets are formed periodically close to the junction resulting in a uniform droplet size. At higher flow velocities, a jet is formed

(C out 1 or W in 1)
which eventually breaks up into droplets downstream of the nozzle due to the Plateau-Rayleigh instability. Therefore, flow rates, hence the production rate of a monodisperse emulsion, is limited by the onset of the jetting regime.

Electric fields for droplet production

Electric fields are a promising tool for external control as they offer interesting engineering capabilities with a high level of control and integration. The response time of fluids to the electric actuation is fast which makes it compatible with the high-throughput capabilities of droplet microfluidics [START_REF] Hwa Tan | The microfluidic jukebox[END_REF]. Electric control of droplet production has been proposed by Link et al. and Kim et al. [START_REF] Link | Electric control of droplets in microfluidic devices[END_REF][START_REF] Sung | Electrohydrodynamic generation and delivery of monodisperse picoliter droplets using a poly (dimethylsiloxane) microchip[END_REF]. They fabricated devices where electrodes were in contact with the fluid. By electrostatic charging of the aqueous fluid they were able to generate electric forces and manipulate the droplet size. However, the applicability of these methods is limited as the electrodes are in contact with the fluid. Due to electrochemical effects the electrodes can degrade and electrolysis occurs at a high voltage which destabilizes the flow. Secondly, charged droplets are produced which are less stable and results in higher dispersity.

To avoid these issues, Tan et al. introduced a method where the electrodes are not in contact with the fluids [START_REF] Hwa Tan | Microfluidic flow-focusing in ac electric fields[END_REF]. Electrodes were manufactured symmetrically around the flow focusing junction, however, separated from the fluid channels by a capacitive PDMS wall.

They make use of AC electric fields to manipulate the behavior at the nozzle. Essential parameters describing the system are: the conductivity of the aqueous phase, the electric field (frequency f and applied voltage U 0 ), and the electrode configuration. Furthermore, they illustrated that the dripping-to-jetting transition was affected by the electrical parameters, however, a complete analysis of this transition is lacking. In follow-up work this system was used to make long slender jets in microchannels [START_REF] Castro-Hernández | Breakup length of ac electrified jets in a microfluidic flow-focusing junction[END_REF][START_REF] Castro-Hernández | Ac electrified jets in a flow-focusing device: Jet length scaling[END_REF].

The aim of the research presented in this chapter is to implement electric fields to alter the breakup dynamics of a jet. It was shown that it is possible to impose external perturbations on a jet [START_REF] María | Quantitative analysis of the dripping and jetting regimes in co-flowing capillary jets[END_REF]. Cordero et al. used a pulsating focused laser to cause local heating in the jet. This heating locally altered the interfacial tension generating a perturbation. The pulsation of the laser was able to alter the breakup dynamics of the jet. Nevertheless, electrically mediated manipulation of droplet production is the most reliable and flexible method. Therefore, the system developed by Tan et al. serves as a robust and easy-to-fabricate device for our study.

We first aim to characterize the dripping-to-jetting transition in this system. Next we use this system to increase the monodispersity of droplets produced in the jetting regime by imposing external perturbations using electric fields.

Materials & methods

System

We use a standard droplet-based microfluidics flow focusing junction with electrodes manufactured symmetrically around the junction (Figure 3.2). The downstream electrodes are grounded while the upstream electrodes are actuated. The microfluidic devices are fabricated using standard soft lithography methods described in Appendix A. The dimensions of the flow focusing junction are 50 µm x 50 µm x 34 µm (Figure 3.

3).

The microfluidic chip is placed on the stage of an inverted microscope and the device is visualized with a high speed camera. The voltage applied to the electrodes is controlled by a frequency generator and amplified 1000 times. The carrier frequency of the electric signal is 30 kHz. To assess the effect of the electric field on the droplet production rate, a laser is guided towards the sample and focused on the microfluidic channel by a microscope objective. The emitted fluorescent light from the droplets is filtered and guided towards a photomultiplier tube (PMT) and recorded. The PMT signal is recorded 5 s for each setting. The sampling rate of the system is 193 kHz. Matlab R2018a is used for all post-processing steps of the recorded signals.

Q i Q o /2 Q o /2

Fluid properties

As outer continuous phase mineral oil (M5904, Sigma-Aldrich) is used. As inner aqueous phase a mixture of deionized water (33 v/v%) and glycerol (67 v/v%; Sigma-Aldrich) is used, in which fluorescein is added to a final concentration of 200 µM.

The surface tension of the two fluids is measured with a pendant drop tensiometer (Teclis Scientific). A glass cuvette is filled with oil while a syringe is filled with the glycerol/water mixture. The volume is chosen such that the pendant drop reaches an equilibrium state without detaching.

The dielectric constant is measured by impedance spectroscopy (Impedance Analyzer 7260, Materials Mates). The impedance analyzer is connected to a fluid cell which contains two opposed platinum electrodes (10 mm x 10 mm) spaced at a distance of 10 mm.

The cell is filled with the formulation and a frequency scan from 1 to 10 MHz with 5 V applied

Dripping-to-jetting transition in electric fields

We first study the dripping-to-jetting transition in the device as a function of the applied voltage U 0 across the electrodes. We fix the inner flow rate (Q i ) to a constant value of 50 µL/h and vary the outer flow rate (Q o ) to increase the viscous stress on the interface. Without electric field, the onset of the jetting regime is observed at We then test the robustness of these results by upscaling the dimensions of the system.

Q o =
We double all the dimensions to obtain a nozzle size of 100 µm x 100 µm x 68 µm, and repeat the experiment while keeping Q i at 50 µL/h. In general, the shape of the flow diagram is unchanged, with a dripping region at small C o and B e and a jet otherwise. The transition values are however modified. Without electric field we find the onset of the jetting regime at

Q o = 2400 µL/h (C o = 0.085; R o = 0.27; W o = 0.024). At the lowest Q o tested,

Rectifying jet breakup

In the second part we focus on the monodispersity of production, both in the dripping and in the jetting regime. We work with the 50 µm device. To measure the monodispersity of

Q o = 1200 µL/h, baseline = 300 V; green: Q o = 1200 µL/h, A pert = 300 V, f pert = 8 kHz.
production in the dripping regime results in a highly stable droplet production. In contrast, droplet production in the jetting regime results in a more heterogeneous PMT signal which results in a broader spectrum of the Fourier transform without a specific peak (Figure 3.5F, J). With our method, we recover here the main features of the absolute and convective instabilities, namely a well defined frequency on the one hand and a broad range of amplified frequencies of perturbations on the other hand. We now actuate the upstream electrodes to apply an electric field to the same hydrodynamic jet (U 0 = 300 V, Q o = 1200 µL/h). Although B e 0.2, we do not observe any notable difference in the frequency spectrum as compared to the case of jetting in absence of electric field. Electrified jets have been shown

to display a shift of the amplified perturbations towards higher frequency for inertial jets [START_REF] Eggers | Physics of liquid jets[END_REF]. The absence of a similar shift in our experimental data might originate from viscous dissipation which changes the dispersion relation, although no detailed calculations of the problem has been found in literature -to the best of our knowledge. At this step, we would nevertheless conclude from the experimental data that the electric field does not significantly alters the dynamics of the jetting. However, the jet behavior changes drastically when we move from a constant AC electric voltage to a modulated voltage.

We now apply an amplitude modulation at a fixed frequency in the range of the amplified frequency of the jet. This modulation acts at the interface as a perturbation of fixed frequency through the modulation of the Maxwell stress. We note f pert as perturbation frequency (here f pert = 8 kHz) and the maximum amplitude of the applied voltage is defined as A pert (here

A pert = 300 V).
The PMT signal of the forced jet shows a higher level in homogeneity of amplitude compared to the unforced jets (Figure 3.5H) and the Fourier transform shows a clear peak at f pert = 8 kHz while the amplitude of the other frequencies is slightly decreased compared to unforced jets. The modulation of the applied voltage is therefore a means to select a frequency among the frequency naturally amplified in the growth dynamics of perturbed jets to increase the monodispersity of jetting.

To further understand the properties of the jet instability, we further use the control that electric actuation easily provides, namely, amplitude and frequency controls. We investigate the effect of the different components of the amplitude modulated (AM) signal (perturbation amplitude A pert , perturbation frequency f pert and baseline voltage) on the jet breakup.

Effect of modulation amplitude and baseline

Firstly we look into the effect of A pert and the baseline voltage by setting f pert to 8 kHz while stepwise increasing A pert from 0 V to 300 V for several baseline voltages. The Fourier transform of the sequential PMT recordings are shown in Figure 3.6. Here the grayscale represents the amplitude of the Fourier transform. We observe that with increasing A pert the intensity at f pert increases while the intensity of other frequencies slightly decreases. To quantify this observation we separate the power spectrum F(f ) into two separate signals as

shown in equation 3.1: (i) a δ(f pert ) peak of amplitude a p at f pert and (ii) a background signal F 0 (f ) spanning the frequency range corresponding to power spectrum of the unperturbed jet (A pert = 0 V) with an amplitude a 0 .

F(f ) = a 0 F 0 (f ) + a p δ(f pert ) (3.1)
a 0 and a p are the parameters to be fitted, representing the intensity of both signals in the power spectrum. The deconvolution of the Fourier transform into a background and a peak signal is done using the frequency spectrum from 0 kHz to 12 kHz for the background signal a 0 . To compute a p , δ(f pert ) is defined as the maximum value in the interval [f pert -50Hz, f pert +50Hz] for each experimental run. Fitting is performed using the least squares method.

A built-in Matlab function detected the minima for both a 0 and a p in the interval [0 1]. a p and a faster decrease of a 0 is observed when applying a baseline voltage. We argue that applying a baseline voltage results in a charged jet which is more stable against perturbations than an uncharged jet. However, for high A pert and a baseline of 500 V, a p decreases while a 0 increases. This is because the jet behavior suddenly transits under the influence of the high electric field. The jet widens and is pulled further down the channel. We finally confirm that the analysis indeed corresponds to improved monodispersity using a second measurement of the monodispersity. In this case, we analyze the signal s(t) to detect the peaks in the PMT signal corresponding to droplets. We then calculate a normalized histogram of the peak width. Afterwards, a Gaussian curve with variables mean µ and standard deviation σ is fitted to the histogram (Figure 3.8). Detection of peaks in the PMT signal is done by a built-in matlab function with the threshold for peak height set to 2•10 -2

V and the threshold for peak width set to 10 -6 s. Normalized histograms of the peak width distribution are compiled with a bin number n = 400. A Gaussian curve is fit using the least squares method, with the maximum number of function evaluations 5•10 4 and the maximum number of iterations 10 4 . The standard deviation is a measure of the spread of the histogram, i.e. a measure of the uniformity in droplet size. We rescale the resulting σ to σ 0 /σ, where σ 0 is the standard deviation at A pert 0 V. This means if σ 0 /σ > 1 the size distribution of the droplet size is more uniform than the initial droplet population of an unperturbed jet. In Figure 3.9 one can find σ 0 /σ and µ as a function of A pert . We observe that when A pert is sufficiently large σ 0 /σ increases and that this increase happens faster when a baseline voltage is applied. The maximum σ 0 /σ observed here is 3.5, meaning that the standard deviation of distribution is decreased 3.5 times. This method confirms that the emergence of the peak in the power spectrum indeed corresponds to a gain in monodispersity through the selection of the most amplified frequency.

Effect of modulation frequency

Secondly, we analyze the effect of f pert on the jet breakup. We set A pert to 200 V and vary f pert from 0 to 12 kHz for a baseline voltage of 0 V and 200 V. The Fourier transform of the recorded PMT signals is shown in Figure 3.10. We again deconvolve the Fourier transform as in Equation 3.1 (Figure 3.11). a 0 changes only slightly for low f pert . For the frequencies around the natural breakup frequency of the jet (± 8 kHz) we see a clear decrease of the background signal. At higher frequencies the effect of the AM signal disappears. For a p we observe an initial increase at ± 1 kHz. This is because the jet breaks up into one big and a train of smaller droplets. At this frequency the time to replenish the whole jet volume is matching the forcing frequency, i.e. f pert ≈ Q i /V jet . This regime corresponds to observations of the production of groups of droplets under influence of the electric field in the dripping regime [START_REF] Castro-Hernández | Droplet group production in an ac electro-flow-focusing microdevice[END_REF]. A second increase is seen around the natural production frequency of the jet, where a 0 decreases. For higher f pert the peak intensity decreases since the perturbations are too fast for the jet to follow. We again analyze the distribution of the width of the peaks in the PMT signal as a measure of the monodispersity of the emulsion by extracting σ 0 /σ and µ (Figure 3.12). Initially a decrease in uniformity is observed for low f pert . This is due to the breakup of the jet in clumps as stated earlier. Around the natural jet frequency σ 0 /σ increases showing a higher level of monodispersity. For higher frequencies the effect of the perturbations disappears as σ 0 /σ goes to 1. In figure 3.13 we aligned micrographs of the jet perturbed at different frequencies. Every fifth drop is colored red for visualization purposes. For lower frequencies we see the disrupting effect of the perturbations. Further, we see that from 7 kHz to 9 kHz the distance between the drops decreases in a controlled fashion. This observation is validated in

Conclusion & perspective

In summary, we investigated the possibility of altering the breakup dynamics of a hydrodynamic jet in a flow focusing junction by electric fields. We first observed that the onset of the jetting regime is affected by the electric field. This did not alter the breakup dynamics significantly. We then modulated the amplitude of the electric field, which allowed to rectify the jet, i.e. there was a correlation between the modulation frequency and the breakup frequency of the jet. We further used the parameters of the electric field, to understand the jet instability. Tuning the electric parameters, we were able to increase the monodispersity of the drop population produced by the jet. We provide here a basic method usable to control microcompartment creation, alleviating the limitations observed when attempting to increase the throughput of production and going beyond other actuation mechanisms by light. We believe that this approach is of interest for applications requiring high-throughput and reliability in production, for example in biomicrofluidics technologies and material sciences.

Dripping-to-jetting transition

The study of the dripping-to-jetting transition in electric fields would deserve a follow-up study. A study of this system covering the full parameter space (η, ε r , γ, Q i /Q o ) is not trivial. Most interesting would be to study the effect of ε r , it is however not straightforward to vary the dielectric constant of a fluid without affecting other parameters such as viscosity or surface tension.

Droplet production

The droplets produced in our system are made with a viscous liquid (η = 26.6 mPa•s) for which we show that monodisperse emulsion can be generated at rates up to 8 kHz. However, in most applications the viscosity of the aqueous phase is around 1 mPa•s.

The volume of droplets produced at 8 kHz is 1.7 pL (V = Q/f ). Production of such small droplets in the dripping regime using a flow focusing junction is not easy to implement in the general case. Scaling down the geometry of the nozzle increases the probability of clogging of the nozzle in practical applications prohibiting the reliable production of a monodisperse emulsion. Moreover, the pressure in the fluidic channels increases which means it is necessary to operate at low flow velocities.

Formulations Because we wanted to control the interfacial properties of our system, we did not use surfactants in the experiments to avoid the effect of the dynamic adsorption of the molecules at the interface, which introduces an additional level of complexity [START_REF] Brosseau | Microfluidic dynamic interfacial tensiometry (µdit)[END_REF][START_REF] Riechers | Surfactant adsorption kinetics in microfluidics[END_REF].

However, in practical applications surfactants are used to avoid droplet coalescence. They decrease the surface tension resulting in an earlier onset of the jetting regime compared to no surfactants. Furthermore, we focused on one formulation in this study.

In order to validate this method, in future work it will be important to determine to what extent the use of surfactants affects the generalization of the results obtained here. Next to that, also the effect of the electric properties of the formulations should be investigated to further characterize the system. Electrocoalescence is a method used for the fusion of surfactant-stabilized droplets. Although it is widely used, there is still a lack of quantitative experimental analysis on the effect of the electrical properties in the system on the phenomenon. The experimental part of this section is based on Paper IV: Quantitative analysis of electrocoalescence as a function of the electric properties of the system. We attempt to quantitatively analyze droplet coalescence in electric fields and we aim to shed light on the effect of fluid parameters on the coalescence efficiency.

Electrocoalescence

Electrocoalescence -the fusion of droplets by the effect of electrostatic interaction -is a well-established principle that has led to a method used in the petroleum industry for oil refining [START_REF] Eow | Electrostatic enhancement of coalescence of water droplets in oil: a review of the current understanding[END_REF]. In the past two decades, the use of electric fields also found applications in the field of droplet-based microfluidics for precise manipulation of surfactant-stabilized droplets [START_REF] Niu | Electro-coalescence of digitally controlled droplets[END_REF][START_REF] Link | Electric control of droplets in microfluidic devices[END_REF]. Fusion of a droplet pair is a tool used for the precise addition of reagents to a sample droplet and finds applications in microfluidics for protein engineering and drug screening [START_REF] Autour | iSpinach: a fluorogenic RNA aptamer optimized for in vitro applications[END_REF][START_REF] Staffan | Multiplex analysis of enzyme kinetics and inhibition by droplet microfluidics using picoinjectors[END_REF]. The use of electric fields for controlled coalescence of surfactant-stabilized droplets has been an interesting tool as it is easy to implement by integrating electrodes in microfluidic devices. Secondly, electrocoalescence is an active method that can be triggered on demand [START_REF] Adrian | On-demand droplet merging with an ac electric field for multiple-volume droplet generation[END_REF]. Similar to fusion of two droplets, picoinjection is also a method that relies on the destabilization of a surfactant-stabilized liquid oil film with the use of electric fields [START_REF] Abate | High-throughput injection with microfluidics using picoinjectors[END_REF].

The electrocoalescence process of a droplet pair follows three steps: (i) in a homogeneous electric field, droplets approach due to dipole-dipole interactions. (ii) The liquid film between the droplets is drained. For surfactant stabilized droplets, the interface will rigidify and counteract drainage of the liquid film between the droplets [START_REF] Baret | Surfactants in droplet-based microfluidics[END_REF]. (iii) A capillary bridge is formed and droplets fuse. [START_REF] Abdou | Breaking of an emulsion under an ac electric field[END_REF] and surfactant adsorption kinetics [START_REF] Mostowfi | Electric field mediated breakdown of thin liquid films separating microscopic emulsion droplets[END_REF]. It has been described as an electric-field-induced dynamic instability of a liquid film which depends on the thickness of the liquid film, and the competition between the capillary pressure γ/R and the Maxwell stress at the interface ε 0 ε r E 2 [START_REF] Priest | Controlled electrocoalescence in microfluidics: Targeting a single lamella[END_REF]. However, Chabert et. al also observed a frequency dependence of the electrocoalescence mechanism in their system, no coalescence was observed using DC fields [START_REF] Chabert | Droplet fusion by alternating current (ac) field electrocoalescence in microchannels[END_REF]. In another study, a rela-tion between the frequency and amplitude of the electric field was observed which has been related to the ionic charge relaxation time in the system [START_REF] Szymborski | Ionic polarization of liquid-liquid interfaces; dynamic control of the rate of electro-coalescence[END_REF]. Nevertheless, the relation between frequency and amplitude of the electric field remains unclear in the microfluidic systems commonly used today, where electrodes are not in contact with the fluid which results in electric loss in the system. Furthermore, the effect of the properties of the continuous oil phase on electrocoalescence has not yet been systematically investigated, leading to optimisation of devices based on trial-and-error: for practical applications nowadays a 'sufficient' electric field strength and frequency are applied to ensure efficient merging. Here we revisit, by the use of microfluidics, the analysis of electrocoalescence of a droplet pair with the aim to further rationalize the mechanism.

Materials & methods

System

Microfluidic devices have been fabricated with the methods described in Appendix A. A monodisperse emulsion of aqueous droplets with a diameter of 50 µm is produced with a standard flow focusing junction. The collected emulsion is reinjected in a second microfluidic chip. The second chip consists of a reinjection nozzle with an array of 36 droplet traps Amplifier Signal generator

Fluid properties

The continuous phase used is a perfluorinated oil (HFE 7500 or FC 40, 3M) containing a non-ionic surfactant (Fluosurf, Emulseo). The material properties of the formulations are summarized in Table 4.1.

Surface tension

The surface tension is measured with a pendant drop tensiometer (Teclis Scientific). A glass cuvette is filled with oil and surfactant while a syringe is filled with millipore water. A reversed needle with an inner diameter of 0.4 mm (100 Sterican, Braun) is used to create a rising water-in-oil droplet. The droplet size ranges from 0.2 to 6 µl. The volume is chosen with surfactant are at the lower limit of the method (∼ 5 mN/m) and we assume an accuracy of ± 0.5 mN/m on the measurement [START_REF] Brosseau | Microfluidic dynamic interfacial tensiometry (µdit)[END_REF]. Tensiometry measurements for different oil mixtures and different surfactant concentrations are found in Figure 4.4.

Electric properties

The electric properties of the oil phase are characterized by impedance spectroscopy (Impedance Analyzer 7260, Materials Mates). The impedance analyzer is connected to a fluid cell which contains two opposed platinum electrodes (10 mm x 10 mm) spaced at a distance of 10 mm.

The cell is filled with the formulation and a frequency scan is performed with 5 V applied.

Experiments: electrocoalescence as a function of fluid properties

To experimentally analyze electrocoalescence in the system, pairs of droplets are trapped in microfluidic traps in between two electrodes. The amplitude of the voltage is manually stepwise increased with 20 V every 5 s until all droplet pairs fuse. The applied voltage is limited to 1000 V, due to the fact that the signal generator has an internal switch in circuit when going from 990 mV to 1 V. This internal switch caused droplet merging in some cases, therefore not allowing to perform correct interpretation of the experiment beyond this voltage. Figure 4.6 shows the fraction of merged droplet pairs as a function of the applied voltage U applied for several frequencies f of the electric field, when using HFE 7500 with 5% w/w surfactant while the aqueous phase is millipore water. Here the fraction of merged drops is the amount of droplet pairs which fused, divided by the total number of droplet traps. We observe that for higher f a lower U applied is required. To characterize this observation we define the threshold voltage U * applied as the voltage necessary for half of the droplet pairs to fuse, i.e. when the fraction of merged drops reaches 0.5. Now we will further use this system to study the effect of the different parameters in our system (surfactant concentration, oil phase formulation, droplet conductivity) on electrocoalescence.

Surfactant concentration

First, we vary the surfactant concentration in the system when using millipore water as aqueous phase and HFE 7500 as continuous phase. We perform the experiment with a surfactant concentration of 0.1% w/w, 1% w/w and 5% w/w. Figure 4.7 shows U * applied as a function of f . U * applied increases rapidly with decreasing f and a shift of this behavior is observed towards lower f for lower surfactant concentrations. The electric properties of HFE 7500 as a function of the surfactant concentration can be found in Figure 4.5A and 4.5B. The relative permittivity ε r is not altered by the addition of surfactant. However, the electric resistivity ρ e is decreased more than 1 order of magnitude when adding surfactant. Our experimental results show here the surprising role of ρ e of the continuous phase on the electrocoalescence process, mediated by the modification of the surfactant dissolved.

Continuous phase

In order to validate our observation we perform a second set of experiments where we vary the composition of the continuous phase using mixtures of oils with different electric properties. We perform the experiment with FC 40, HFE 7500 and 2 mixtures of HFE 7500 and FC 40 while keeping the surfactant concentration at 5% w/w. The electric properties of the formulations are found in Figure 4.5C and 4.5D. We find an exponential relation between ρ e and the volume fraction of FC 40, which is a deviation from the case of an ideal mixture.

This type of relation has been previously observed for binary mixtures, it however still lacks a theoretical explanation [START_REF] Taylor | Electrical conductivity and viscosity in binary organic liquid mixtures: Participation of molecular interactions and nanodomains[END_REF]. Nevertheless, these formulations allow to increase ρ e over of U * applied for decreasing f shifts towards lower frequencies when increasing the fraction of FC 40 in the mixture (increased ρ e , decreased ε r ), similar to the case of decreased surfactant concentration. Furthermore, we observe a plateau value of U * applied for FC 40 at higher frequencies with an intermediate minimum.

Droplet resistivity

Finally, the electrical resistivity of the aqueous phase ρ e,drop in the system is varied by addition of NaCl (0 M, 4 • 10 -4 M and 2 M) (Figure 4.9). First, the sharp increase of U * applied at lower f is not affected by the change in ρ e,drop , which is validated for both FC 40 and HFE 7500 at 5% w/w surfactant concentration. Next to that, the plateau value for U * applied at higher f decreases with decreasing ρ e,drop .

Data rescaling

To characterize the frequency shift when changing formulation, we rescale f with the rescaling factor f 0 so the experimental data collapses (Figure 4.10A). In Figure 4.10B and C we plot f 0 in function of the electrical properties of the oil phase. We find that there is no clear relation between f 0 and ε r . On the other hand we find that f 0 ∼ ρ -1.2 e . This is close to an inverse relation which means that when ρ e is decreased the cutoff frequency for droplet merging in the system is increased. At low f the sharp increase of U * applied observed is to be expected, as the capacitors in our system (PDMS and oil phase) are reducing the resulting electric field over the oil film between the droplets when decreasing the frequency. By changing the formulation we alter the electric loss in the system and in this way change the behavior as a function of the frequency.

When the electrical loss in the system is minimal, at higher f , a plateau value of U * applied is found. The plateau value is dependent on ρ e,drop . We suspect that an increased NaCl concentration increases the surface charges and dipole-dipole interaction between the drops. It has been previously shown that an increased salt concentration would induce faster electrocoalescence of drops in a chamber when they move freely, by increasing the speed at which droplets approach each other and by speeding up the draining of the liquid film between the droplets, due to increased dipole-dipole interaction [START_REF] Szymborski | Ionic polarization of liquid-liquid interfaces; dynamic control of the rate of electro-coalescence[END_REF]. However, Priest et al. found that the conductivity of the aqueous phase did not affect the coalescence [START_REF] Priest | Controlled electrocoalescence in microfluidics: Targeting a single lamella[END_REF].

Minimal electrical model

To gain a better understanding on the frequency dependence of our system we develop a minimal equivalent electric circuit of one droplet trap by modeling the components as resistors and capacitors (Figure 4.11).

Regarding the impedance Z of electrical components we know that: the impedance Z C of a capacitor with capacitance C is Z C = 1 iωC with ω = 2πf ; the impedance Z R of a resistor with resistance R is Z R = R; the impedance Z RC of a resistor and capacitor in parallel is

Z RC = R 1+iωCR .
For the equivalent electrical circuit the PDMS layer is modeled as a capacitor, the droplets are modeled as a resistor and the oil phase and the thin oil film between the two droplets are modeled as a capacitor and resistor in parallel. This gives:

U app Z pdms Z oil Z drop Z oil Z drop Z pdms Ground Z film
Z pdms = 1 iωC pdms Z drop = R drop Z oil = R oil 1 + iωC oil R oil Z f ilm = R f ilm 1 + iωC f ilm R f ilm with C pdms = ε 0 ε r,pdms l pdms h pdms w pdms R drop = ρ e,drop w drop l drop h drop C oil = ε 0 ε r,oil l oil h oil w oil R oil = ρ e,oil w oil l oil h oil C f ilm = ε 0 ε r,oil l f ilm h f ilm w f ilm R f ilm = ρ e,oil w f ilm l f ilm h f ilm
Here are ρ e,drop and ρ e,oil the resistivity of the aqueous and oil phase (in Ω • m) and ε r,pdms , ε r,oil the relative permittivity of PDMS and the oil phase. l, h and w are the geometrical parameters specific to the microfluidic chip design. The following geometrical dimensions are used: h oil , l oil , h pdms , l pdms , w drop , l drop , h drop = 50 µm w oil , w pdms = 20 µm h f ilm , l f ilm = 10 µm

w f ilm = 1 µm
We argue that the voltage over the liquid film between the droplets is the important factor affecting droplet coalescence. By the voltage divider formula we calculate the relative voltage over the film compared to the applied voltage to the electrodes (Equation 4.1).

U f ilm U applied = 1 + 2(Z drop + Z pdms + Z oil ) Z f ilm -1 (4.1)
We solve equation 4.1 by inserting the measured electrical parameters ε r and ρ e and the geometrical dimensions of our system (Figure 4.12A). We find that the relative voltage over the film decreases at lower f which corresponds to the experimental results where a higher U applied is required at low f to achieve coalescence. Further we observe a shift along f when varying the electric properties of the oil. We now perform a similar rescaling as was performed with the experimental data (Figure 4.12B, C). We find that the data collapses when f 0,model ∼ ρ -1 e . This means that in our model the cutoff frequency depends on ρ e . Below this cutoff frequency, U f ilm /U applied decreases rapidly because the electric loss in the system is too large to get a significant voltage over the liquid film for coalescence. Above the cutoff frequency the voltage over the liquid film reaches a plateau value. At high f the plateau value varies for different oil properties. In the model, this shift is caused by the difference in ε r and we find that ρ e,drop does not affect the plateau value, as opposed to what we observed experimentally.

All in all, the frequency dependence of electrocoalescence can be rationalized in first order by the electric model which helps to estimate the electric loss in the system. However the model does not paint the full picture as it does not incorporate the surface energy and any dynamic effects. Therefore it does not allow to predict the threshold voltage required for merging at high frequencies, when the electric loss is minimal.

Conclusion

In brief, we present an experimental analysis of the efficiency of droplet merging in electric fields for various formulations. We find that the merging efficiency is dependent on the frequency of the applied electric field. At low frequency a higher voltage is required due to electric loss in the system. The electric loss is altered by changing the formulation of the oil phase. By rescaling the data, and by validating it by a simplified electric model, we find that the resistivity of the oil -a parameter which is generally neglected as the oil is assumed as a perfect dielectric -is the parameter linking the oil formulation to the observed frequency dependence. Furthermore, we find that increased droplet conductivity facilitates electrocoalescence. This finding may result in optimisation of electric fields which might avoid adverse effects on biological content encapsulated in droplets and provide insights for the optimisation of formulations. In this chapter we describe the integration of a microfluidic workflow for directed evolution of the enzyme glucose oxidase. This chapter focuses on the technological development and the integration of the microfluidic tools, including fluorescent activated droplet sorting.

Despite these findings there remain open questions as electrocoalescence is a difficult sys-

Microfluidic workflow for directed evolution of glucose oxidase

We do not focus on the biological workflow as it is outside the scope of this thesis. The biological experiments were performed by Alejandra Gadea, a fellow PhD student within the EVOdrops consortium.

Introduction

The use and advantages of droplet microfluidics as a tool for high-throughput screening of cells has been introduced in Section 2.5. Furthermore, in Paper I: Directed evolution in drops: molecular aspects and applications the successful cases of directed evolution of biomolecules in the recent years are summarized.

In brief, single cell analysis with the use of droplet microfluidics has several advantages compared to analysis with microtiter plate. It has an increased screening throughput and lower cost, and is therefore advantageous for screening a large number of cells. Another tool for high-throughput screening of cells is fluorescent-activated cell sorting (FACS). This method is easy to use, however, the assays amenable to FACS are limited as there is no compartmentalization of the cells, i.e. the genotype-phenotype linkage is at the cell level [START_REF] Autour | Ultrahigh-throughput improvement and discovery of enzymes using droplet-based microfluidic screening[END_REF].

Whereas in microtiter plates the well physically confines the genotype and the phenotype, and for droplet microfluidics the linkage is provided by the droplet. The properties of microtiter plate, FACS and droplets for cell screening are summarized in Table 5.1. [START_REF] Autour | Ultrahigh-throughput improvement and discovery of enzymes using droplet-based microfluidic screening[END_REF]. Here, we develop a workflow based on droplet microfluidics for the directed evolution of glucose oxidase (GOx) towards increased glucose sensitivity. GOx is an enzyme that catalyzes the oxidation of glucose to gluconolactone and hydrogen peroxide. The enzyme is of special interest for the use in biosensors and enzymatic biofuel cells [START_REF] Sandip B Bankar | Glucose oxidase-an overview[END_REF]. Enzymatic biofuel cells are systems that are able to generate electric energy by using biocatalysts. These systems can be used in various applications such as miniaturized electronic devices and self-powered sensors [START_REF] Scott Calabrese Barton | Enzymatic biofuel cells for implantable and microscale devices[END_REF]. For example, an implanted biofuel cell could use body fluids such as blood as a fuel source for the generation of electrical power. This may then be used to drive insulin pumps or biosensors [START_REF] Heller | Integrated medical feedback systems for drug delivery[END_REF]. In a glucose/O 2 enzymatic biofuel cell, GOx is immobilized at the anode for the oxidation of glucose, and laccase at the cathode for the reduction of O 2 , while the anode and cathode are separated by a proton exchange membrane [START_REF] Kavanagh | Performance of a glucose/o2 enzymatic biofuel cell containing a mediated melanocarpus albomyces laccase cathode in a physiological buffer[END_REF]. Currently, the magnitude of the power output and stability of the enzymes are the main concerns for the applications of enzymatic biofuel cells, the power output is limited by the performance of the enzymes [START_REF] Zhu | Making glucose oxidase fit for biofuel cell applications by directed protein evolution[END_REF]. Therefore, we aim to enhance the catalytic efficiency of GOx by directed evolution. In this chapter we focus on the technological development of the workflow. The methods designed for the preparation of cells and generation of the mutant library are not discussed. For more information on this we refer to the Ph.D. thesis of Alejandra Gadea.

Table 5.1: Comparison of the properties of cell screening with microtiter plate, FACS and droplets

Microtiter plate FACS Droplets

Materials & methods

System

The setup used for fluorescence measurement of droplets and droplet sorting is presented in Appendix A, Figure A.6. The flow in the channels is controlled by Nemesys syringe pumps.

Fluorescence-activated sorting is controlled by an in-house built Labview program.

Biological workflow

Yeast cells for GOx display and generation of mutant library

Yeast cells are prepared to display GOx on the cell surface. Display expression allows to assess the enzymatic activity without the need to perform cell lysis, which allows to regrow the cells after droplet sorting. In this way, display expression allows several rounds of selection and regrowing before sequencing. The mutant library is constructed by using error-prone PCR (epPCR). For full details on the materials & methods of the preparation of the cells and the construction of the library we refer to the Ph.D. thesis of Alejandra Gadea.

GOx detection assay

The detection assay for GOx activity is presented in Figure 5.1. GOx reacts with glucose to form gluconolactone and hydrogen peroxide. Hydrogen peroxide (H 2 O 2 ) reacts with Amplex Ultra Red (AUR) in the presence of horseradish peroxidase (HRP) to generate the fluorescent molecule resorufin. All reagents are purchased from Thermo Fisher Scientific.

For the microfluidic experiments the cell suspension is prepared at an optical density (OD) of 0.2. As barcode dye we add dextran-cascade blue at 20 µM, and we add 0.1 % Tween 80 to avoid cells sticking to the channel walls. The assay mix for the microfluidic experiments is prepared with AUR at 100 µM, HRP at 4 U/ml, and glucose at 100 µM.

GOx HRP

Microfluidic devices

Microfluidic devices have been fabricated with the methods presented in Appendix A. Two devices are used for the experiments: one device serves for the kinetic analysis of GOx in droplets, and one integrated device for fluorescent-activated droplet sorting (FADS). The oil used in the devices is HFE 7500 containing 1 % surfactant (Fluosurf, Emulseo). To flow the cell suspension we use a glass syringe (2.5 ml Hamilton gastight 1002 TLL) with a teflon tubing with an inner diameter of 100 µm. A small inner diameter is used to avoid cell aggregation. The content of the syringe is stirred with a magnetic stirrer to avoid cell sedimentation.

Kinetic analysis

The device in Figure 5.2 is used for the analysis of the enzymatic assay in droplets. Droplets are produced with a co-flow flow focusing junction which allows to co-encapsulate a cell suspension and assay mix in droplets. Excess oil is extracted after droplet production to pack the droplets in the incubation line. The flow focusing junction has a width of 30 µm, the channel height of the flow focusing junctions is 30 µm and of the incubation lines is 70 µm.

The incubation line allows for on-chip incubation up to 13 min and has measurement points along the incubation line to assess the droplet fluorescence at different time points.

Fluorescence measurement

1. Co-ow droplet production 2. Incubation 1.

3.

2.

Figure 5.2: Microfluidic device for kinetic analysis with on-chip incubation. Oil is extracted after droplet production to pack the droplets together in the incubation line. Measurement points along the incubation line allow to assess the droplet fluorescence. Scale bar is 200 µm.

Integrated cell encapsulation, incubation and sorting

The device presented in

Results

Biochemical assays in droplets

First, we analyze if the GOx detection assay presented in Figure 5.1 works in droplets. For this, we co-encapsulate two solutions: (i) the cell suspension at an OD of 0.2 with 20 µM dextran-cascade blue which serves as barcode dye and 0.1 % Tween 80. (ii) The assay mix with AUR (100 µM), HRP (4 U/ml), and glucose (100 µM). The droplets are produced at a co-flow flow focusing junction with a nozzle size of 30 µm and are collected in an observation chamber.

We find that the droplets containing a cell are bright fluorescent indicating that the assay works in droplets (Figure 5.4). We further observe from Figure 5.4 that the fluorescent product tends to leak out the drops as the drops around the brightly fluorescent drops are brighter than the rest. It was demonstrated that the molecular transport of resorufin equilibrates two populations with a different concentration in three hours [START_REF] Skhiri | Dynamics of molecular transport by surfactants in emulsions[END_REF]. The molecular exchange of resorufin in the emulsion limits the incubation time in our system and suggests that on-chip incubation is preferred.

Microfluidic kinetic analysis

Next, we analyze the kinetics of the reaction in droplets with the microfluidic device presented in Figure 5.2A. The assay mix and cells are flowed at 10 µl/h each, oil for droplet production is flowed at 180 µl/h. After droplet production the oil is extracted at -170 µl/h. The fluorescence is measured at four points along the incubation line with a laser spot resulting in the histograms presented in Figure 5.5. A compact population forms after 13 min of incubation at 1 V to 1.2 V. We see that the population size of the brightly fluorescent drops is 1% to 1.5%, which is lower than the 10% which we aim for, following the Poisson statistics.

Nevertheless, this means that the reaction happens fast and an incubation time of 10 to 15 minutes is sufficient for detecting wild type GOx activity. Variations in activity of droplets containing a cell could be caused by differences in cellular expression level of the enzyme.

Therefore, for the integrated droplet sorting device we aim for an incubation time of 10 to 15 minutes for consistent detection.

Integrated droplet sorting of GOx

Next, we use an integrated device for the directed evolution of GOx with an incubation time of ∼ 10 min. We first test the device by using wildtype GOx and then apply the set-up for sorting a GOx mutant library.

Workflow set-up with wild type GOx

We use the device in Figure 5. In this time sequence we find two peaks which are significantly higher than the rest. These peaks trigger an electric pulse for sorting (Figure 5.7C). The active electrode is triggered at 700 V pp at 30 kHz for 30 cycles. The positive outlet is collected in an eppendorf tube.

This system is used to sort the variant library, however, no variants with increased activity

were detected yet.

Conclusion & perspective

In summary, we first demonstrated the detection of GOx activity in droplets. We then presented a workflow for directed evolution of GOx towards increased glucose sensitivity. The workflow involves cell encapsulation, incubation, and sorting integrated in one microfluidic device at a throughput of 700 Hz. We utilized this method for measuring the activity of a GOx library and subsequent sorting of positive hits. Unfortunately we were not able to detect any active variants in the library. Nevertheless, the platform is adapted for measurements of different libraries of GOx for directed evolution purposes. My main contribution in this project consisted of developing the microfluidic set-up.

In future work, we aim to improve the throughput of the device by integrating a novel sorter design. A layered sorting junction which was demonstrated to be able to sort at ultrahigh throughput [START_REF] Abate | High-throughput injection with microfluidics using picoinjectors[END_REF]. The production nozzle and incubation line will need to be adapted to fit with the increased sorting rate.

Next to that, it would be interesting to determine the recovery efficiency of cells after droplet sorting. It would be interesting to optimize this process in order to be able to identify all the positive hits. In this chapter we discuss the use of droplet microfluidics to study the effect of liquidliquid phase separation (LLPS) on biochemical reaction rates. The chapter first introduces the role of LLPS in intracellular organization. Further, we study the use of LLPS in droplets as a tool for improved limit-of-detection towards the concentration of substrate, enzyme, or product of a biochemical reaction. The main part of the experimental data and exerts of the text presented in this chapter are based on Paper V: Droplet microfluidics for multiplexed analysis of the effect of coacervation on enzyme kinetics.

Biochemical intracellular organization

Being a cell is challenging: you have to take care of a complex network of biochemical reactions to stay out-of-equilibrium while being exposed to fluctuations in temperature, accessibility to nutrients, chemical environment, ... Compartmentalization is an essential feature for the cell to organize its complex highly crowded interior system. Intracellular compartmentalization allows to concentrate species and maintain an out-of-equilibrium chemical gradient inside the cell to drive biochemical reactions.

Within cells, many compartments are separated from the environment by a membrane.

The interior of a membrane-bound organelle is typically regulated by specific membrane transport machineries which are able to transport substances across the membrane. In mitochondria, proton pumps in the membrane maintain a chemical gradient required for the production of ATP [START_REF] Schultz | Structures and proton-pumping strategies of mitochondrial respiratory enzymes[END_REF]. The nucleus is a membrane-bound structure which holds the genetic information of the cell and controls transcription. Pores within the nuclear membrane control the passage of proteins and nucleic acid [START_REF] Newport | The nucleus: structure, function, and dynamics[END_REF]. Other examples of membrane-bound organelles are the Golgi aparatus and the endoplasmic reticulum.

A second class of compartments the cell creates to organize biochemical reactions are membraneless organelles, also named biomolecular condensates (Figure 6.1). Examples of such condensates are: nucleoli which make ribosomes in the nucleus [START_REF] Franc ¸ois-Michel | The multifunctional nucleolus[END_REF], stress granules which take various functions under stress conditions [START_REF] Buchan | Eukaryotic stress granules: the ins and outs of translation[END_REF], and P-bodies which play a role in post transcriptional regulation [START_REF] Luo | P-bodies: composition, properties, and functions[END_REF]. These compartments are not membrane-bound but are still able to locally concentrate biochemical species in the cell. It is counter-intuitive that these membraneless compartments can co-exist in the cytoplasm or nucleus as we would expect a homogeneous distribution of the components driven by diffusion. It has been shown that these biomolecular condensates have liquid-like properties: they take a drop-like shape, fuse when in contact, and are deformed under shear flow [START_REF] Clifford P Brangwynne | Germline p granules are liquid droplets that localize by controlled dissolution/condensation[END_REF]. Therefore, these compartments are nowadays described as liquid-like droplets which are formed through the process of liquid-liquid phase separation (LLPS).

Liquid-liquid phase separation

Liquid-liquid phase separation is the phenomenon in which a liquid mixture spontaneously demixes in two or more distinct phases. To understand this spontaneous thermodynamic process we need to consider the free energy of a mixture [START_REF] Shin | Liquid phase condensation in cell physiology and disease[END_REF]. The free energy in the system is given by F = E -T S, with S the contribution of the entropy, T the temperature and E the interaction energy between the molecules. When E is small, F is minimized by entropically driven spontaneous mixing. When the interaction energy between the molecules Reprinted from [START_REF] Edward M Courchaine | Droplet organelles?[END_REF].

is significant the free energy curve becomes multimodal (Figure 6.2A). Now F is minimized by spontaneous demixing into two phases with concentration c sat for the diluted phase and c in for the condensed phase (Figure 6.2C). A full phase diagram can now be described showing the conditions under which phase separation occurs depending on temperature, pH or ionic strength (Figure 6.2B) [START_REF] Shin | Liquid phase condensation in cell physiology and disease[END_REF]. The chemical potential of the components in the dense and dilute phase is equal. There is no driving force for diffusive transport and therefore no net flux of molecules between the two phases [START_REF] Banani | Biomolecular condensates: organizers of cellular biochemistry[END_REF]. In this way LLPS allows to maintain a chemical gradient within the cell without membrane or input of energy.

The occurrence of phase separation in the cell is controlled by the concentration and solubility of the components. The cell is able to control the assembly or disassembly of condensates by changing the expression levels of the key components of the condensate, by changing its volume and in this way changing concentrations or by post-translational modifications which can change the intrinsic solubility of components or the interaction strength between proteins [START_REF] Banani | Biomolecular condensates: organizers of cellular biochemistry[END_REF][START_REF] Stephanie | Inverse size scaling of the nucleolus by a concentration-dependent phase transition[END_REF].

Molecular sequestration

Solutes not involved in LLPS may spontaneously sequester into the dense or the dilute phase as they can move freely in the solution. The distribution of the solute between the two phases is governed by the relative free energy of the solute in the two phases [START_REF] Karina K Nakashima | Biomolecular chemistry in liquid phase separated compartments[END_REF]. There are several factors which contribute to the difference in free energy. The local polarity is generally lower in the dense phase which drives the partitioning of hydrophobic solutes [START_REF] Karina K Nakashima | Biomolecular chemistry in liquid phase separated compartments[END_REF]. The relative

(A) LLPS when a binary mixtures minimizes its free energy by demixing into two phases. (B)

The free energy in the system is dependent on the temperature which gives rise to a phase diagram under which phase separation occurs. (C) In a binary mixture the system spontaneously demixes into a dense and a diluted phase. Reprinted from [START_REF] Shin | Liquid phase condensation in cell physiology and disease[END_REF].

permittivity of the dense phase is estimated to be between 45 and 60 [START_REF] Spruijt | Direct measurement of the strength of single ionic bonds between hydrated charges[END_REF]. Next to that, interaction of charged regions of the solute and the condensate matrix is the driving force for sequestration of the majority of the biomolecules towards the condensed phase. Furthermore, the release of bound counter-ions upon complexation in the condensed phase is entropically favorable [START_REF] Karina K Nakashima | Biomolecular chemistry in liquid phase separated compartments[END_REF]. To quantify the molecular sequestration, the partitioning coefficient K is defined as K = c in /c sat , with c in and c sat the concentration of the solute in the dense and dilute phase.

Cellular function of condensates

Selective sequestration of molecules in the cell may have several effects on biochemical reactions [START_REF] Banani | Biomolecular condensates: organizers of cellular biochemistry[END_REF]. First of all, biomolecular condensates may serve as a reaction crucible (Figure 6.3, left). Condensates may increase the local concentration of biochemicals which in the simplest case increases the reaction rate. Selective sequestration of a specific substrate in the condensate while excluding others accelerates the reaction rate towards this substrate while the rate towards other substrates is reduced. Selective sequestration of certain enzymes in a forked metabolic pathway directs the metabolites towards one pathway [START_REF] Brian | The role of liquid-liquid phase separation in regulating enzyme activity[END_REF]. An example of biomolecular condensates serving as reaction crucible are Cajal bodies. It was demonstrated that the presence of Cajal Bodies in the nucleus was required for the correct splicing of mRNA.

It is hypothesized that the presence of Cajal Bodies, and the subsequent concentration of small nuclear ribonucleoproteins within them, is essential to overcome rate-limiting reaction steps [START_REF] Strzelecka | Coilin-dependent snrnp assembly is essential for zebrafish embryogenesis[END_REF]. Another example are the biomolecular condensates in the nucleus which form at DNA damage sites. For DNA repair to occur diverse enzymes are required that work in a highly organized fashion. It is hypothesized that the concentration of DNA repair enzymes in the proximity of the damage sites accelerates the repair process [START_REF] Alberti | The wisdom of crowds: regulating cell function through condensed states of living matter[END_REF]. However, increased concentration of components does not always result in increased reaction rates. Interactions of the scaffold of the condensates with the enzyme may decrease the specific activity of the enzyme in the condensate compared to their activity in solution [START_REF] Banani | Biomolecular condensates: organizers of cellular biochemistry[END_REF]. Furthermore, the material properties of the condensates are closely linked to the molecular dynamics [START_REF] Shin | Liquid phase condensation in cell physiology and disease[END_REF].

Changes in physical properties of the condensate, such as increasing viscosity, may slow the diffusion of molecules and decrease reaction rates. For example, a 60-fold decrease in activity of a ribozyme was observed in the condensed phase despite increased concentrations of the enzyme and substrate [START_REF] Drobot | Compartmentalised rna catalysis in membrane-free coacervate protocells[END_REF].

A second function of condensates is the selective sequestration of molecules to inhibit Reprinted from [START_REF] Shin | Liquid phase condensation in cell physiology and disease[END_REF].

their activity (Figure 6.3, right). An enzyme may be selectively sequestered and separated from the substrate, inhibiting the reaction. For this to be effective, a high partitioning coefficient is required. The prime example of this type of condensate are stress granules. Stress granules in the cytoplasm have been related to sequestering and protecting RNA and translational proteins in the cytoplasm. They are often found in cells exposed to stressful conditions such as heat stress or energy depletion [START_REF] Anderson | Stress granules[END_REF]. They function as microcompartments protecting translational complexes hereby suppressing signaling pathways [START_REF] Alberti | The wisdom of crowds: regulating cell function through condensed states of living matter[END_REF]. It was demonstrated that the activity of a specific kinase enzyme regulated the condensation/dissolution of the stress granule. When the kinase was inactive, it prevented stress granule dissolution, inhibiting the release of the sequestered molecule and inhibiting the signaling pathway. When the kinase was active, it allowed stress granule dissolution and it further promoted the signaling pathway [START_REF] Wippich | Dual specificity kinase dyrk3 couples stress granule condensation/dissolution to mtorc1 signaling[END_REF]. Furthermore, it was demonstrated that the kinase activity affected the material properties of the stress granule from liquid-like droplet for transient expression of the kinase, to solid-like aggregate for a completely inactive kinase.

Finally, biomolecular condensates may serve as organizational hub (Figure 6.3, bottom).

The organization in the nucleus is achieved entirely without membrane-bound organelles.

Forces related to the surface tension of the condensates likely play a role in the internal structure of the nucleus [START_REF] Shin | Liquid phase condensation in cell physiology and disease[END_REF].

Coacervates as a model system

Studying and characterizing biomolecular condensates in cells is challenging. Model systems could provide a better understanding on the molecular interactions responsible for the functioning of biomolecular condensates [START_REF] Yewdall | Coacervates as models of membraneless organelles[END_REF]. Complex coacervates, which are systems formed through LLPS of two oppositely charged molecules driven by electrostatic interactions, have

shown great potential as a model system for biomolecular condensates [START_REF] Martin | Dynamic synthetic cells based on liquid-liquid phase separation[END_REF].

The use of microfluidics for the synthesis and analysis of coacervates has become increasingly interesting as it allows spatiotemporal control of coacervate formation and manipulation. It was demonstrated that by the use of a flow focusing junction the size distribution of the formed coacervate droplets was narrower compared to using bulk methods [START_REF] Van Swaay | Microfluidic formation of membrane-free aqueous coacervate droplets in water[END_REF]. Furthermore, it was demonstrated that by the use of acoustic fields it was possible to spatially organize the coacervate formation in a microfluidic chamber [START_REF] Tian | Spontaneous assembly of chemically encoded two-dimensional coacervate droplet arrays by acoustic wave patterning[END_REF].

Droplet-based microfluidic methods are of special interest as it allows to create monodisperse compartments for the coacervation process to take place, which allows to spatially organize and study the system with a high degree of control on local concentrations. In this respect, the formation of coacervates in liposomes has been demonstrated. One coacervate component is encapsulated in the liposome while the second coacervate component is seeded later in the emulsion to induce LLPS inside the liposome [START_REF] Deshpande | Spatiotemporal control of coacervate formation within liposomes[END_REF]. Next to that, by using a similar method a reversible coacervate formation/dissolution system was developed which responded to changes in pH [START_REF] Love | Reversible ph-responsive coacervate formation in lipid vesicles activates dormant enzymatic reactions[END_REF]. The controlled formation of coacervates in w/o droplets was also demonstrated by co-encapsulation of oppositely charged polyelectrolytes [START_REF] Linsenmeier | Dynamics of synthetic membraneless organelles in microfluidic droplets[END_REF].

Droplets containing the components driving phase separation could be statically trapped for optical analysis [START_REF] Alexander M Bergmann | Evolution and single-droplet analysis of fuel-driven compartments by droplet-based microfluidics[END_REF][START_REF] Sokolova | Enhanced transcription rates in membrane-free protocells formed by coacervation of cell lysate[END_REF]. More recently, this method was used together with accurate onchip temperature control to extract the phase diagram and kinetics of LLPS in droplets [START_REF] Villois | Droplet microfluidics for the label-free extraction of complete phase diagrams and kinetics of liquid-liquid phase separation in finite volumes[END_REF].

However, statically trapping droplets does not make use of the high-throughput capabilities of droplet microfluidics.

Beneyton et al. demonstrated that high-throughput synthesis and analysis of coacervates in droplets is possible using standard droplet-based microfluidic methods [START_REF] Beneyton | High-throughput synthesis and screening of functional coacervates using microfluidics[END_REF]. They demonstrated the rapid formation of coacervates in drops with a high level of monodispersity.

A flow focusing junction was used to co-encapsulate oppositely charged polyelectrolytes in droplets, rapid mixing of the polyelectrolytes induced the coacervation process (Figure 6.4).

With fluorescence analysis of the droplets it was possible to estimate the partition coefficients of fluorescent compounds and to estimate rates of a biochemical reaction. Nevertheless, a complete systematic quantitative analysis of the effect of coacervation on enzyme kinetics was not developed.

The aim of the research presented in this chapter is to implement droplet-based microfluidic methods for the systematic quantitative analysis of the effect of LLPS on enzyme kinetics.

Secondly, we aim to study the use of coacervates in droplets for enhanced limit-of-detection towards biochemical reactions.

Materials & methods

Materials

The fluorinated oil used in the system is HFE 7500 with 1% w/w surfactant (Fluosurf, Emulseo). Coacervates are synthesized in droplets made up of carboxymethyl-dextran (CMdex)

and poly(diallyldimethylammonium chloride) (PDDA). Two enzymatically driven reactions were selected for the study (Figure 6

Bulk partition coefficients

The partition coefficients of all the components of the reaction were determined in bulk and are reported in Table 6.1. The partition coefficient of fluorescein, resorufin, FDG and RBG were determined by spectrophotometry. Absorbance readout was performed using a microtiterplate reader (λ em = 490 nm or λ em = 570 nm; SpectraMax Paradigm, Molecular Devices) in a 96-well plate (Thermo Fischer). Tubes were prepared in 60 mM sodium phosphate buffer containing CMdex (166 mM), PDDA (28 mM) and fluorescein, resorufin, FDG or RBG (0 µM, 50 µM and 100 µM). The tubes were vortexed and afterwards centrifuged for 20 min at 15 000 g. The volume of the coacervate was determined by pippeting, and the coacervate phase was separated from the depleted phase into a separate tube. For fluorescein and resorufin, 100 µL of the depleted phase and 10 µL of the coacervate phase were dispensed in a 96-well plate. For FDG and RBG, 10 µL of both the depleted and coacervate phase were dispensed, and 10 µL of 50 U/ml β-gal was added to the wells and incubated for 1h to convert all the substrate into fluorescein or resorufin. 20 µL of NaCl at 2 M was added to break the coacervate phase. Afterwards, 60 mM sodium phosphate buffer was used to fill the wells to reach a volume of 100 µL. The partition coefficient of β-gal was determined by measuring the concentration of β-gal after phase separation in the depleted phase by kinetic measurements. Tubes were prepared in 60 mM buffer containing β-gal (0 U/ml, 2.5 U/ml and 5 U/ml) in a solution of 750 µL containing CMdex (166 mM) and PDDA (28 mM). The tubes were centrifuged for 15 min at 10 000 g. The volume of the coacervate was determined by pipetting. The enzyme concentration in the depleted phase was determined by measuring the initial rate of the reaction, 50 µL of FDG (100 µM) was added to 50 µL of the depleted phase (Figure 6.6B). A calibration curve for the initial rate vs enzyme concentration was prepared by using depleted phase without enzyme and adding a known enzyme concentration (0, 0.625, 1.25, 2.5, 5 and 10 U/ml) (Figure 6.6A). The fluorescence was measured over time (λ ex = 473 nm, λ em = 513 nm)

and the enzyme concentration in the depleted phase was determined by linear interpolation of the initial slope (Figure 6.6C). The partition coefficient was then calculated by the known volumes of the coacervate and depleted phase and by the known concentrations.

Microfluidic devices

The microfluidic devices for this study were fabricated with standard soft lithography and photolithography methods described in Appendix A. The channels have a depth of 25 µm and a depth of 70 µm for the delay line. Four microfluidic devices were used: the first two designs were used for the production and analysis of coacervates in drops, the third device was used for the production of a 10-bit emulsion with coacervate, and the final device was used for multiplexed kinetic analysis of two 10-bit emulsions.

Droplet with coacervate: production and analysis

The device for the production of droplets containing coacervates is presented in Figure 6.7A.

The device has three aqueous inlets: two polyelectrolyte inlets and one buffer inlet. The polyelectrolytes are spaced by a buffer stream in the center which ensures that the electrolytes only mix after droplet formation. For fluorescence analysis of coacervates in droplets we use the device in Figure 6.7B. Droplets are reinjected in the device and spaced by oil for individual analysis. A local constriction in the analysis section ensures that we are able to measure the coacervate fluorescence in a repeatable way.

10-bit emulsion production with coacervate

The device for the production of a 10-bit emulsion is presented in Figure 6

Multiplexed kinetic analysis

The device for multiplexed kinetic analysis is shown in Figure 6.9. Two emulsions are reinjected in the kinetics device (0.5-0.8 bar): a 10-bit emulsion with coacervates and a 10-bit emulsion without coacervates which serves as control measurement. Droplets are spaced with oil and picoinjected with β-gal (0.5-0.8 bar) by applying an AC electric field (100 V pp , 10 kHz). Excess oil is extracted after picoinjection (0-25 µL/h). Droplet fluorescence is measured at several measurement points along the delay line with an incubation time up to 30 minutes. The incubation time and picoinjected volume is determined by image analysis.

Set-up & data processing

A schematic of the optical set-up for fluorescence measurements is shown in

Effect of CMdex/PDDA coacervates on enzyme kinetics of βgal

In this section we study the effect of CMdex/PDDA coacervates on enzyme kinetics of β-gal.

We first determine the coacervate and droplet volume by image processing. Secondly, we study the partitioning of the enzyme. Finally we estimate the kinetic parameters K M and V max for the substrates FDG and RBG.

Coacervate volume

Droplets containing CMdex/PDDA coacervates are produced with the device in Figure 6.7A.

CMdex (1 M; 37.5 µl/h), sodium phosphate buffer (60 mM; 150 µl/h) and PDDA (166 mM;

β-galactosidase partitioning

To study the effect of coacervation on the enzyme kinetics of β-gal in droplets it is essential that the partitioning of β-gal is fast when it is picoinjected in the droplet compared to the reaction kinetics.

In order to study the partitioning of the enzyme over time we follow the workflow presented in Figure 6.12. First, droplets containing CMdex/PDDA coacervates are produced. The result of this experiment is shown in Figure 6.13. The partition coefficient F coacervate /F depleted does not vary significantly over time which means that the partitioning happens fast. However, we find different values of F coacervate /F depleted for the different enzyme concentrations.

We suspect that this is because the partitioning of β-gal in the coacervate is very efficient which causes F depleted to be close to the noise level of the detection system.

To validate this observation we analyze F coacervate /F depleted for fluorescein as a function of the concentration (Figure 6.14). We produce a 10-bit emulsion with a fluorescein concentration ranging from 20 nM to 150 nM with the device presented in Figure 6.8 and measure the fluorescence with the device presented in Figure 6.7B.

We find that for a decreased concentration the partition coefficient decreases. This illustrates a limitation of the method for determining the partition coefficient with droplet microfluidics, as presented by Beneyton et. al [START_REF] Beneyton | High-throughput synthesis and screening of functional coacervates using microfluidics[END_REF]. It is not reliable to determine partition coefficients with droplets for very efficient partitioning or at very low concentrations because the depleted phase is too close to the noise level. Therefore, it is required to determine the partition coefficients in bulk.

Microfluidic workflow for multiplexed kinetic analysis

Now, the enzyme kinetics of β-gal for FDG and RBG is analyzed. The entire microfluidic workflow for multiplexed kinetic analysis is summarized in Figure 6. erence population, we are able to apply a weighting to the signal to avoid the influence of small differences in the positioning of the laser line at the different MPs.

β-galactosidase enzyme kinetics

We apply the workflow presented in 6.

Estimation kinetic parameters

Now we estimate the kinetic parameters K M and V max of β-gal for the reaction involving FDG and RBG. For droplets with coacervate, we first calculate the total concentration of product in the droplets by using the following equation:

C tot = Vcoacervate V drop C coacervate + V depleted
V drop C depleted . In Figure 6.19, we extract the initial reaction velocity v for droplets with and without coacervates by fitting a linear slope to the first three time points of the kinetic data presented in Figure 6.17 and 6.18. Furthermore, the catalytic turnover number k cat is calculated from V max using the enzyme concentration. The kinetic parameters are summarized in Table 6.2.

Overall, we find that the kinetic parameters do not vary much between the control droplets and the droplets with coacervate. comparing the values obtained in droplets to bulk measurements, we find that they agree well. We find the same relative difference between bulk with control conditions and with depleted phase as we find between droplets with control and with coacervate. Absolute differences between measurements in droplet and bulk may be due to the fact that a different enzyme batch was used to perform the bulk experiments. Next to that, for resorufin, it is known that it tends to leak out of the droplet into the oil phase. Nevertheless, we demonstrated that we can extract the kinetic parameters of a dynamically partitioning system with this workflow.

Improved limit-of-detection in droplets

In this part of the experimental section we study the use of coacervates in droplets as a tool for improving the limit-of-detection (LOD) of our system. Here, we focus on the reaction FDG → fluorescein. To determine the improvement in LOD we define the signal-to-noise ratio (SNR).

The signal in the system is the fluorescence level of the coacervate phase, depleted phase or control droplet respectively. The noise is defined as the median fluorescence value of the raw signal excluding the fluorescence of the droplets. We investigate the effect of the presence of a coacervate on SNR as a function of the concentration of substrate (FDG), enzyme (β-gal) and product (fluorescein).

We first study SNR as a function of fluorescein concentration. We produce two 10-bit emulsions, one with and one without coacervate, with a varying fluorescein concentration ranging from 20 to 150 nM using the device presented in Figure 6.8. The emulsions are reinjected in the device presented in Figure 6.7B for fluorescent readout. Figure 6.22 shows SNR as a function of fluorescein concentration. The dotted line at SNR = 1 represent the point when the signal is not detectable from the noise. We see that the coacervate increases SNR compared to the control emulsion. This increase is solely due to the sequestration of fluorescein in the coacervate phase.

In order to study the SNR as a function of FDG concentration we use the same workflow as presented in Section 6.3.3. We produce 10-bit emulsions with varying FDG concentration ranging from 20 to 150 µM and picoinject β-gal to a concentration of 2.0 U/ml. To study the SNR as a function of β-gal concentration we produce 10-bit emulsions with varying β-gal concentration ranging from 0.5 to 5.5 U/ml. The emulsions are reinjected in the kinetics device and FDG is picoinjected in the droplets to a concentration of 65 µM. SNR as a function of β-gal and FDG is determined at three time points (1 min, 5 min and 14 min).

The results of these experiments are presented in Figure 6.23. We find a clear increase of SNR for FDG in the coacervate phase. However, for β-gal concentration the difference between the coacervate phase and control is rather limited. This is most likely due to the fact that the overall kinetic rate in the droplets with coacervates was measured to be lower than for the control droplets, as was shown in Figure 6.20.

Conclusion & discussion

In summary, coacervates in droplets were produced for two purposes: (i) to study the effect of coacervation on enzyme kinetics and (ii) to use coacervates in droplets as a tool for enhanced limit-of-detection.

(i) We demonstrated a microfluidic workflow to study the effect of coacervation on enzyme kinetics. We validated that the partitioning of the enzyme happens fast after picoinjection compared to the timescale of the reaction kinetics. Two one-step enzymatic reactions, catalyzed by β-gal, were analyzed in CMdex/PDDA coacervate and the kinetic parameters were extracted. The partition coefficients of substrate, enzyme and product of the reactions were determined with spectrophotometry in bulk as we demonstrated that determining the partition coefficient in microfluidics depends highly on the detection system. We believe that this workflow could be further used study the effect biomolecular condensates have on enzyme kinetics in cells.

In future experiments we would like to analyze the enzyme kinetics in other coacervate system such as polylysine/ATP, PDDA/ATP and polylysine/CMdex. Also investigating more complex reactions, such as multi-step reactions or reactions with a co-factor would be interesting to investigate. Furthermore, it would be interesting to study more biologically relevant systems such as the dynamic condensation/dissolution of coacervates due to kinase or phosphatase activity. Furthermore, coacervates existing out of RNA, and how this affects translation of proteins would be interesting to study. However, we believe the main constraint in this system is the determination of the bulk partition coefficients of all the components. Determining the partition coefficients in bulk is not trivial due to low concentrations of compounds in the depleted phase and due to low volumes of the coacervate phase. Moreover, interactions of the coacervate matrix with absorbance measurements further complicate concentration measurements. Next to that, a fluorogenic assay is required to be compatible with this workflow.

(ii) Coacervates were used in droplets as a tool to improve the limit-of-detection in the system for substrate, enzyme and product concentration. Mainly due to the sequestration of the product we observed an improved limit-of-detection for all the experiments. Therefore, to use coacervates as a tool for droplets it is necessary to perform more research on the sequestration of molecules in the coacervates to be able to predict which molecules will highly partition and in this way to be able to design coacervate systems for specific applications.

For example, the detection and discovery of antibodies secreted by a cell is usually done with fluorescent tags and a functionalized bead which binds to the antibody-fluorescent tag complex [START_REF] Gérard | High-throughput single-cell activity-based screening and sequencing of antibodies using droplet microfluidics[END_REF]. The functionalized bead bind to the anitbodiesto be able to detect the weakly fluorescent signal. Here one could envision the use of coacervates in droplets as a system to passively capture the antibodies, driven by thermodynamics. This could possibly increase capturing efficiency and avoid the necessity to functionalize beads.

93

Concluding remarks

In this thesis, I explored and developed tools for manipulation of droplets at high-throughput.

At first I focused on the implementation of electric fields as they offer external control to manipulate droplets with a high precision and a fast response time. I targeted the essential manipulation steps in droplet microfluidics: (i) droplet production, (ii) droplet coalescence and (iii) droplet sorting. I implemented electric fields at the droplet production nozzle and first demonstrated that electric fields may be used as a way to induce the jetting regime. Next, I used amplitude modulated electric fields to impose external perturbations on a hydrodynamic jet. The variation in electric field caused systematic variations in Maxwell stress which altered the breakup dynamics of the jet. I was able to increase the monodispersity of the droplets produced in the jetting regime and to select the frequency of production to a certain extent. This method could increase the overall throughput of production of monodisperse droplets which is usually limited to the dripping regime. However, more formulations should be tested including oils with surfactant to make this a robust tool.

I investigated the phenomenon of electrocoalescence on a microfluidic device. By varying the surfactant concentration and the properties of the oil in the system and, I found that the voltage required for electrocoalescence depends on the frequency of the electric field. For 'low' frequencies the voltage over the liquid film was not sufficient due to electric loss in the system. Changing the properties of the oil caused a shift in frequency dependence. This shift was linked to the change in electric resistivity of the oil by a minimal electric model. To the best of our knowledge this was the first study systematically varying the properties of the formulations in the system. I implemented electric fields for sorting of cells in droplets in a completely integrated device. The device consisted of droplet production, incubation and sorting. I demonstrated the operation of the device at a throughput of 700 Hz. Nevertheless, the throughput could be increased in the future by implementing novel designs for the sorting junction. In future experiments this system would allow to screen libraries of glucose oxidase variants.

In a final study I made use of coacervates in droplets. The aim of this study was two-fold.

First, I used droplet microfluidics as a tool for the analysis of enzyme kinetics in the presence of a coacervate. This proof-of-principle allowed to extract kinetic parameters and could help to shed light on the function of biomolecular condensates in cells. For this, more biologically relevant reactions and coacervate systems should be studied. Secondly, I used coacervates as a tool for droplet microfluidics. I demonstrated that by the sequestration of the product in the coacervate the limit-of-detection in the system was decreased. The improvement in limit-of-detection is highly dependent on the partitioning of the product. To further improve the use of coacervates for a better limit-of-detection different coacervate matrices should be studied to be able to predict the sequestration of the molecules.

Despite its promising outlook, the utilization of high-throughput screening with droplets is still in its industrial infancy as the microfluidic workflow for screening and sorting droplets requires specialized experimental setups. The method nowadays relies on a lot of in-house built devices (chips, set-ups, formulations, software) and microfluidic experimentation requires experience and patience. It is undoubtedly important to advance the technical features of droplet microfluidics. To this extent, several microfluidic companies have focused on the development of automated microfluidic equipment for high-throughput screening in the recent years. With these advances the technology may find its way into labs. In this thesis, the focus has been on the technological development and improvement of microfluidic capabilities, but I believe with collaborations between engineers, physicists, biologists, and chemists the true potential of droplet microfluidics will further be unveiled.

Coalescence des gouttelettes dans les champs électriques

L'électrocoalescence est une méthode utilisée pour la fusion de gouttelettes stabilisées par un tensioactif. Bien qu'il soit largement utilisé pour modifier la teneur en gouttelettes, il manque encore une analyse expérimentale quantitative de l'effet des propriétés électriques du système sur le phénomène.

Dans ce projet, je présente une analyse expérimentale de l'efficacité de la fusion de gouttelettes dans des champs électriques pour diverses formulations. Nous constatons que l'efficacité de la fusion dépend de la fréquence du champ électrique appliqué. À basse fréquence, une tension plus élevée est nécessaire en raison de la perte électrique dans le système. La perte électrique est modifiée en changeant la formulation de la phase huileuse.

En remettant à l'échelle les données, et en les validant par un modèle électrique simplifié, nous constatons que la résistivité de l'huile -paramètre généralement négligé car l'huile est supposée être un diélectrique parfait -est le paramètre reliant la formulation de l'huile à la (ii) Les coacervats sont utilisés dans les gouttelettes comme outil pour améliorer la limite de détection dans le système pour la concentration du substrat, de l'enzyme et du produit.

Principalement en raison de la séquestration du produit, nous observons une amélioration de la limite de détection pour toutes les expériences. Pour utiliser les coacervats comme outil pour les gouttelettes, il est nécessaire d'effectuer plus de recherches sur la séquestration des molécules dans les coacervats pour pouvoir prédire quelles molécules se partitionneront fortement et ainsi pouvoir concevoir des systèmes de coacervats pour des applications spécifiques.

Conclusion et perspectives

Dans cette thèse, j'ai exploré et développé des outils de manipulation de gouttelettes à haut débit. Dans un premier temps, nous nous sommes concentrés sur la mise en oeuvre de champs électriques car ils offrent un contrôle externe pour manipuler les gouttelettes avec une grande précision et un temps de réponse rapide. J'ai ciblé les étapes de manipulation essentielles en microfluidique des gouttelettes : (i) la production de gouttelettes, (ii) la coalescence des gouttelettes et (iii) le tri des gouttelettes.

J'ai mis en place des champs électriques au niveau de la buse de production de gouttelettes pour augmenter la monodispersité des gouttelettes produites dans le régime de jet.

Cette méthode pourrait augmenter le débit global de production de gouttelettes monodisperses qui est généralement limité au régime de goutte à goutte. Cependant, davantage de formulations devraient être testées, y compris des huiles avec tensioactif pour en faire un outil robuste. vacuum pump the PDMS is cured overnight at 70°C. Afterwards, the replica is peeled off from the master and holes for the inlets and outlets are made using a biopsy puncher.

Channel sealing

The PDMS microchannels are sealed by bonding it to a glass substrate upon exposure to air plasma (Diener electronic, Pico). The air plasma introduces silonal groups on the surface of the PDMS which condensate with the functional groups of alochol, carboxylic acid or ketone on the substrate when brought into contact [START_REF] Mcdonald | Fabrication of microfluidic systems in poly (dimethylsiloxane)[END_REF]. This method is able to withstand a pressure up to 2-3 bar. Moreover, the high elasticity of PDMS ensure tight sealing and avoids leakage [START_REF] Mcdonald | Fabrication of microfluidic systems in poly (dimethylsiloxane)[END_REF].

Electrodes

If electrodes are required, the PDMS slab is bound to the non-conducting side of an Indium Tin Oxide (ITO) coated glass substrate (Corning). The ITO coating serves as a counter electrode, ensuring a local controlled electric field. To manufacture the electrodes, the chip is heated to 120°C and the electrode channels are filled with low temperature melting solder (Indium Corp.). Electric wires are placed in both inlets of the electrode channels to ensure electric connection. The wires are strengthened by UV-curable glue. Manufactured electrodes with connections can be seen in figure A.4.

Surface chemistry

As a result of the wetting properties of water and glass, a surface treatment is required for the microfluidic chips to avoid wetting of aqueous droplets on the glass substrate. The channels are made fluorophilic by flushing the channels with Aquapel (PPG Industries) before use.

Microfluidic setup for fluorescence measurements

For fluorescence measurements of the droplets, the setup in

  Paul Pascal -UMR 5031 115, Avenue du Dr Albert Schweitzer, 33600 Pessac, France i Titre: Développement d'outils microfluidiques à base de gouttelettes pour le criblage à haut débit Mots clés: Microfluidique en goutte -champs électriques -haut débit -coacervats

2. 4 . 3

 43 Droplet incubation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2. 4 . 4 19 2. 5

 44195 Droplet analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4.5 Droplet sorting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Life science applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Figure 2 . 1 :

 21 Figure 2.1: The coalescence of two spheres reduces the total surface area in the system.

Figure 2 . 2 :

 22 Figure 2.2: Typical surfactant for droplet-based microfluidics. The surfactant molecule is a tri-block copolymer with a hydrophilic head group and two hydrophobic tails. The surfactant is present in the oil phase because the fluorinated tails result in a very low solubility of the molecule in the aqueous phase. This property minimizes interference of the surfactant with biochemical reactions inside the droplet.

Figure 2 . 3 :

 23 Figure 2.3: Streaming flow generated in a droplet. Malsch et al. performed microparticle imaging velocimetry (µPIV) to characterize two-phase flows in microchannels. Internal flows are induced in a droplet due to boundary conditions at the interface. (A) In a linear microchannel this results in an axial symmetric flow field. (B) A curved microchannel results in the superposition of the internal flow with a circular flow field which enables efficient mixing. Reprinted from [24].

Figure 2 . 4 :

 24 Figure 2.4: Effect of a uniform and nonuniform electric field on a droplet. We consider ε r,oil < ε r,drop . (A) No field. (B) Homogeneous field: the droplet is stretched along the direction of the electric field. (C) Heterogeneous field: the droplet migrates toward the direction of the highest field intensity.

13 2. 4

 134 Droplet modules

Figure 2 . 5 :

 25 Figure 2.5: Methods for the manipulation of the content of surfactant-stabilized droplets with the use of electric fields. The red electrode is active and the black electrode is grounded. (A) Electrocoalescence of a droplet pair. (B) Picoinjection of a small volume into a droplet.

AhnFigure 2 . 6 :

 26 Figure 2.6:The evolution of dielectrophoretic droplet sorting. Adapted from[START_REF] Schütz | Rational design of a high-throughput droplet sorter[END_REF].

  testing and research. It is used for the identification of infectious agents, e.g. for the detection of COVID-19 in recent years. The method consists of two steps: (i) by increasing the temperature, the DNA strands are separated; (ii) primers bind to the target region, and an enzyme, DNA polymerase, synthesizes the complementary DNA strand. This cycle is repeated several times which results in an exponential amplification of the target gene, as the newly synthesized strand serves as a template in the next cycle. To quantify the amount of target DNA in a sample one uses qPCR which relies on fluorescent dyes or fluorescent labeling of the specific sequences. The fluorescence intensity is related to the initial DNA concentration by the use of a standard curve.

Figure 2 . 8 :

 28 Figure 2.8: Droplet-based microfluidics serves as a high-throughput method for the analysis of variants in directed evolution which increases the likelihood of discovering new improved variants. Reprinted from [81].

Figure 2 . 9 : 3 Droplet production in electric fields Contents 3 . 1

 29331 Figure 2.9: Workflow for directed evolution in droplets. (A) The gene of interest is identified and (B) a library is created. (C) The library is transformed into a host cell which produces the enzyme. (D) The cells are encapsulated with the assay. (E-F) Droplets are incubated on-chip and the enzyme yields a fluorescent product. The amount of product is related to the activity of the mutant. (G) The active variants are actively sorted and collected. Reprinted from [58].

3. 3 3 . 4 3 . 5

 33435 Dripping-to-jetting transition in electric fields . . . . . . . . . . . . . . . Rectifying jet breakup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Effect of modulation amplitude and baseline . . . . . . . . . . . . . . 3.4.2 Effect of modulation frequency . . . . . . . . . . . . . . . . . . . . . Conclusion & perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . In this chapter we describe the implementation of electric fields for production of monodisperse droplets. We first introduce the different flow regimes and limitations of them for droplet production. The main part of the experimental data and exerts of the text on which this chapter is based on Paper III: Rectifying jet breakup by electric forcing.

Utada

  et al., who used glass capillaries in a co-flow configuration[START_REF] Utada | Dripping to jetting transitions in coflowing liquid streams[END_REF]. The phase diagram of their system is shown in Figure3.1. The dripping-to-jetting transition in this system is characterized by two dimensionless numbers: (i) the Capillary number of the outer fluid C out , which describes the relative magnitude of the viscous shear stress of the outer fluid on the interface compared to the surface tension (C out = ηu/γ); (ii) the Weber number of the inner fluid W in , which describes the relative magnitude of the inertial force of the inner phase to the surface tension (W in = ρdu 2 /γ). The transition occurs when either of these numbers passes a threshold value (C out 1 or W in 1). In other words, it occurs when either the viscous stress on the interface of the outer fluid, or the inertial force of the inner fluid gain importance over the surface tension.

Figure 3 . 1 :

 31 Figure 3.1: Dripping-to-jetting transition. (A) Dripping: the droplet pinches off close to the nozzle. (B-C) Jetting: droplet production happens further downstream from the nozzle. Open symbols: jetting; Closed symbols: dripping. The transition from dripping to jetting occurs when either W in or C out passes a threshold value. (B) A slender jet is formed when the outer flow is increased. (C) A widening jet is formed when the inner flow is increased. Reprinted from [83].

Figure 3 . 2 :

 32 Figure 3.2: Micrograph of the flow focusing junction with a schematic of the electrode connections. The dark regions on the micrograph are the electrodes. The upstream electrodes can be actuated by a frequency generator while the downstream electrodes are grounded. The scale bar is 100 µm.

Figure A. 6

 6 shows a detailed schematic of the optical set-up.

  is performed. The measurements are corrected with an open and closed circuit measurement to account for the impedance of the equipment. The viscosity of the fluids is measured with a rotational rheometer (Discovery HR-2 rheometer) with a cone (diameter: 40 mm; turnication: 55 µm; angle: 1 deg 59 min 10 sec) at 20°C. The shear rate during the measurements was stepwise increased from 1 to 100 s -1 . The properties of the formulations are summarized in Table 3.1.

Figure 3 . 3 :

 33 Figure 3.3: Details of the microfluidic device. (A) CAD design: (1) Inlet of the aqueous phase; (2) Inlet of the oil phase; (3) Electrodes which are manufactured symmetrically around the nozzle. Scale bar is 1 mm. (B) Profile of the flow focusing junction of the photoresist mold. Scale bar is 100 µm.

  950 µL/h (C o = 0.14; R o = 0.21; W o = 0.03) consistent with the dripping-to-jetting transition in capillaries. The transition threshold is then measured for different applied voltages U 0 . The threshold Q o decreases with increasing voltages. No dripping is observed for voltages above 220 V. In Figure 3.4A the phase diagram of our system is shown as a function of B e and C o (B e = ε 0 ε r U 2 0 /r; C o = ηu/γ 0 ). The dripping-to-jetting transition occurs when one of the two numbers becomes larger than a threshold: C o 0.14 or B e 0.20. Interestingly here, one can notice the analogy in the flow diagram with the inertial case (Figure 3.1). Yet, electric fields provide an orthogonal means to control the dripping-to-jetting transition keeping fixed hydrodynamic conditions.

Figure 3 . 4 :

 34 Figure 3.4: Dripping-to-jetting transition at the flow focusing junction rescaled to the dimensionless capillary number C o and electric bond number B e . (A) Nozzle size of 50 x 50 x 34 µm. (B) Nozzle size of 100 x 100 x 68 µm.

  droplets over large populations we use a method based on fluorescence. A 473 nm laser spot is focused in the center of the channel downstream of the nozzle and 200 µM of fluorescein is added to the aqueous phase. A photomultiplier tube (PMT) converts the emitted light from the fluorescent drops to a recorded electric signal s(t). Each droplet appears as a peak in the time series s(t). The frequency of the signal directly relates to the monodispersity of the droplet production. We compare the droplet formation in the dripping regime (Q o = 600 µL/h, Figure3.5A) and the hydrodynamic jetting regime (Q o = 1200 µL/h, Figure 3.5B) in the absence of electric field. Figures 3.5E and F show the signal acquired by the PMT for ∼ 80 consecutive droplets in both regimes. Figures 3.5I, J show the amplitude of the Fast Fourier Transform (FFT) of a five second recording of the PMT signals (∼ 4 • 10 4 droplets)F(f ) = |FFT[s(t)]|.In the dripping regime the PMT signal is very homogeneous which results in one peak in the frequency spectrum F(f ) (Figure3.5E, I). We recover here that the droplet

  Figures 3.5C, G and K show the corresponding micrograph, PMT signal and frequency spectrum.

Figure 3 .Figure 3 . 6 :

 336 Figure 3.7 presents the evolution of a 0 and a p for the amplitude sweep. a 0 decreases while a p increases with A pert .This experiment is repeated with additional baseline voltages up to 500 V to investigate the effect of a baseline voltage on the jet breakup (Figure3.6 and 3.7). A faster increase of

Figure 3 . 7 :

 37 Figure 3.7: Deconvolution of the Fourier transform into (A) a background signal a 0 and (B) a peak signal a p following Equation 3.1.

Figure 3 . 8 :

 38 Figure 3.8:Fitting of a Gaussian distribution to the histogram of peak widths for A pert = 0 V, A pert = 150 V, and A pert = 300 V with fitting parameters σ and µ using the least-squares method. The red line is the fitted Gaussian distribution.

Figure 3 . 9 :

 39 Figure 3.9: Gaussian fit to the histogram of peak widths. (A) Normalized standard deviation σ 0 /σ. (B) Mean µ. Error bars represent the standard deviation (N = 3).

Figure 3 . 10 :

 310 Figure 3.10: Fourier transform of one sweep of f pert with baseline 0 V and 200 V and A pert = 200 V. The grayscale corresponds to the amplitude of the Fourier transform.

Figure 3 . 11 :

 311 Figure 3.11: Deconvolution of the Fourier transform into a background signal a 0 (open symbols) and a peak signal a p (closed symbols) for A pert = 200 V. Yellow: baseline = 0 V; green: baseline = 200 V.

Figure 3 . 12 :

 312 Figure 3.12: Gaussian fit to the histogram of peak widths. (A) Normalized standard deviation σ 0 /σ. (B) Mean µ. Yellow: baseline = 0 V; green: baseline = 200 V. Error bars show the standard deviation (N = 3)

Figure 3 .Figure 3 . 13 :

 3313 Figure 3.12B, where we see a steady decrease of µ between 7 kHz and 9 kHz. Altogether, this suggests that we can control the droplet size to a certain extent without changing flow properties.

4 Droplet coalescence in electric fields Contents 4 . 1 49 4. 4 51 4. 5

 441494515 Electrocoalescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.2 Materials & methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2.1 System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2.2 Fluid properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.3 Experiments: electrocoalescence as a function of fluid properties . . . . 47 4.3.1 Surfactant concentration . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.3.2 Continuous phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.3.3 Droplet resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.3.4 Data rescaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Minimal electrical model . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Figure 4 . 1 :

 41 Figure 4.1: Electrocoalescence of two aqueous droplets under influence of an AC electric field.Reprinted from[START_REF] Chabert | Droplet fusion by alternating current (ac) field electrocoalescence in microchannels[END_REF].

Figure 4 . 2 :

 42 Figure 4.2: Sketch of the microfluidic system. An array of droplet traps is loaded and unloaded by the use of a pressure driven system. The electric field is applied by the use of a signal generator and a high voltage amplifier to one of the electrodes while the other one is grounded. Scale bar is 200 µm.

Figure 4 . 3 :

 43 Figure 4.3: Calibration of output voltage of the high voltage amplifier for different frequencies of the electric field.

Figure 4 . 4 :

 44 Figure 4.4: Pendant droplet tensiometry. (A) Mixtures of FC 40 and HFE 7500 at 5% w/w surfactant concentration. (B) HFE 7500 at 0.1, 1 and 5% w/w surfactant concentration.

Figure 4 . 5 :

 45 Figure 4.5: Electrical properties of the continuous phase. (A-B) The electric resistivity and relative permittivity of HFE 7500 as a function of surfactant concentration. The solid and dotted lines represent the average and standard deviation of the measurement without surfactant. (C-D) The electric resistivity and relative permittivity of mixtures of FC 40 and HFE 7500 at a surfactant concentration of 5% w/w. Error bars represent the standard deviation (N = 3).

Figure 4 . 6 :

 46 Figure 4.6: (A) Micrographs of a section of the droplet trapping array for 0 V, 340 V and 380 V of applied voltage at a frequency of 10 kHz. Scale bar is 200 µm. (B) Fraction of merged droplet pairs as a function of the applied voltage U applied for different frequencies of the electric field. The continuous phase is HFE 7500 with 5% w/w surfactant while the dispersed phase is millipore water (N=3).

Figure 4 . 7 :

 47 Figure 4.7: Effect of surfactant concentration on electrocoalescence. Threshold voltage U * applied for droplet merging as a function of the frequency f of the electric field when varying the surfactant concentration. The oil phase is HFE 7500 and the aqueous phase is millipore water.

Figure 4 . 8 :

 48 Figure 4.8: Effect of oil formulation on electrocoalescence. Threshold voltage U * applied as a function of the frequency f of the electric field for several mixtures of FC 40 : HFE 7500. The surfactant concentration is 5% w/w and the aqueous phase is millipore water.

Figure 4 . 9 :

 49 Figure 4.9: Effect of aqueous phase resistivity ρ e,drop on electrocoalescence. Threshold voltage U * applied as a function of the frequency f of the electric field when varying the concentration of NaCl in the aqueous phase. The experiments are performed for FC 40 and HFE 7500 at a surfactant concentration of 5% w/w.

FC 40 - 4 Figure 4 . 10 :

 404410 Figure 4.10: Rescaling of experimental data with f 0 . (A) U * applied as a function of the rescaled frequency f /f 0 . (B-C) The rescaling factor f 0 as a function of the relative permittivity ε r and the resistivity ρ e of the continuous phase.

Figure 4 . 11 :

 411 Figure 4.11: Equivalent electrical circuit of one trapped droplet pair.

Figure 4 . 12 :

 412 Figure 4.12: Minimal electrical model. (A) Calculation of U f ilm /U applied with the experimentally measured parameters and geometrical estimations. (B) U f ilm /U applied rescaled with f 0,model . The data collapses for f 0,model ∼ ρ -1 e . (C) Rescaling factor for the model f 0,model as a function of ρ e .

Contents 5 . 1 60 5. 3 62 5. 3 . 1 64 5. 4

 516036231644 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.2 Materials & methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.2.1 System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.2.2 Biological workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.2.3 Microfluidic devices . . . . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Biochemical assays in droplets . . . . . . . . . . . . . . . . . . . . . . 62 5.3.2 Microfluidic kinetic analysis . . . . . . . . . . . . . . . . . . . . . . . 63 5.3.3 Integrated droplet sorting of GOx . . . . . . . . . . . . . . . . . . . . Conclusion & perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Figure 5 . 1 :

 51 Figure 5.1: Biochemical assay for the detection of GOx activity.

Figure 5 .

 5 3 allows high-throughput co-encapsulation of cells and substrate, on-chip incubation of ∼ 10 min and fluorescent-activated sorting of droplets by the use of electric fields. Droplets are produced with a co-flow flow focusing junction which allows to co-encapsulate a cell suspension and assay mix in droplets. Excess oil is extracted after droplet production to pack the droplets in the incubation line. Droplets are spaced at the end of the incubation line before sorting by 2 oil flows. By default droplets flow in the outlet with the lowest hydrodynamic resistance (negative outlet). Hits in the screening process are detected by a fluorescence measurement at the sorting junction which triggers a pulse at the sorting electrode deflecting the drop towards the positive outlet due to dielectrophoresis. The width of the flow focusing junction is 20 µm. The channel height of the the flow focusing and sorting junction is 23 µm and of the incubation lines is 70 µm.

Figure 5 . 3 :

 53 Figure 5.3: Microfluidic device for sorting of droplets based on fluorescence. Oil is extracted after droplet production to pack the droplets in the incubation line. Before the sorting junction droplets are spaced by oil. Droplets can be deflected by a sorting electrode towards the positive outlet. Scale bar is 200 µm.

Figure 5 . 4 :

 54 Figure 5.4: Observation of droplets containing cells and assay mix in a microfluidic chamber. (Left) Brightfield image of the droplets. The encircled droplets contain a cell. (Right) An epifluorescent image of the same area (λ exc = 550 nm). Scale bar is 50 µm.

Figure 5 . 5 :

 55 Figure 5.5: Scatter plot of resorufin and barcode fluorescence at 0 min, 1 min, 5 min, 9 min, and 13 min of incubation. PMT 1 measures the fluorescence of the barcode dye and PMT 3 the fluorescence of resorufin. The gain of PMT 1 is set to 0.5 and the gain of PMT3 is set to 0.4.

Figure 5 . 6 :

 56 Figure 5.6: Fluorescence of yeast cells expressed with wild type GOx. (A) Fluorescent scatter plot of PMT 1 vs PMT 3. PMT 1 measures the fluorescence of the barcode dye and PMT 3 the fluorescence of resorufin. (B) Histogram plot of resorufin fluroescence. Gains of the PMTs were set to 0.4 V for PMT 1 and 0.45 V for PMT 3.

Figure 5 .

 5 Figure 5.7 shows a time sequence of the recorded PMT signals during the sorting process.

Figure 5 .

 5 Figure 5.7A gives the fluorescence of the barcode dye, which is equal for all the droplets, while Figure 5.7B gives the fluorescence of the product of the assay in the drops. In this time

Figure 5 . 7 :

 57 Figure 5.7: Time sequences of the PMT signals during the sorting process. (A) Barcode fluorescence (PMT1). (B) Resorufin fluorescence (PMT3). (C) Generated electric pulse for droplet sorting.

Figure 6 . 1 :

 61 Figure 6.1: Examples of biomolecular condensates in cells. Reprinted from [119].

Figure 6 . 2 :

 62 Figure 6.2: Thermodynamic driving force for LLPS. (A) LLPS when a binary mixtures minimizes its free energy by demixing into two phases. (B)The free energy in the system is dependent on the temperature which gives rise to a phase diagram under which phase separation occurs. (C) In a binary mixture the system spontaneously demixes into a dense and a diluted phase. Reprinted from[START_REF] Shin | Liquid phase condensation in cell physiology and disease[END_REF].

Figure 6 . 3 :

 63 Figure 6.3: Functions of biomolecular condensates in cells. (Left) Condensates may enhance reates of biomolecular reactions by increasing local concentrations. (Right) By selective sequestration the condensate can serve as storage compartment to inhibit the activity. (Bottom) Condensates may serve as organizational structure. Reprinted from [120].

Figure 6 . 4 :

 64 Figure 6.4: Droplet microfluidics for the synthesis of coacervates. The components of the coacervates are co-flowed and encapsulated in a droplet. LLPS happens fast in the droplet and results in monodisperse coacervates. Scale bar is 30 µm. Reprinted from [141].

Figure 6 . 5 :

 65 Figure 6.5: Selected biochemical assays. (A) Enzyme-driven assays tested in droplet microfluidics. (B) Micrographs of coacervation in bulk with CMdex/PDDA coacervates. The epifluorescent images show the fluorescence of fluorescein and resorufin.

Figure 6 . 6 :

 66 Figure 6.6: β-galactosidase partition coefficient. (A) β-gal kinetics in depleted phase to make a standard curve for the initial slope with known β-gal concentration. (B) Enzymatic activity of the depleted phase after phase partitioning at a starting enzyme concentration of 2.5 and 5 U/ml. Error bars represent the standard deviation (N = 3). (C) The concentration of β-gal in the depleted phase after phase partitioning is determined by linear interpolation.

Figure 6 . 7 :

 67 Figure 6.7: Coacervate production and analysis. (A) Coacervate formation in droplets by coencapsulation of oppositely charged polyelectrolytes. The nozzle size is 30 µm. (B) Droplets with coacervate are reinjected in a device where they are spaced by oil and individually measured at a local constriction in the channel. The reinjection channel has a width of 30 µm and the constriction a width of 10 µm. Scale bar is 100 µm.

3 Figure 6 . 8 :

 368 Figure 6.8: Microfluidic device to produce a 10-bit emulsion. (A) CAD design of the microfluidic chip used for emulsion production. The nozzle size has a width of 30 µm. (B) Programmed dilution scheme for the substrate inlets. The flow rate of the 4 inlets is stepwise changed to produce 10 populations while the total flow rate of the 4 inlets remains constant at 150 µl/h. (C) Fluorescence measurement at the droplet production nozzle during the dilution scheme. Barcode dye fluorescence relates directly with the concentration of substrate.

Figure 6 . 9 :

 69 Figure 6.9: Microfluidic device for kinetic analysis. 1. Two 10-bit emulsions are reinjected in the kinetics device. 2. After reinjection the enzyme is picoinjected. Oil is extracted and the droplets are packed together before the incubation line. 3. Measurement points along the incubation line for a fluorescent readout. Scale bar is 100 µm.

  Figure A.6. Data processing of the fluorescent signal is performed with Matlab R2020a and Origin 2020.

Figure 6 . 10 :

 610 Figure 6.10: Calibration for fluorescein and resorufin concentration in droplets and bulk.

37. 5

 5 µl/h) are co-flowed to produce droplets at a rate of 1.35 kHz. Droplets are collected in an observation chamber and the volume of the droplet and coacervate are determined by image processing of Figure 6.11A. The histogram of the resulting coacervate and droplet volume can be found in Figure 6.11B. The droplet volume is 40.9 ± 0.5 pl (CV = 0.8%) and the coacervate volume is 1.39 ± 0.06 pl (CV = 4.0%).

Figure 6 . 11 :

 611 Figure 6.11: Determining the coacervate and droplet volume. (A) Micrograph of droplets containing CMdex/PDDA coacervates for image processing. Scale bar is 100 µm. (B) Histogram of coacervate and droplet volume (N = 164).

Two inlets are used for the polyelectrolytes ( 1 MFigure 6 . 12 :

 1612 Figure 6.12: Workflow for analyzing β-gal partitioning in droplets. 1. Droplets are produced by a microfluidic device with three aqueous inlets. 2. The emulsion is reinjected in the kinetics device and picoinjected with FITC-β-gal. 3. Droplet fluorescence is recorded at several measurement points.

Figure 6 . 13 :

 613 Figure 6.13: β-gal partitioning in CMdex/PDDA coacervates. F coacervate /F depleted represents the partitioning coefficient as a function of time. The partitioning was tested for two concentrations: 1.14 µM (orange) and 11.4 µM (blue). The error bars represent the standard deviation.

Figure 6 . 14 :

 614 Figure 6.14: Fluorescein partitioning in CMdex/PDDA coacervates as a function of fluorescein concentration.

Figure 6 . 15 :

 615 Figure 6.15: Microfluidic platform for multiplexed analysis of enzyme kinetics in droplets with coacervates. (A) Droplet production: two 10-bit emulsions are produced by a programmed dilution scheme. (B) Reaction activation: the reaction is started by picoinjection of the enzyme in the droplet. (C) Fluorescent readout: droplets are incubated on-chip in serpentine incubation lines after picoinjection. Constrictions along the incubation line serve as measurement points for fluorescent measurements with a laser line. (D) Fluorescence measurement: fluorescence at several time points for a droplet with and without coacervate of the same starting concentration of substrate. Scalebar is 100 µm.

3 . 3

 33 to analyze the kinetics of β-gal for two reactions in CMdex/PDDA coacervates: (i) FDG → fluorescein; (ii) RBG → resorufin. FDG → fluorescein β-gal hydrolyzes fluorescein di-β-D-galactopyranoside (FDG) into fluorescein. The coacervate sequesters the components of the enzymatic reaction. Most of β-gal is partitioned in the coacervate making the coacervate a reaction chamber (Figure 6.16A). The barcode dye used for distinguishing the different populations is sulforhodamine. The FDG concentration in the drops ranges from 19.7 to 142.4 µM, and the concentration of β-gal is 2.0 U/ml.

Figure

Figure 6 . 16 :Figure 6 . 17 :Figure 6 . 18 :

 616617618 Figure 6.16: Kinetics of compartmentalized reactions in droplets with and without phase separation. (A) Sketch of sequestered reaction in droplets with and without phase separation. (B) 2D histograms of fluorescein fluorescence and barcode fluorescence (sulforhodamine B) at different incubation times (1.3 min, 8.0 min and 24.8 min). 2D fluorescence histograms are plotted for droplets without coacervate (top) the depleted phase fluorescence (mid) and the coacervate phase fluorescence (bottom). (C) Fluorescein concentration versus time for two droplet populations. Reactions are performed in sodium phosphate buffer (60 mM, pH 7.0).

Figure 6 . 19 :

 619 Figure 6.19: Extraction of initial reaction velocity v. A linear fit is performed to the first three data points of the kinetic data in Figure 6.17 and 6.18. (A-B) For the reaction FDG → fluorescein. (A) No coacervate present. (B) A coacervate present in the droplet. (C-D) For the reaction RBG → resorufin. (C) No coacervate present. (D) A coacervate present in the droplet.

Figure 6 . 22 :

 622 Figure 6.22: Signal-to-noise ratio as a function of fluorescein concentration for the coacervate phase (orange), depleted phase (yellow), and control emulsion (blue). The inset presents the data with a logarithmic y-axis. Error bars represent the standard deviation.

Figure 6 . 23 :

 623 Figure 6.23: Signal-to-noise ratio as a function of FDG and β-gal concentration for the coacervate phase (orange) depleted phase (yellow) and control emulsion (blue). SNR is determined after 1 min, 5 min and 14 min of reaction. β-gal is 2.0 U/ml for SNR as a function of FDG. FDG is 65 µM for SNR as a function of β-gal. The inset presents the data with a logarithmic y-axis. Error bars represent the standard deviation.

  Au cours des deux dernières décennies, la microfluidique des gouttelettes est devenue une technologie qui pourrait combler les lacunes des méthodes traditionnelles d'analyse cellulaire. Il s'agit d'une technologie dans laquelle de petites gouttelettes d'un fluide (généralement de l'eau) sont manipulées dans un autre fluide non miscible (généralement de l'huile). La technologie est intéressante pour les études sur une seule cellule car les cellules individuelles peuvent être encapsulées dans des gouttelettes, et les gouttelettes servent de récipients de réaction pour l'analyse. Il est possible de produire des gouttelettes dans la gamme de volumes de picolitres à un débit élevé (kHz), ce qui réduit les coûts des réactifs et augmente le débit d'analyse. Cependant la manipulation précise des volumes en picolitres n'est pas triviale. Une variété de méthodes pour produire et manipuler des gouttelettes sont essentielles pour répondre aux diverses exigences des différents tests biochimiques pour les études sur une seule cellule. Le développement de méthodes nouvelles et améliorées est nécessaire pour faire progresser l'intégration et l'automatisation de la microfluidique des gouttelettes en laboratoire. Pour permettre la mise en oeuvre complète de la microfluidique des gouttelettes dans la recherche biomédicale, une variété d'outils microfluidiques est nécessaire pour traduire les processus de laboratoire standard en outils microfluidiques avec des capacités à haut débit. L'objectif de ce projet de doctorat, qui se déroule au sein du réseau de formation européen EVOdrops, est de développer de nouveaux outils pour la microfluidique des gouttelettes. L'objectif général du réseau EVOdrops est de rassembler des partenaires pour la mise en oeuvre de la microfluidique en gouttelettes pour l'évolution dirigée de biomolécules. Dans ce projet de doctorat, nous nous concentrons sur le développement technologique des méthodes microfluidiques. Nous ciblons l'utilisation de champs électriques externes car ils offrent un haut degré de capacités de contrôle et d'automatisation. A côté de cela, les méthodes microfluidiques existantes sont appliquées et adaptées pour l'étude des systèmes biologiques dans le cadre d'EVOdrops.Production de gouttelettes dans les champs électriquesLa production d'une goutte est le premier module essentiel de la microfluidique des gouttes.Les propriétés essentielles du module sont que les gouttelettes produites sont de taille uniforme et que la méthode est reproductible. Selon les propriétés du fluide et les paramètres d'écoulement, différents régimes d'écoulement existent. Les deux régimes d'écoulement qui se produisent à des débits modérés sont le goutte à goutte et le jet. Il existe une différence entre les régimes d'écoulement et cela a des implications sur la fiabilité de la production de gouttelettes. Les gouttelettes se forment périodiquement à proximité de la jonction, ce qui donne une taille de gouttelette uniforme. À des vitesses d'écoulement plus élevées, un jet se forme qui finit par se briser en gouttelettes en aval de la buse en raison de l'instabilité de Plateau-Rayleigh. Par conséquent, les débits et donc le taux de production d'une émulsion monodispersée sont limités par le début du régime de jet.Dans le premier projet, j'ai étudié la possibilité de modifier la dynamique de rupture d'un jet hydrodynamique dans une jonction focalisant l'écoulement par des champs électriques pour augmenter la monodispersité. Nous avons contrôlé des champs électriques autour de la jonction de focalisation du flux et appliqué un champ électrique à l'électrode en amont tandis que l'électrode en aval était mise à la terre. Nous avons d'abord observé que le début du régime de jet est affecté par le champ électrique. Cela n'a pas modifié la dynamique de rupture de manière significative. Nous avons ensuite modulé l'amplitude du champ électrique, ce qui a permis de redresser le jet, c'est-à-dire qu'il s'est établi une corrélation entre la fréquence de modulation et la fréquence de rupture du jet. Nous avons en outre utilisé les paramètres du champ électrique, pour comprendre l'instabilité du jet. En ajustant les paramètres électriques, nous avons pu augmenter la monodispersité de la population de gouttes produites par le jet.Nous pensons que cette approche est intéressante pour les applications nécessitant un haut débit et une fiabilité en production.

  température observée. dépendance en fréquence. De plus, nous constatons qu'une conductivité accrue des gouttelettes facilite l'électrocoalescence. Cette découverte peut entraîner une optimisation des champs électriques qui pourrait éviter les effets néfastes sur le contenu biologique encapsulé dans les gouttelettes et fournir des informations pour l'optimisation des formulations. Process microfluidique pour l'évolution dirigée de la glucose oxydase Dans ce projet, nous décrivons l'intégration d'un flux de travail microfluidique pour l'évolution dirigée de l'enzyme glucose oxydase. Ce chapitre se concentre sur le développement technologique et l'intégration des outils microfluidiques, y compris le tri des gouttelettes activées par fluorescence. Nous ne nous concentrons pas sur le flux de travail biologique car il sort du cadre de cette thèse. Les expériences biologiques ont été réalisées par Alejandra Gadea, doctorante au sein du consortium EVOdrops. Nous développons un process basé sur la microfluidique des gouttelettes pour l'évolution dirigée de la glucose oxydase (GOx) vers une sensibilité accrue au glucose. GOx est une enzyme qui catalyse l'oxydation du glucose en gluconolactone et en peroxyde d'hydrogène. L'enzyme présente un intérêt particulier pour l'utilisation dans les biocapteurs et les biopiles enzymatiques. Actuellement, l'amplitude de la puissance de sortie et la stabilité des enzymes sont les principales préoccupations pour les applications des biopiles enzymatiques, la puissance de sortie étant limitée par les performances des enzymes. Par conséquent, améliorer l'efficacité catalytique de GOx par évolution dirigée est un objectif important. Nous démontrons d'abord la détection de l'activité GOx dans les gouttelettes. Nous présentons ensuite un flux de travail pour l'évolution dirigée de GOx vers une sensibilité accrue au glucose. Le flux de travail implique l'encapsulation, l'incubation et le tri des cellules intégrés dans un dispositif microfluidique à un débit de 700 Hz. Nous utilisons cette méthode pour mesurer l'activité d'une bibliothèque GOx et le tri ultérieur des résultats positifs. Malheureusement, nous n'avons pu détecter aucune variante active dans la bibliothèque. Néanmoins, la plate-forme est adaptée aux mesures de différentes bibliothèques de GOx à des fins d'évolution dirigée. Gouttelettes pour l'analyse de la cinétique enzymatique dans les coacervats La compartimentation est une caractéristique essentielle pour que la cellule organise son système intérieur complexe très encombré. La compartimentation intracellulaire permet de concentrer les espèces et de maintenir un gradient chimique hors d'équilibre à l'intérieur de la cellule pour provoquer des réactions biochimiques. Une classe intéressante de compartiments que la cellule crée pour organiser les réactions biochimiques sont les organites sans membrane, également appelés condensats biomoléculaires. Ces compartiments ne sont pas liés à la membrane mais sont toujours capables de concentrer localement des espèces biochimiques dans la cellule et sont formés par séparation de phases liquide-liquide (LLPS) créant un compartiment dense et une phase diluée autour. Les solutés peuvent se séquestrer spontanément dans la phase dense ou diluée car ils peuvent se déplacer librement. La séquestration sélective de molécules dans la cellule peut avoir plusieurs effets sur les réactions biochimiques. Étudier et caractériser les condensats biomoléculaires dans les cellules est un défi. Les coacervats complexes, qui sont des systèmes formés par LLPS de deux molécules de charges opposées entraînées par des interactions électrostatiques, ont montré un grand potentiel en tant que système modèle pour les condensats biomoléculaires [132]. Il a été récemment démontré que la synthèse et l'analyse à haut débit des coacervats dans les gouttelettes sont possibles en utilisant des méthodes microfluidiques standard à base de gouttelettes. L'objectif de la recherche présentée dans ce chapitre est double : (i) mettre en oeuvre des méthodes microfluidiques à base de gouttelettes pour l'analyse quantitative systématique de l'effet de la LLPS sur la cinétique enzymatique ; (ii) étudier l'utilisation de coacervats dans les gouttelettes pour améliorer la limite de détection des réactions biochimiques. (i) Nous démontrons un flux de travail microfluidique pour étudier l'effet de la coacervation sur la cinétique enzymatique. Nous avons validé que la partition de l'enzyme se produit rapidement après la picoinjection par rapport à l'échelle de temps de la cinétique de la réaction. Deux réactions enzymatiques en une étape, catalysées par β-galactosidase, ont été analysées dans un coacervat CMdex/PDDA et les paramètres cinétiques ont été extraits. Les coefficients de partage du substrat, de l'enzyme et du produit des réactions ont été déterminés par spectrophotométrie en masse car nous avons démontré que la détermination du coefficient de partage en microfluidique dépend fortement du système de détection. Dans de futures expériences, nous aimerions analyser la cinétique enzymatique dans d'autres systèmes de coacervat et analyser des réactions plus complexes, telles que des réactions en plusieurs étapes ou des réactions avec un cofacteur.

JFigure A. 2 :

 2 Figure A.2: Master production. The measured height of the reticulated layer for various types of photoresist as a function of the rotation velocity of the spin coater.

Figure A. 3 :

 3 Figure A.3: Optical images of the different steps in the microfabrication process. (A) The mask is printed in high resolution and used for the production of the master. (B) The mixture of PDMS and curing agent is poured onto the wafer and cured at 70°C. (C) The microfluidic slab with the channel geometry imprinted in the PDMS after removal from the master. (D) Inlets and outlets are punched and the PDMS is bonded to a glass slide by exposing it to air plasma. The scalebar is 1 cm. Reprinted from [145].

Figure A. 4 :

 4 Figure A.4: Optical image of electrodes which are manufactured for droplet manipulation. The channels which serve for electrodes are filled with solder. Connections are ensured with electrical wires and UV-curable glue.

Figure A. 6 Figure A. 6 :

 66 Figure A.6: Detailed schematic of the optical set-up used for the experiments. Three lasers (375nm with 20 mW, Omicron; 473nm with 250 mW, Cobolt; 532nm with 25 mW, Cobolt Samba) are focused on the microfluidic chip using a set of mirrors (M1 = PF10-03-F01-10, Thorlabs), dichroic mirrors (D1 = F38-M03, AHF; D2 = F38-M01, AHF; D3 = F73-049, AHF), a cylindrical lens and an objective lens (40x, Olympus). The microfluidic chip is placed on an inverted microscope (Olympus, IX73) and visualized with a high-speed camera (v411, Phantom).The emitted fluorescent light is guided through filters (N1 = F40-473, AHF; N2 = F40-532, AHF; B1= F37-580, AHF; B2 = F37-524; B3 = F39-438, AHF) and split using a beamsplitter (S1 = F21-002 80R/20T, AHF) and dichroic mirrors (D4 = F38-458, AHF; D5 = F33-563, AHF) towards three photomultiplier tubes (H9656-20; Hamamatsu). The light is focused onto the photomultiplier tubes and camera by lenses (L1 = 30mm lens; L2 = 100mm lens). The windows of the photomultiplier tubes are: 565-595 nm (PMT1), 497-545 nm (PMT2), and 424-453 nm (PMT3). The electric field of the signal generator was amplified 1000 times by a high-voltage amplifier (623B, Trek).

Table 2 .

 2

	Formulation	Dielectric constant ε r Electric resistivity ρ e
		(-)	Ω/m
	Deioninzed water 80.1	10 5
	PBS	79.0	10 2
	HFE 7500	5.8	10 10
	PDMS	2.3	10 14

1: Electric properties of typical formulations in droplet microfluidics.

Table 2 .2: Reported

 2 methods for droplet analysis with the achieved detection limit and frequency.

	Analysis method	Detection limit Measurement frequency Ref
		µM	Hz
	Fluorescence	10 • 10 -3	2000	[58]
	Absorbance	10 • 10 3	300	[59]
	DDPI	1.4	1000	[60]
	Raman spectroscopy /	260	[62]
	Light scattering	/	243	[61]
	Image processing	/	10	[65]
	Mass spectrometry	30	0.7	[64]
	Electrochemical	100	10	[66]

Table 3 .

 3

	Fuid	Density ρ Viscosity η Dielectric	Surface
				constant ε r tension γ
		kg/m 3	mPa•s		mN/m
	Mineral oil	840	30.7	2.2	-
	Glycerol:Water (2:1) 1173	25.4	63.1	33

1: Material properties of the formulations used in the experiments.

Table 4 . 1 :

 41 Material properties of the fluid mixtures used for electrocoalescence experiments.

	Fluid	[Surfactant] Resistivity	Dielectric	Interfacial
			ρ e	constant ε r	tension γ
		% w/w	10 5 Ω•m		mN/m
	HFE 7500	0.1	17.0 ± 1.0	9.62 ± 0.01	2.7
		1	6.4 ± 0.3	9.62 ± 0.003	3.7
		5	1.9 ± 1.0	9.76 ± 0.26	3.9
	HFE 7500 -FC40 5	9.5 ± 1.0	6.63 ± 0.85	7.0
	(0.5:0.5)
	HFE 7500 -FC40 5	49.0 ± 4.2	4.76 ± 0.001	5.2
	(0.25:0.75)
	FC40	5	463.0 ± 17.1 3.52 ± 0.22	5.3
		[NaCl]
		M	Ω•m
	Water	0	2710	78.43 ± 0.10 [105] -
		4 • 10 -4	117.2	-	-
		2	69.7 • 10 -3	-	-

such that the pendant drop reaches an equilibrium state without detaching. The densities used for calculation of the surface tension are ρ FC 40 = 1.85 g/ml, ρ HFE 7500 = 1.641 g/ml, ρ water = 0.998 g/ml. The surface tension without surfactant present are measured to be 46 mN/m for HFE 7500 and 49 mN/m for FC 40. The interfacial tension measured for oil

6 Droplets for the analysis of enzyme kinetics in coacervates Contents 6.1 Biochemical intracellular organization

. . . . . . . . . . . . . . . . . . . 68 6.1.1 Liquid-liquid phase separation . . . . . . . . . . . . . . . . . . . . . . 68 6.1.2 Cellular function of condensates . . . . . . . . . . . . . . . . . . . . 70 6.1.3 Coacervates as a model system . . . . . . . . . . . . . . . . . . . . . 72 6.2 Materials & methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6.2.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6.2.2 Bulk partition coefficients . . . . . . . . . . . . . . . . . . . . . . . . 75 6.2.3 Microfluidic devices . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.2.4 Set-up & data processing . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.3 Effect of CMdex/PDDA coacervates on enzyme kinetics of β-gal . . . . . 81 6.3.1 Coacervate volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.3.2 β-galactosidase partitioning . . . . . . . . . . . . . . . . . . . . . . . 81 6.3.3 Microfluidic workflow for multiplexed kinetic analysis . . . . . . . . 83 6.3.4 β-galactosidase enzyme kinetics . . . . . . . . . . . . . . . . . . . .

85 6.4 Improved limit-of-detection in droplets . . . . . . . . . . . . . . . . . . . 90 6.5 Conclusion & discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Table 6 . 1 :

 61 Partition coefficients of components of the enzymatic reaction in CMdex/PDDA coacervates.

	Component	K
	β-galactosidase 49.2 ± 15.6
	FDG	1.50 ± 0.05
	Fluorescein	7.22 ± 0.43
	RBG	0.95 ± 0.06
	Resorufin	1.76 ± 0.17

  The presence of a coacervate, and the increased concentration of enzyme in the coacervate, do not accelerate the reaction significantly. When

	A											B
					FDG		uorescein							RBG	resoru n
													0.06
		0.12	Control Coacervate									Control Coacervate
		0.10	Vmax 0.512 ± 0.112					0.05	Vmax 0.128 ± 0.006
				Km	463.5 ± 123.0							Km		195.8 ± 14.4
	v (µM/s)	0.06 0.08					Vmax 0.220 ± 0.004	v (µM/s)	0.04 0.03					Vmax 0.125 ± 0.018 Km 224.1 ± 46.2
		0.04					Km		209.8 ± 5.4
													0.02
		0.02
													0.01
			0	20	40	60	80	100	120	140	160			20	40	60	80	100	120	140	160
							[FDG]										[RBG]
	Figure 6.20: Estimation of kinetic paramaters K M and V max for droplets with coacervates
	(circle, red) and control droplets without coacervates (square, black). (A) FDG → fluorescein.
	(B) RBG → resorufin.
	A											B
					FDG		uorescein							RBG	resoru n
			0.025											0.14
				Control Depleted phase							0.12		Control Depleted phase
	v (µM/s)	0.010 0.015 0.020	Vmax 0.044 ± 0.005 Km 114.7 ± 26.9					v (µM/s)	0.06 0.08 0.10	Vmax 0.197 ± 0.030 Km 35.3 ± 12.4
							Vmax 0.056 ± 0.019			0.04
			0.005				Km	226.0 ± 113.7			0.02					Vmax 0.114 ± 0.017
																			Km	47.6 ± 14.0
			0.000											0.00
				0	20	40	60	80	100	120	140	160			0	10	20	30	40	50	60	70	80
							[FDG] (µM)									[RBG] (µM)

Figure 6.21: Estimation of kinetic paramaters K M and V max in bulk. The kinetic parameters are estimated in depleted phase of the coacervate (circle, red) and in the control condition (CMdex 194 mM) (square, black). (A) FDG → fluorescein. (B) RBG → resorufin.

Table 6 . 2 :

 62 Kinetic parameters in droplets and bulk for β-gal.

	Condition	FDG → fluorescein	RBG → resorufin
		K M (µM)	k cat (s -1 )	K M (µM)	k cat (s -1 )
	Droplet -coacervate	209.8 ± 5.4	110.0 ± 4.0 195.8 ± 14.4 35.6 ± 1.7
	Droplet -control	463.5 ± 123.0 91.4 ± 20.0 224.1 ± 46.2 96.2 ± 5.0
	Bulk -depleted phase 114.7 ± 26.9	22.0 ± 2.5	47.6 ± 14.0	31.7 ± 4.7
	Bulk -control	226.9 ± 113.7 28 ± 8.5	35.3 ± 12.4	54.7 ± 8.3

This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 813786. and the papers are listed.

tem to study because coalescence is a drastic event and prone to be influenced by external instabilities. For example the peculiar observation for FC [START_REF] Eggersdorfer | Wetting controls of droplet formation in step emulsification[END_REF], where we observe an intermediate minimum for U * applied at 10 Hz remains unexplained. Next to that the influence of surfactants in the system was not regarded. In future experiments it would be interesting to perform finite element modeling of the system to give a better view on the resulting voltage over the liquid film between the droplets.

55

A

Realization of devices and experiments for droplet microfluidics

A.1 Fabrication of microfluidic devices

The fabrication process of a microfluidic device can be split up into five steps: (i) master production; (ii) replica molding; (iii) sealing of the channel; if required (iv) the production of electrodes; and (v) surface treatment. The whole workflow is summarized in figure A.1.

Master production

The master is produced by photolithography methods [START_REF] Xia | Soft lithography[END_REF][START_REF] Mcdonald | Fabrication of microfluidic systems in poly (dimethylsiloxane)[END_REF]. First, the desired structure of the device is created using computer-aided design software (AutoCAD 2020) and commercially printed with high resolution on a transparent paper (Selba). The printed design serves as photomask for the photolithography process. The master is produced on a silicon wafer (Si-Mat) using an epoxy-based negative photoresist (SU-8 3000 series, MicroChem).

A layer of photoresist is spincoated on the silicon wafer and placed on a hotplate at 95°C for soft baking. The silicon wafer is subsequently placed on a mask aligner (MJB4, SUSS MicroTech) and covered with the desired photomask. The mask aligner illuminates the wafer with ultraviolet (UV) light. The exposed areas of the wafer reticulate upon UV-exposure, while the areas covered by the photomask do not reticulate. After UV-exposure the wafer is post baked at 95°C for several minutes. Finally, the wafer is developed, i.e. the unexposed photoresist is washed away resulting in a master which can be used for replica molding. The lithographic process can be repeated to create a master with several layers with a various height. Adjusting the rotation velocity of the spincoating process and utilizing photoresists with a different viscosity allows to tune the height. The master is subsequently characterized using a 3D optical microscope (Contour GT, Bruker). In

Replica molding

Once the master is fabricated, it can be used to create microfluidic channels by replica molding. For replica molding, a prepolymer is cast onto the master which creates a negative replica of the master. Polydimethylsiloxane (PDMS) is widely used as polymer for microfluidic channels as it is a cheap, fast, and easy-to-handle substance allowing high resolution microfabrication [START_REF] Xia | Soft lithography[END_REF]. Moreover, as PDMS is transparent to visible light it allows microscopic imaging and further integration of optical methods. Some considerations which need to be taken into account when using PDMS are its elastic properties, the incompatibility of PDMS with some solvents, and the high permeability towards water.

Practically, PDMS (Sylgard 184) is mixed with a curing agent (Dowsil 184 Silicone Elastomere Curing Agent) in a 10:1 ratio and cast onto the master. After degassing using a

A.2 Experimentation

Driving a flow

Two different systems have been utilized in the presented work to produce reliable flows in microchannels. First of all, syringe pumps (neMESYS, Cetoni) have been used for many of the experiments. Flow rates can be set with high accuracy on these pumps. However, due to the compliance of the channels and tubing, a certain time is required for the equilibration of the flows. Secondly, a pressure-driven system (MFCS-4C, Fluigent) has been used for certain experiments to have a faster response and equilibration. The downside of the pressure-driven system is that the exact flow rate is unknown.

Collection and injection of drops