Mengqi Li

Ruiping Tian

David Monchaud

Wenli Zhang

Omics studies of DNA G-/C-quadruplexes in plants

Genome-wide studies of DNA G-and C-quadruplexes (G4s and i-motifs, respectively) can boost the pace of progress towards a comprehensive understanding of their biological implications and practical applications in plants. We summarize the current state of knowledge about omics studies in order to highlight the current challenges and propose future directions to take studies of plant quadruplexes to the next step.

Introduction

DNA G-quadruplexes (G4s) (see Glossary) and i-motifs (iMs) are two main types of quadruplexes (i.e., four-stranded DNA structures) located within G-or C-rich genomic DNA regions, respectively. The distribution of Gs/Cs in these regions is not randomthey must be gathered in runs (comprising usually two to four units) and several runs must be consecutive (with four runs or more), which makes these sequences known as putative G4-forming sequences (PQFSs) or putative iM-forming sequences (PiMFSs), respectively, readily identifiable. Both quadruplexes are physically prevalent in gene promoters and functional chromatin regions, such as telomeres and centromeres. They are functionally implicated in critical cellular processes in humans, including maintenance of genome stability, regulation of gene expression, and human diseases [START_REF] Rhodes | G-quadruplexes and their regulatory roles in biology[END_REF][START_REF] Bacolla | Non-B DNA conformations, genomic rearrangements, and human disease[END_REF][START_REF] Ruggiero | A dynamic i-motif with a duplex stem-loop in the long terminal repeat promoter of the HIV-1 proviral genome modulates viral transcription[END_REF][START_REF] Niu | BmILF and i-motif structure are involved in transcriptional regulation of BmPOUM2 in Bombyx mori[END_REF]. Their formation and biological relevance in vivo are being increasingly accepted for G4s and emerging for iMs in the human genome, but remain largely unknown in the plant genome. Further and massive effort must thus be invested to decipher the exact roles of quadruplexes, particularly iMs, in the regulation of gene transcription on a genome-wide scale in both humans and plants. The advent of high-throughput sequencing experimental methodologies has provided a key turning point to improve our understanding of their genomic/epigenomic features and subsequent biological implications in plants. Here, we summarize the omics studies developed for both DNA quadruplexes, discuss the challenges already met and those that remain to be addressed for in vivo applications, and propose future directions to advance their studies and applications in plants.

Existing methodologies for the identification of DNA G4s or iMs in plants. The experimental methodologies for the identification of both quadruplexes can be generally classified into low-and high-throughput methodologies (Figure 1). The former comprise structural (NMR, CD, X-ray crystallography, etc.), biochemical (PAGE, equilibrium dialysis, PCR-based assays, etc.), and biophysical investigations (SPR, ESI-MS, UV-and fluorescence-based assays, etc.). While being time-and labor-consuming, these techniques are still largely used for studying individual genomic 'loci' and useful for both validating high-throughput methodologies and studying quadruplex-molecule interactions. The latter can be classified into theoretical investigations (computer-aided prediction) and experimental identification (sequencing-based methods). Several customized algorithms or scripts have been applied for genome-wide prediction of quadruplexes in both mammals and plants [START_REF] Bedrat | Re-evaluation of G-quadruplex propensity with G4Hunter[END_REF][START_REF] Belmonte-Reche | G4-iM Grinder: when size and frequency matter. G-Quadruplex, i-Motif and higher order structure search and analysis tool[END_REF] (Figure 1). It is worth mentioning that even if in silico prediction is an efficient way to identify PQFSs and PiMFSs, it eventually requires an experimental validation.

Sequencing-based approaches have been applied for the identification of DNA G4s both in vitro (i.e., in purified DNA) and in vivo (i.e., in a chromatin context) in humans: G4-seq allows for the detection of G4s in vitro, relying on the use of a small-molecule ligand (pyridostatin) coupled with G4-mediated polymerase stop assays [START_REF] Marsico | Whole genome experimental maps of DNA G-quadruplexes in multiple species[END_REF][START_REF] Chambers | High-throughput sequencing of DNA G-quadruplex structures in the human genome[END_REF]. G4 ChIP-seq allows for the detection of G4s in vivo thanks to the immunoprecipitation of G4s by the antibody BG4 [START_REF] Hänsel-Hertsch | G-quadruplex structures mark human regulatory chromatin[END_REF], while G4P-ChIP-seq relies on the use of an artificially truncated G4 helicase DHX36 to precipitate G4s [START_REF] Zheng | Detection of genomic G-quadruplexes in living cells using a small artificial protein[END_REF], and G4DP-seq relies on the use of a small molecular ligand BioTASQ for G4 affinity capture [START_REF] Feng | Chemo-versus immuno-precipitation of G-quadruplex-DNA (G4DNA): a direct comparison of the efficiency of the antibody BG4 versus the smallmolecule ligands TASQs for G4 affinity capture[END_REF] (Figure 1). However, these approaches suffer from a limitation related to the different G4 binding capacity between antibodies (e.g., BG4) and proteins (e.g., helicase). Only BG4-DNA-IP-seq [START_REF] Feng | Epigenomic features of DNA G-quadruplexes and their roles in regulating rice gene transcription[END_REF] and G4-seq [START_REF] Marsico | Whole genome experimental maps of DNA G-quadruplexes in multiple species[END_REF] have been adapted for the identification of DNA G4s in vitro in rice and Arabidopsis, which paves the way for a global characterization of plant DNA G4s (Figure 1). More sequencing and chemical biology methodologies are still needed for in vitro/in vivo G4 studies that can deepen our understanding of their biological relevance in plants. The global identification of DNA iMs lags far behind that of G4s in both humans and plants. The advent of the iMab antibody, specific for binding to human iMs [START_REF] Zeraati | I-motif DNA structures are formed in the nuclei of human cells[END_REF], achieves a big step towards genome-wide studies of iMs in both humans and plants [START_REF] Ma | Genome-wide characterization of i-motifs and their potential roles in the stability and evolution of transposable elements in rice[END_REF][START_REF] Martinez | Human genomic DNA is widely interspersed with i-motif structures[END_REF]. The iMab antibody-based iM-IP-seq methodology was recently developed for the identification of in vitro DNA iMs in the rice genome [START_REF] Ma | Genome-wide characterization of i-motifs and their potential roles in the stability and evolution of transposable elements in rice[END_REF] (Figure 1). This can be considered as a breakthrough and opens the way for genome-wide studies of DNA iMs in both mammals and plants, but in vivo studies are still missing. Further massive effort must thus be invested to push the boundaries of such omics studies, which aim at advancing our understanding of their functional relevance in plants.

Potential biological implications of DNA G4s or iMs in plants.

Recently obtained results help better understand the G4 functions in the regulation of gene transcription, DNA damage and repair, chromatin organization, interaction with epigenetic marks, diseases, and pharmacogenomics in humans [START_REF] Rhodes | G-quadruplexes and their regulatory roles in biology[END_REF]. However, global DNA G4 studies in plants were only reported in Arabidopsis [START_REF] Marsico | Whole genome experimental maps of DNA G-quadruplexes in multiple species[END_REF] and rice [START_REF] Feng | Epigenomic features of DNA G-quadruplexes and their roles in regulating rice gene transcription[END_REF]. BG4-DNA-IP-seq uniquely uncovered genomic-dependent functions of DNA G4s in the regulation of gene transcription and potential interrelations between G4s and epigenomic signatures in rice [START_REF] Feng | Epigenomic features of DNA G-quadruplexes and their roles in regulating rice gene transcription[END_REF] (Figure 2). It also raised questions about mechanistic studies in plants, such as those about the interrelationships between DNA or histone modifications and G4 formation. Studies of G4s in related mutants will help address those questions.

It was originally assumed that iMs could only form under acidic conditions, due to the requirement of the hemi-protonation of Cs that is required for the formation of C-C + base pairs. This might explain why the studies of iMs under physiological cellular functions have been long in coming. The recent characterization of the iM-specific iMab has invigorated iM studies as this antibody provided the first strong evidence of iM formation under physiological conditions in human cells [START_REF] Zeraati | I-motif DNA structures are formed in the nuclei of human cells[END_REF]. This undoubtedly generates a renewed interest in reconsidering iM functions in human cells, in addition to their involvement in the maintenance of genome stability [START_REF] Bacolla | Non-B DNA conformations, genomic rearrangements, and human disease[END_REF] and the regulation of gene transcription (e.g., HIV-1 and BmPOUM2) [START_REF] Ruggiero | A dynamic i-motif with a duplex stem-loop in the long terminal repeat promoter of the HIV-1 proviral genome modulates viral transcription[END_REF][START_REF] Niu | BmILF and i-motif structure are involved in transcriptional regulation of BmPOUM2 in Bombyx mori[END_REF], which needs to be further verified at a genome-wide level. Similar to BG4-DNA-IP-seq described above, the recently developed iM-IP-seq provided the first global mapping of iMs in rice [START_REF] Ma | Genome-wide characterization of i-motifs and their potential roles in the stability and evolution of transposable elements in rice[END_REF], revealing its potential functions in the regulation of gene transcription and genome stability through regulation of TE (transposable element) activity. This very first genome-wide characterization of iM landscapes in plants (Figure 2) pioneered iM genomic studies but also raised several questions that still await further exploration, including those related to the interrelationships between DNA methylation or histone modifications and iM formation, or how iMs act as cis-regulatory elements (CREs) or act as platforms for recruitment of trans-acting factors in the regulation of gene transcription or TE activities in plants.

In vivo omics studies are urgently needed in plants. The omics studies in plants discussed above primarily reflect folding potentials of PQFSs or PiMFSs in vitro, which cannot truly pinpoint quadruplex formation within the chromatin context (i.e., in vivo).

An illustrative example is the comparison of G4-seq and G4 ChIP-seq datasets that brightly demonstrates the suppressive role of chromatin for G4 formation in cells (the number of G4s detected in vivo representing ~1% only of the G4s detected in vitro).

Therefore, more efforts must be invested in profiling the G4/iM landscapes in vivo in plants. There are several possible ways that deserve to be assayed, which involve: (i) the discovery of more accurate antibodies against G4/iM along with the adaptation and optimization of the related ChIP-seq methods developed in human cells and implemented for the identification of quadruplexes in plants; (ii) the development of multivalent small molecules (ligands) implementable as molecular baits for chemoprecipitation of G4/iM followed by sequencing, or Chem-seq (as performed with BioTASQ for plant G4s). Of note, while dozens of G4 ligands have been designed and used, including ad hoc molecular G4 baits, reliable iM ligands are yet to be found, which somehow curtails the development of this field; and (iii) the production of artificially truncated plant-specific G4/iM-binding proteins for ChIP-seq-like investigations (as performed with the truncated DHX36 for human G4s).

Comprehensive comparisons of G4/iM landscapes using plant cells that transiently or stably express tagged G4/iM-binding proteins could help decipher the dynamics of G4/iM folding/ unfolding related to the expression of G4/ iM-binding proteins across the genome.

Any advance that will enable us to portray in vivo quadruplex landscapes more accurately will greatly improve our understanding of the biological functions of G4/iM in developmental stages, phenotypic changes, genome stability, chromatin structure and stress responses (as a function of environmental stimuli including salt, heat and acidic conditions).

Concluding remarks

While still in their early stages as compared to those performed in human cells, the studies of G4s and iMs in plants are nevertheless fascinating and exciting. The handful of studies reported to date have provided invaluable insights into the functional relevance of G4s/iMs in plant cells but also raised a plethora of key questions that impatiently await further investigations. For example, how the dynamics of these quadruplexes are linked to development changes or to stress responses? Do they act as autonomous genetic regulators or cooperatively with chromatin marks to regulate gene expression during normal growth, different development stages and stress responses? To unravel these conundrums, in vivo omics studies are urgently needed as they will boost functional studies, help design potential sensors usable in climate change adaptation and provide key 'loci' for genomic editing towards desirable agronomic traits formation. Please see the online supplemental information for an additional reading list.

Figure 1 .

 1 Figure1. Summary of methodologies for study of DNA G4s or iMs. They include low-and highthroughput methodologies. Low-throughput ones can be divided into biophysical and biochemical methods. High-throughput ones can be classified into computer-based prediction[START_REF] Bedrat | Re-evaluation of G-quadruplex propensity with G4Hunter[END_REF][START_REF] Belmonte-Reche | G4-iM Grinder: when size and frequency matter. G-Quadruplex, i-Motif and higher order structure search and analysis tool[END_REF] and experimental omics studies. Experimental omics studies include small-molecule ligand coupled with DNA polymerases top assay (G4-seq)[START_REF] Marsico | Whole genome experimental maps of DNA G-quadruplexes in multiple species[END_REF][START_REF] Chambers | High-throughput sequencing of DNA G-quadruplex structures in the human genome[END_REF], antibody [BG4-(Ch)IP-seq, iM-IP-seq] [9,12,14,15], truncated native protein (G4P-seq)[START_REF] Zheng | Detection of genomic G-quadruplexes in living cells using a small artificial protein[END_REF], and small-molecule ligand affinity capture (G4DP-seq)[START_REF] Feng | Chemo-versus immuno-precipitation of G-quadruplex-DNA (G4DNA): a direct comparison of the efficiency of the antibody BG4 versus the smallmolecule ligands TASQs for G4 affinity capture[END_REF] sequencing. Black arrows indicate methods used in plants, red question mark indicates methods used in humans but not in plants, and the blue question mark indicates the potential method not applied in both humans and plants. Abbreviations: DNA G4s, DNA G-quadruplexes; iMs, i-motifs.

Figure 2 .

 2 Figure 2. Biological relevance of DNA G4s and iMs in humans and plants. They include diseases, genome stability, intersect with epigenetic marks and regulation of gene expression in human (green) [1-4,7,15], and various stress responses, plant development and regulation of gene expression, TE activities in plants (yellow) [7,12,14]. Abbreviations: DNA G4s, DNA G-quadruplexes; iMs, i-motifs; TE, transposable element; TF, transcription factor; TSS, transcription start site.

Acknowledgments

We apologize to researchers whose work could not be cited due to space restrictions. This work is supported by the National Natural Science Foundation of China (32070561 and U20A2030), the National Key Research and Development Program of China (2020YFE0202900), the Fundamental Research Funds for the Central Universities (KYZZ2022003), and the Graduate Research and Practice Innovation Program of Jiangsu Province (KYCX20_0579). We thank the Bioinformatics Center in Nanjing Agricultural University for providing facilities to assist with sequencing data analyses.

Author contributions

W.Z. conceptualized the idea and provided financial support. M.L. and R.T. drafted the manuscript. M.L. prepared the figures. D.M. edited the manuscript. W.Z. rewrote and finalized the manuscript. All authors proofread the final manuscript.

Declaration of interests

The authors declare that they have no competing interests.

Glossary


Adrien Bussonnière

Arnaud Antkowiak

Francois Ollivier

Michael Baudoin

Régis Wunenburger

Acoustic sensing of forces driving fast capillary flows

Acoustic sensing of forces driving fast capillary flows

Adrien Bussonnière 1,2 , Arnaud Antkowiak 1 , François Ollivier 1 , Michaël Baudoin 2 , and Régis Wunenburger 1 1 Sorbonne Université, CNRS, Institut Jean Le Rond d'Alembert, F-75005 Paris, France 2 Univ. Lille, CNRS, ECLille, ISEN, Univ. Valenciennes, UMR 8520 -IEMN, F-59000 Lille, France (Dated: November 26, 2019)

The popping sound of a bursting soap bubble is acquired using microphone arrays and analyzed using spherical harmonics decomposition. Using the theoretical framework of aeroacoustics, we demonstrate that this acoustic emission originates mainly from the capillary stresses exerted by the liquid soap film on the air and that it quantitatively reflects the out-of-equilibrium evolution of the flowing liquid film. This constitutes the proof of concept that the acoustic signature of violent events of physical or biological origin could be used to measure the forces at play during these events.

The analysis of the sound emitted or scattered by fluid flows provides a profusion of quantitative information on their causes and features. For example the velocity of invivo flowing blood is routinely deduced from the sound scattered by blood. The vorticity field of unsteady flows such as aerodynamic jets or wakes can be analyzed from the sound they either emit ("aerodynamic sound" [START_REF] Lighthill | Waves in Fluids[END_REF]) or scatter [START_REF] Lund | [END_REF]3]. The size of gas bubbles can be assessed from the frequency of the sound emitted by their free pulsations [4]. At last, the energy of explosions can be deduced from the N-shaped pressure signal they emit [START_REF] Whitham | Linear and nonlinear waves[END_REF]. Fluid momentum variation is also known to result in sound radiation. Its detection could, in principle, enable to determine non intrusively the external forces causing the fluid acceleration in situations where they are largely unknown, such as flows triggered by the rupture, coalescence, atomization or impact of liquid free surfaces, films or elastic membranes, or by propulsive, defensive or preying motions of animals. Such a force remote-sensing technique should be considered as a useful complement to high-speed imaging that gives access only to the shapes of the evolving surfaces.

To determine the external forces at play, their acoustic emission has to be discriminated from those due to volume or vorticity variations. As described by the theory of aeroacoustics [START_REF] Lighthill | Waves in Fluids[END_REF], fluid volume variations result in a monopolar acoustic radiation pattern, whereas fluid momentum variations result in a dipolar pattern and vorticity variations in a quadrupolar one. Thus, these radiation patterns can be discriminated by using microphone arrays and spherical harmonics decomposition [START_REF] Rafaely | Fundamentals of spherical array processing[END_REF]. In this letter, we demonstrate that the forces triggering a rapid hydrodynamic event can be quantitatively assessed from the analysis of their acoustic signature acquired using arrays of sensors. To achieve this aim, we focus on the familiar popping sound of a bursting soap bubble, considered as a paradigm of violent flows driven by surface tension. Using the framework of aeroacoustics, we show that the bubble acoustic emission can be mainly ascribed to the capillary stresses exerted by the liquid soap film on the air and that it quantitatively reflects the out-ofequilibrium evolution of the flowing liquid film. This constitutes the proof of concept that acoustic remote sensing can be used to measure the forces driving fluid flows.

Soap bubbles of 1 mL typical volume are blown up with air using a syringe pump atop a vertical capillary tube, see Fig. 1 a. The liquid soap used is a 0.25 g • L -1 sodium dodecyl sulfate (SDS)-water solution with equilibrium surface tension at ambient temperature γ 0 = (50 ± 1) mN • m -1 [7]. Bursting events are either spontaneous or triggered using a hydrophobic needle located 10 -15 mm above the tube outlet, visible on top of the pictures of bursting bubble shown in Fig. 1 a. As known since more than a century [START_REF] Bull | [END_REF], bubble bursting usually begins with the spontaneous or triggered opening of a hole in the soap film followed by the growth of a circular rim gobbling up the soap film in its path at a typical speed v r ∼ 10 m • s -1 up to its complete disappearance, as evidenced by the pictures acquired using a high-speed camera [7] shown in Fig. 1 a. In a first series of experiments, the acoustic emission of the bursting bubble is recorded using three circular acoustic antennae each made of eight microphones [7] sketched in Fig. 1 b. The eight pressure signals recorded by the 44 mm radius antenna during the triggered bursting of a fresh bubble, shown in Fig. 1 c, evidence that the bubble radiates sound during the whole bursting duration. Remarkably, although these signals exhibit the same shape, their sign and amplitude depend on the microphone colatitude θ m (as defined in Fig. 1 b), the signals recorded above and below the bubble having opposite signs: the bursting bubble behaves as an acoustic dipole with vertical axis. To identify the sources of sound during bubble bursting, we compute from the 24 signals the three pressure fields associated respectively to the monopolar, dipolar and quadrupolar radiations by applying spherical harmonics decomposition and spatial filtering [7]. The corresponding three multipolar contributions to the pressure signal measured by the microphone located on the bubble top are shown in Fig. 1 e. Their comparison confirms that the dipolar radiation actually dominates the monopolar and quadrupolar radiations.

Such a simple acoustic signature can be explained by first describing the bursting process. Before bursting, the air contained in the spherical bubble with radius R 6 mm is pressurized at Laplace overpressure ∆P 0 = 4γ 0 /R 30 Pa by the isotropic capillary stresses f 0 = 2γ 0 κ 0 n exerted by the two curved liquid-air interfaces constituting the soap film, where κ 0 = 2/R is the film curvature and n the unit vector normal to the film, see Fig. 1 d. According to [START_REF] Taylor | Proc. R. Soc. Lond. A[END_REF][START_REF] Culick | [END_REF][11], when a hole is formed in the liquid film, the hole rim retracts at the velocity

v r = 2γ 0 ρ f e 0 , (1)
where ρ f = 1.0 × 10 3 kg • m -3 is the liquid mass density and e 0 ∼ 1 µm the film typical thickness, as the result of the balance between pulling surface tension and liquid inertia. Thus, film retraction is expected to last for T = πR/v r 5 ms, in agreement with observations. As soon as the film opens, the capillary stresses exerted by the soap film on the inner air do not balance anymore, as illustrated in Fig. 1 d. Their addition results in a capillary force F = F e z that varies with the hole opening (see Fig. 1 d). This force accelerates the inner air vertically upward and therefore triggers a dipolar acoustic radiation with vertical axis and duration T . The monopolar radiation due to the expansion of inner air and the quadrupolar radiation due to vorticity production in the rim wake are estimated as negligible compared to the dipolar radiation [7].

During the film opening, the air is accelerated by the capillary stresses f (y, t) where y scans the bursting liquid film at time t (see Fig. 1 d). Linearized Euler equation written for air is thus : ρ a ∂ t v = -grad p + f (y, t)δ y where v is the air velocity, p the acoustic pressure perturbation, ρ a air mass density at equilibrium, δ y the 1D Dirac function defined along n and centered on y.

Combining it with the linearized equation of mass conservation ∂ t (c -2 p) = -ρ a div v (c is the speed of sound in air) results in the linearized equation of propagation c -2 ∂ tt p -∆p = -div [f (y, t)δ y ] . According to [START_REF] Howe | Theory of Vortex Sound[END_REF], the resulting acoustic pressure perturbation p D at position x and time t is

p D (x, t) = 1 4π film at t div f (y, t ) |x -y| dS ( 2
)
where div is the divergence operator with respect to x, t = t -|x-y| c the retarded time and dS the elementary film area. For |x| R, Eq. ( 2) can be approximated by:

p D (r, θ, t) = 1 4πr cos (θ) 1 c Ḟ(t ) + 1 r F(t ) (3)
where r = |x| and

F(t) = film at t f z (y, t) dS, (4)
is the capillary force exerted by the soap film on the inner air, with f z = f • e z and Ḟ the time derivative of F [7].

To model the distribution of stresses exerted by the film on the inner air during bursting, we observe that the bubble does not significantly deflate during the rim retraction, as shown in Fig. 1 a. Thus we assume the liquid film in front of the rim to be at rest and at thermodynamic equilibrium with uniform curvature R and surface tension γ 0 throughout bursting. Accordingly, f = f 0 along the bursting film and:

F(t) = ∆P 0 πR 2 sin 2 [θ r (t)] (5)
where θ r (t) is the rim colatitude defined in Fig. 1 d. In the frame of this quasistatic model, sound emission originates only from film area reduction.

To quantitatively test the validity of this description of sound radiation, in a second series of experiment we use two large bandwidth microphones [7] distant of r = 30 mm from a R = 6.2 mm bubble and positioned above and below the bubble, named BK1 and BK2 in Fig. 1. The two acoustic pressure signals acquired during the triggered burst of a fresh bubble are compared to their prediction using Eqs. ( 3), [START_REF] Whitham | Linear and nonlinear waves[END_REF] in Fig. 1 f (dashed curve). θ r (t) has been previously extracted from the images of bubble bursting and interpolated at acoustic sampling frequency. The model catches the shape and amplitude of the measured signals but overestimates their duration and maximal amplitude by approximatively 30 % and 10 % respectively. As shown in the following, the limitation of this model does not rely on the description of the acoustic emission process but actually on the roughness of the quasistatic model of film dynamics.

As reported and analyzed in several previous studies [11,[START_REF] Frankel | [END_REF][14][15], the opening of a hole in a soap film may put the surfactant monolayers strongly out-of-equilibrium. The decrease of the soap film area resulting from the rim retraction indeed induces a rapid compression of the surfactants located at the film surface. Since their desorption kinetics is generally slow compared to the film shrinking rate, surfactants behave as if they were insoluble [16] and concentrate at the surface. Due to this rapid increase of the surfactant surface concentration, the surface tension of the compressed films decreases and departs from its equilibrium value. Since acoustic emission relies on the unsteadiness of the capillary stresses exerted by the liquid film on the air, the departure of surface tension from its equilibrium value is expected to have a noticeable impact on the acoustic emission during bubble bursting.

To gain insight into the film dynamics, a time-resolved mapping of its thickness distribution during bursting is required. To this aim, long-lived bubbles are considered. Interestingly, due to gravity-driven drainage, such bubbles indeed exhibit strong vertical thickness stratification and film thinning down to thicknesses comparable to visible wavelengths. Consequently, when illuminated by a source of white light and observed in transmission, long-lived bubbles display light interference fringes (see Fig. 2 a) from which the film thickness distribution just before and during bursting can be determined by analyzing the interference patterns [7].

After typically one minute of lifetime, long-lived bubbles ultimately spontaneously burst by opening always at their top where the film is the thinnest. Neglecting the weak departure from sphericity of the bubble during film retraction, the rim velocity v r (t) can be calculated from θ r (t) using v r = R θr . As shown in Fig. 2 b, the variation of v r (θ r ) with the local film thickness before bursting e 0 (θ r ) quantitatively agrees with its prediction using Eq. ( 1), which demonstrates the validity of Eq. ( 1) along a curved and stratified soap film.

A careful observation of the light interference pattern during spontaneous bubble bursting events reveals that a thickness discontinuity starting from the hole actually propagates along the film downward ahead of the rim, as indicated by red arrow tips in the pictures shown in Fig. 2 a. The occurence of a thickness shock wave depends on the relation between the out-of-equilibrium surface tension and the surfactant surface concentration that is specific to each surfactant [START_REF] Frankel | [END_REF]. Shock waves have been observed during film retraction along planar films made of SDS-water solution [11].

Thickness shock wave formation is expected to affect acoustic emission in several First, the capillary stresses unsteadiness due to the surface tension discontinuity propagating in front of the rim constitutes a supplementary source of sound. Moreover, the shock wave triggers a flow of the soap film that further decreases the stresses exerted by the film on the air, as demonstrated in the following. Assuming a thickness shock wave located at colatitude θ s (t) to propagate at velocity v s along a planar film initially at rest and at equilibrium, surfactant effective insolubility assumption, mass conservation and momentum balance across the shock indeed entail the motion of the whole film behind the shock wave at velocity v f (θ - s ) that satisfies both [START_REF] Frankel | [END_REF]:

v f (θ - s ) = v s [1 -e 0 (θ + s )/e 1 (θ - s )] and 2 [γ 0 (θ + s ) -γ 1 (θ - s )] = ρ f e 0 (θ + s )
, where e 0 (θ + s ) is the thickness of the film at rest and at equilibrium in front of the shock wave, e 1 (θ - s ) and γ 1 (θ - s ) the thickness of the compressed film and its out-of-equilibrium surface tension behind the shock wave, respectively. Applying these results to a spherical film, behind the shock, each moving fluid element runs a circular trajectory with radius R around the bubble center at tangential velocity v f (see Fig. 2 c) and is thus subjected to the centripetal acceleration v 2 f /R. Application of second Newton's law to such an accelerated fluid element with thickness e 1 submitted to external pressure P 0 , internal pressure P in and surface tension γ 1 , as sketched in the enlargement B in Fig. 2 c, reveals that the centripetal acceleration of the moving noticeably reduces the overpressure it exerts on the inner air, i.e.

∆P 1 = P in -P 0 = 4 γ 1 R -ρ f e 1 v 2 f R < 4 γ 1 R . (6)
Such an influence of the tangential film motion on the pressure jump across curved films is known to be responsible for the large variety of shapes of water bells [17][18][19][START_REF] Taylor | Proc. R. Soc. Lond. A[END_REF].

All the quantities involved in this description of the soap film dynamics can be experimentally assessed from image analysis. As shown in Fig. 2 b, the shock wave velocity inferred from θ s (t) using v s = R θs is found to be proportional to v r , whereas e 1 /e 0 is found to be constant along the moving film. These two observations combined with the assumption of surfactant insolubility lead to prove that ∆P 1 is uniform all along the moving film [7]. This leads us to conclude that the only sources of unsteadiness of the capillary stresses, and therefore of acoustic emission, are the moving rim and shock wave. Accordingly, f = ∆P 1 n in the range θ ∈ [θ r (t); θ s (t)] and f = ∆P 0 n in the range θ ∈ [θ s (t); π]. Use of Eq. ( 4) results in the following expression for the capillary force exerted by the soap film on the inner air:

F(t) = πR 2 (∆P 0 -∆P 1 ) sin 2 [θ s (t)] + ∆P 1 sin 2 [θ r (t)]
(7) from which the acoustic emission away from the bubble can be evaluated using Eq. (3) (out-of-equilibrium model). of the thin film located on the bubble top combined with the dependence of the radiated sound on Ḟ ∝ θr = v r /R. The signals detected by the broadband microphone BK2 located below the bubble are found to be quantitatively described by the out-of-equilibrium model (solid curve). The observed gap between this model and the signal detected by BK1 may be ascribed to a bandwidth narrower than BK2 which affects the high-frequency content of this sharp signal. On the contrary, the agreement between experimental data and the quasistatic model Eqs. ( 3) and (5) (dashed curve) is only qualitative, as in the case of fresh bubbles.

Extrapolating this refined description of film dynamics to fresh bubbles allows us to predict and to quantitatively describe the propagation of a thickness shock wave along bursting fresh bubbles, although they are made of thick films that display no light interference fringes and hardly visible shock waves. This is possible because the whole description of the film dynamics requires only the knowledge of the equilibrium surface tension γ 0 and of the rim colatitude θ r (t) that is as easily measurable on fresh bubbles as on long-lived ones. When applying this refined model of acoustic emission Eqs (3), (7) to fresh bubbles, we observe a quantitative agreement between the acoustic signals measured during the needle-triggered bursting of fresh bubbles and their prediction (solid curve), as shown in Fig. 1 f. This confirms that the thickness shock wave propagating along the bursting soap film noticeably contributes to sound emission in the case of fresh bubbles too.

We have shown that the description of the acoustic emission by a bursting bubble we propose is fully consistent with the current understanding of soap film retraction dynamics. This demonstrates that the forces at play during the rapid evolution of liquid interfaces and more generally during violent events of physical of biological origin could be determined from remote dipolar acoustic radiation monitoring by spherical harmonics decomposition and integration of Eq. ( 3), thus potentially constituting a precious diagnostic complementary to high-speed imaging.

15 FIG. 1 .

 151 FIG. 1. (a), High speed imaging of the bursting of a 2 mL triggered bubble. (b) Sketch of the setup showing one circular acoustic antennae of eight MEMS microphones (coloured circles) and the two large bandwidth microphones BK1 and BK2. (c) Signals acquired by the 44 mm radius acoustic antenna. (d) Schematic of the bubble bursting showing the capillary forces. (e) Monopolar, dipolar and quadrupolar contributions to the pressure signal measured on the bubble top. (f) Pressure acquired by top BK1 (blue curve) and bottom BK2 (red curve) microphones at 30 mm from a 1 mL fresh bubble. Solid lines correspond to the average over 5 experiments and shaded areas are bounded by the maximum and minimum. Quasistatic model (resp. out-of-equilibrium model) is plotted as dashed lines (resp. solid lines).

FIG. 2 .

 2 FIG. 2. (a)High-speed images of the spontaneous bursting of a 0.5 mL volume bubble. The red arrow tips indicate the thickness shock wave. (b) Thickness shock wave velocity vs (blue) and of the rim velocity vr (red) as function of the initial film thickness e0. Inset: Film thickness after the shock wave (e1(θ, t)) versus its initial thickness before the shock wave e0(θ). (c) Sketch of the bursting soap bubble illustrating the influence of the shock wave on the bursting dynamic. Enlargements : Capillary forces when the film is at rest (A) and is out-of-equilibrium flowing (B). The in-plane flow induced a centripetal acceleration (bold, black arrow). (d) Pressure signals of the spontaneous bursting of 0.5 mL bubbles recorded by top BK1 (blue curve) and bottom BK2 (red curve) microphones at 30 mm, averaged over three bursting events (solid lines), the shaded areas being bounded by the maximum and minimum of the three signals. Quasistatic model (resp. out-of-equilibrium model) is plotted as dashed lines (resp. solid lines).

Fig. 2 d

 2 displays typical acoustic signals acquired during the bursting of long-lived bubbles. They are initially steeper than in the case of fresh bubbles, as the consequence of the initially large retraction velocity v r ∝ e -1/2 0


Fatima Ezahra Annanouch
email: fatima.annanouch@im2np.fr

Nicolas Morati
email: nicolas.morati@im2np.fr

Virginie Martini-Laithier
email: virginie.laithier@im2np.fr

Tomas Fiorido
email: tomas.fiorido@im2np.fr

Khalifa Aguir
email: khalifa.aguir@im2np.fr

Marc Bendahan
email: marc.bendahan@im2np.fr

Gilles Bouchet
email: gilles.bouchet@univ-amu.fr

Pierre Perrier
email: pierre.perrier@univ-amu.fr

Design and Optimization of Gas Sensor Testing Chamber

Keywords: gas sensor, gas testing chamber, metal oxides, tin oxide, mathematical modeling, simulation. I

It is important to size and optimize the chamber in which gas sensors are tested. Indeed, the amplitude, as well as the response and recovery times are very dependent on the testing chamber. In this study, we show that by optimizing the design and reducing the volume of the testing chamber, the responses of metal oxide microsensors are highly enhanced and faster, and therefore closer to the real answers of the sensor.

INTRODUCTION

Metal oxide gas sensors have become one of the most active research areas, owing to their low cost and flexibility in production, simplicity of their use and their large number of detectable gases. They are employed in a wide spectrum of applications, such as environmental monitoring, domestic safety, disease detection and many more [START_REF] Fine | Metal oxide semi-conductor gas sensors in environmental monitoring[END_REF].

So far, many works have been reported on the enhancement of gas sensing performances, either with catalysts nanoparticles modification, or by the nanostructuring of metal oxide sensitive material [START_REF] Annanouch | Aerosol-Assisted CVD-Grown PdO Nanoparticle-Decorated Tungsten Oxide Nanoneedles Extremely Sensitive and Selective to Hydrogen[END_REF]. However, few works have studied the influence of the gas testing system on the sensors performances. Achieving a reliable and highly sensitive sensor, with fast response and recovery times, cannot be done without an optimized gas testing chamber design. Such a design needs to be modeled and simulated in terms of chamber volume, placement of sensor and gas flow direction.

In this work we study and compare the influence of gas testing chamber design on the sensor performances, namely Cross chamber (old one) and Boat chamber (new optimized testing chamber). The paper is structured as follows. Section II describes the gas microsensor platform and the testing chamber design. Section III presents and discusses the obtained results (simulation results and experimental validation of the optimized chamber). We conclude the work in Section IV.

II. GAS SENSORS AND TESTING CHAMBERS

A. Gas sensors

The microelectromechanical systems (MEMS) based microsensor platform was patented by our laboratory and fabricated using clean room facilities and various microfabrication steps including photolithography, metallization and backside etching (DRIE) of the substrate to define the membrane as the transducer [START_REF] Aguir | Gas sensor based on heated sensitive layer[END_REF]. This latter has a size of 400μm × 400 μm. It carries three transducers S1, S2, S3 and two heaters (Fig. 1). The gap between the electrodes is 4 μm, the resistance of each heater is 100 Ω and the temperature coefficient is 3 10-3/°C. An SnO2 sensing layer (50 nm) was directly deposited over the microsensor platform, by reactive radio frequency magnetron sputtering technique [START_REF] Kaur | RF sputtered SnO2: NiO thin films as sub-ppm H2S sensor operable at room temperature[END_REF][START_REF] Sberveglieri | Radio frequency magnetron sputtering growth and characterization of indiumtin oxide (ITO) thin films for NO2 gas sensors[END_REF]. It is worth noting that before depositions, the microsensor platform was cleaned with acetone and then with ethanol, dried with air, and then placed inside the shadow mask.

B. Testing chambers

Gas-sensing tests were carried out in two different chambers (Fig. 2). The first one (Fig. 2.a) was made from stainless steel with total volume of 0.3 L and gas flow range between 0.1L/min and 1.5L/min. Besides, it has an inlet, an outlet, and the sensor optimal position is at the center, in front of the gas flow direction. The second chamber (the new one) is illustrated by Figure 2.b. It was made from polylactic acid (PLA) with a small volume of 2.35 10 -3 L and gas flow range between 0.01 L/min and 0.5 L/min. It has a boat shape with a planar inlet and outlet. Additionally, the optimal sensor position is at the center of the boat back-side, in the same plan as the gas flow direction. In both chambers, the gas flow was maintained at 0.1 L/min, the sensor response was defined as R=Ra/Rg, where Ra and Rg are the sensor resistances at the stationary state in air and after 1 min of exposure to the target gas, respectively.

III. RESULTS AND DISCUSIION

A. Mathematical modelling and simulation results

The flow is modeled by a finite volume method solving the Navier-Stokes and the energy equations in the two 3D geometries, with no-slip and adiabatic boundary conditions everywhere, except on the inlet and outlet boundaries and on the sensor. Velocity fields are presented in Figure 3. As we can see, in the cross chamber, at the sensor surface, the gas flow velocity is very important (0.1 m/s), which leads to the creation of many turbulences and negatively affects the sensor detection. However, in the boat chamber, it is almost zero and the gas flow direction is linear with the sensor position, which eliminate the creation of gas turbulences.

The target gas is injected at the inlet (0.1 L/min during 1 min, 50 ppm ethanol in air) and the ethanol concentration is measured on the sensor position. The gas testing transport is modeled by a convection-diffusion equation applied to a passive scalar. In Figure 4, we can observe that the gas concentration in the optimized testing chamber is very similar to the setpoint (50 ppm). In addition, the speed of the filling and emptying in boat chamber is much faster compared to the cross one. In contrast, the ethanol concentration simulated for the cross-chamber does not reach 50 ppm with a flow rate of 0.1 L/min during 60 seconds, due to the greater volume of the cross-chamber and the presence of turbulences. The simulations show that an injection lasting 10 minutes is necessary to reach 50 ppm with such flow rate; at the same time, an injection with a flow rate of 0.5 L/min for 120 seconds allows us to reach the same level of ethanol concentration (50 ppm).

These results will be experimentally validated in the next paragraph by measuring the electrical sensor response towards 50 ppm of ethanol for an exposer of 1 minute, in both chambers.

B. Validation of the optimized gas testing chamber

In order to validate the simulation results, we have exposed SnO2 sensor (S2) to 50 ppm of ethanol, using the same measurements parameters, in both testing chambers (Fig. 5). The results show that the sensor performances are highly enhanced using the optimized chamber. For instance, the response and recovery times in the boat chamber are 4 s and 89 s, respectively. However, they are five times higher when using the cross chamber.

IV. CONCLUSION

In this study, we have highlighted the strong influence of the test chamber design with respect to the electrical response of the sensor towards ethanol. To achieve our goals, we have reduced the dimensions of the test chamber while adapting the geometry. Besides, we have eliminated dead volumes, obtained a homogeneous gas concentration, and reduced the gas flow velocity at the sensor surface. The experimental results are in agreement with the mathematical modelling and simulation results.

Figure 1 .

 1 Figure 1. MEMS-based microsensor platform [3].

Figure 2 .

 2 Figure 2. Photographs of: (a) cross and (b) boat chamber

Figure 3 .

 3 Figure 3. Velocity field of the converged flow in the Cross Chamber (a) and in the Boat chamber (b)

Figure 4 .

 4 Figure 4. Ethanol concentration simulation in both chambers; injection at t=134s during 1 min

Figure 5 .

 5 Figure 5. Experimental sensor response toward 50 ppm of ethanol in both chambers -injection during 1 min

ACKNOWLEDGMENT

The authors would like to acknowledge NANOZ, a company specialized in gas sensors; SATT Sud-Est, "Accelerator of Technology Transfer", which is a key player in regional economic development associated with innovation and Mr. A. Combes for his technical support.