Marc Pascual

Poquet Arthur

Alexandre Vilquin

Marie-Caroline Jullien
email: marie-caroline.jullien@univ-rennes1.fr

Arthur Poquet

Phase separation of an ionic liquid mixture assisted by a temperature gradient

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I. INTRODUCTION

Last decade, temperature-responsive binary systems made of ionic liquids (IL) and water have shown promising applications such as in metal and rare-earth extraction [START_REF] Dupont | Rare-earth recycling using a functionalized ionic liquid for the selective dissolution and revalorization of y 2 o 3: Eu 3+ from lamp phosphor waste[END_REF][START_REF] Depuydt | Homogeneous liquid-liquid extraction of metal ions with non-fluorinated bis (2-ethylhexyl) phosphate ionic liquids having a lower critical solution temperature in combination with water[END_REF], protein stabilisation [START_REF] Kohno | Extraction of proteins with temperature sensitive and reversible phase change of ionic liquid/water mixture[END_REF][START_REF] Douglas R Macfarlane | New dimensions in salt-solvent mixtures: a 4th evolution of ionic liquids[END_REF], catalytic synthesis [START_REF] Qiao | Temperature-responsive ionic liquids: fundamental behaviors and catalytic applications[END_REF][START_REF] Ohno | Functional design of ionic liquids: Unprecedented liquids that contribute to energy technology, bioscience, and materials sciences[END_REF], forward osmosis water desalination [START_REF] Hsu | Enhanced forward osmosis desalination with a hybrid ionic liquid/hydrogel thermoresponsive draw agent system[END_REF][START_REF] Kamio | Fundamental investigation of osmolality, thermoresponsive phase diagram, and water-drawing ability of ionic-liquid-based draw solution for forward osmosis membrane process[END_REF][START_REF] Deguchi | Thermoresponsive ionic liquid/water mixtures for separation and purification technologies[END_REF] and low grade heat valorization [START_REF] Cai | Energy-efficient desalination by forward osmosis using responsive ionic liquid draw solutes[END_REF][START_REF] Zhong | Osmotic heat engine using thermally responsive ionic liquids[END_REF]. Those techniques are built on the reversible phase separation of the system with temperature loops. As ionic liquids are costly and generally available in limited volumes, isolating separately the two phases is crucial. This issue has rekindled the interest of phase-separation widely studied since the 70s, both experimentally and theoretically [START_REF] Onuki | Dynamic van der waals theory[END_REF]. Besides the industrial centrifugation techniques or the sedimentation mechanisms [START_REF] Jk Platten | Phase separation under a temperature gradient[END_REF][START_REF] Araki | Hydrodynamic delocalization of phase separation in a locally cooled fluid mixture[END_REF], microfluidics appears as an excellent alternative since it enhances capillary mechanisms, especially when wetting effects, which are marked in binary mixtures [START_REF] Michael | An interface phase transition: complete to partial wetting[END_REF][START_REF] Beysens | Adsorption phenomena at the surface of silica spheres in a binary liquid mixture[END_REF][START_REF] Puri | Surface-directed spinodal decomposition[END_REF], are known to boost the phase-separation kinetics of such systems [START_REF] Tanaka | Interplay between phase separation and wetting for a polymer mixture confined in a two-dimensional capillary: wetting-induced domain ordering and coarsening[END_REF][START_REF] Tanaka | Dynamic interplay between phase separation and wetting in a binary mixture confined in a onedimensional capillary[END_REF][START_REF] Tanaka | Wetting dynamics in a confined symmetric binary mixture undergoing phase separation[END_REF][START_REF] Tanaka | Double phase separation in a confined, symmetric binary mixture: Interface quench effect unique to bicontinuous phase separation[END_REF][START_REF] Tanaka | Spinodal decomposition of a symmetric binary fluid mixture in quasi two dimensions: Local orientational ordering of fluid tubes[END_REF][START_REF] Binder | Spinodal decomposition in confined geometry[END_REF][START_REF] Tanaka | Interplay between wetting and phase separation in binary fluid mixtures: roles of hydrodynamics[END_REF]. As an example, the use of a confinement gradient is an interesting method where separation relies on a well understood capillary effect [START_REF] Keiser | Washing wedges: capillary instability in a gradient of confinement[END_REF]: the most wetting phase is dragged toward the wedge, i.e. toward the thinner part of the cavity. Such experiments have been performed (see Supplemental Movie S1) and the separated phases are recovered in two well-defined regions. This wetting-based strategy is expected to occur up to confinement below the interfacial capillary length (l c = γ/∆ρg ≈ 300 µm at 35 o C). As the physics at play are understood, the results are not discussed here. In this paper, we present a strategy that takes advantage of Marangoni effects at small scales. A temperature-induced interfacial tension gradient is known to cause an interfacial stress generating thin film flow [START_REF] Cazabat | Fingering instability of thin spreading films driven by temperature gradients[END_REF][START_REF] Miralles | Foam drainage control using thermocapillary stress in a two-dimensional microchamber[END_REF][START_REF] Menesses | Surfactant-free persistence of surface bubbles in a volatile liquid[END_REF][START_REF] Koleski | Azimuthal instability of the radial thermocapillary flow around a hot bead trapped at the water-air interface[END_REF] and droplets or colloids motion [START_REF] Young | The motion of bubbles in a vertical temperature gradient[END_REF][START_REF] Würger | Thermally driven marangoni surfers[END_REF][START_REF] Araki | Illumination-induced motion of a janus nanoparticle in binary solvents[END_REF][START_REF] Ruben Gomez-Solano | Transient coarsening and the motility of optically heated janus colloids in a binary liquid mixture[END_REF][START_REF] Zinn | Phoretic dynamics of colloids in a phase separating critical liquid mixture[END_REF][START_REF] Dietrich | Microscale marangoni surfers[END_REF], thereby affecting the phase separation kinetics [START_REF] Beysens | Liquid-vapor phase separation in a thermocapillary force field[END_REF]. Note that concerning the phase transition of a pure fluid, the mechanisms of droplets or bubbles migration in a temperature gradient are not induced by Marangoni stresses [START_REF] Onuki | Droplet motion with phase change in a temperature gradient[END_REF][START_REF] Vadim S Nikolayev | Evaporation condensation-induced bubble motion after temperature gradient set-up[END_REF]. Previous studies on the phase separation of binary mixtures in a temperature gradient focused on bulk migration: drop migration assisted by thermocapillarity [START_REF] Assenheimer | Phase separation of a critical binary mixture subjected to a temperature gradient[END_REF][START_REF] Morick | Convection generated by a gradient of interfacial tension in a phase separated binary liquid mixture with a miscibility gap[END_REF], or drop sedimentation under gravity [START_REF] Jk Platten | Phase separation under a temperature gradient[END_REF][START_REF] Araki | Hydrodynamic delocalization of phase separation in a locally cooled fluid mixture[END_REF]. We propose an alternative approach that combines sedimentation and thin film interfacial flow. The coupling of surface and volume convection, generating a complex three-dimensional flow structure, is crucial in the separation dynamics. Together, they lead to remarkable phase separated patterns. The mechanisms are first detailed using an IL-water mixture, and their universality in term of wetting properties is validated with another well-known binary system: the lutidine-water mixture.

II. MATERIALS & METHODS

The microfluidic system is sketched in Fig. 1(a). The polydimethylsiloxane cavity is replicated from a micromilled brass mold and bonded on a glass coverslip with oxygen plasma treatment. The cavity is a cylinder of 1 cm in diameter whose height ranges from 20 to 200 µm. Its bottom surface is layed onto a glass wafer with micropatterned resistance (50×500 µm 2 ), electrically isolated by spincoating a 30 µm PDMS layer [START_REF] Kerdraon | Self-similar relaxation of confined microfluidic droplets[END_REF]. The potential applied to the heating resistor can be tuned up to 10 Volts. Phase separation dynamics is observed using bright-field transmitted light video microscopy. The main binary system under investigation is a mixture of MilliQ water with the ionic liquid tetrabutylphosphonium trifluoroacetate (P 4444 CF 3 CO 2 ) [START_REF] Kohno | Material design of ionic liquids to show temperature-sensitive lcst-type phase transition after mixing with water[END_REF][START_REF] Nitta | Mixing scheme of an aqueous solution of tetrabutylphosphonium trifluoroacetate in the water-rich region[END_REF] already used in different applications [START_REF] Hsu | Enhanced forward osmosis desalination with a hybrid ionic liquid/hydrogel thermoresponsive draw agent system[END_REF][START_REF] Kamio | Fundamental investigation of osmolality, thermoresponsive phase diagram, and water-drawing ability of ionic-liquid-based draw solution for forward osmosis membrane process[END_REF][START_REF] Cai | Energy-efficient desalination by forward osmosis using responsive ionic liquid draw solutes[END_REF], at an IL mass fraction of 25% (separation temperature T sep = 31 o C). This system is known as a Lower Critical Solution Temperature (LCST) binary solution, i.e. it phase separates above a critical temperature (see Fig. 1(b)). The interfacial tension of LCST mixtures increases with temperature and as a consequence the thermocapillary stress is directed toward the warmer region. Fig. 2(a) displays the measurements of the interfacial tension between the two separated phases versus the temperature of the mixture. They are performed in rising drop configuration (PSA30-Kruss), a circulating water-bath (Julabo HL-4) sets the temperature of the sample. The data of the IL-water mixture are compared to lutidine-water data from the literature [START_REF] Grattoni | Lower critical solution coexistence curve and physical properties (density, viscosity, surface tension, and interfacial tension) of 2, 6-lutidine+ water[END_REF].

The temperature mapping is performed independently using a temperature sensitive fluorescent solution (rhodamine-B, Sigma-Aldrich, 50 mg.L -1 ) [START_REF] Selva | An optimized resistor pattern for temperature gradient control in microfluidics[END_REF]. We did not achieve to measure the temperature in the cavity during a phaseseparation experiment: the rhodamine fluorescence is affected by the elevated Ionic Liquid concentration. The calculated Péclet number, P e = (Hv r )/α T ≈ 0.1 with H = 100 µm, α T = 1.5.10 -7 m.s -2 and v r = 150 µm.s -1 (see Fig. 6 for typical velocities), shows that the impact of convection on the temperature profile can be neglected. Moreover IL-water mixtures at 25wt% and rhodamine solutions have similar heat capacity and thermal diffusivity. Thus, we fill the same cavity (among others the same resistance) with a rhodamine solution and apply the same voltage. Once the voltage is applied to the resistor, the temperature suddenly increases at the resistor location. At early time, i.e. in the first second (see discussion on r out in section III.A), the temperature diffuses above the resistor displaying a 3D profile in the microfluidic cavity. After this transient stage, the temperature profile can be considered as 2D, i.e. diffuses radially along the cavity, and writes T (r, t). Fig. 2(b) displays the radial temperature profiles at different times and the inset shows the same curves rescaled by √ α T t, where α T = 1.5 × 10 -7 m 2 .s -1 is the thermal diffusivity of water. All profiles collapse on a single curve proving the 2D diffusion of temperature along the cavity with time. As for the dynamics of binary mixtures under homogeneous temperature, the initial composition of the solution imposes the phase separation pattern and kinetics [START_REF] Siggia | Late stages of spinodal decomposition in binary mixtures[END_REF][START_REF] Daniel | Kinetics and morphology of phase separation in fluids: The role of droplet coalescence[END_REF]. In the following, we focus on the case where the wetting phase (the IL-rich phase here) is the dispersed phase, i.e. the IL mass fraction is smaller than 35% (consolute point of the mixture). The other system is a mixture of MilliQ water with 2,6-lutidine (Sigma Aldrich) at 40 wt% in lutidine (T sep = 34 o C). In this case the wetting phase (the water-rich phase as the lutidine-rich phase is non-wetting with the plasma treated chips) is also the dispersed phase. The separation curves of both systems are displayed on Fig. 1(b).

III. RESULTS

A. Description of the separation pattern

The temperature diffusion triggers the phase separation which propagates from the center towards the edges. The separation temperature (T sep ) isotherm is directly visible at the front of the dark cloud stemming from the light scattering of the dense two phase system, whose droplets sizes are much smaller than the cavity thickness.

Qualitatively, the droplets size distribution in this cloud is not monodisperse as the droplets undergo ageing from the outside to the inside. The temperature steady state is reached after 6 ± 3 minutes depending on room temperature. For the whole span of cavity heights we observe the following behavior: the opaque cloud of droplets appearing above the resistor expands isotropically in 2D with the T sep isotherm diffusion (Fig. 3(a)): this front is tracked as r out following a square root dependence with time (cf. Fig. 4). The cloud opens up in its center (Fig. 3(b)) to reveal a darker IL-rich drop of radius r c , and in-between this drop and the cloud, a few droplets come back toward the central drop from r in (Fig. 3(b)-(d)). To clarify our explanation, the cavity is divided into four regions: I the region located outside the isotherm T sep in which the binary mixture is not separated yet (r > r out ), II the region within which the mixture is phase separated and the droplets move outwards following the temperature diffusion front (r in < r < r out ), III the region enriched in water in which small droplets are driven inwards (r c < r < r in ), and IV the region enriched in IL (r < r c ). Surprisingly, the droplets of regions II and III are driven in opposite sides (see Supplemental Movie S2 & S3). Fig. 4 represents the temporal evolution of the cloud outer radius r out which coincides with the propagation of the separation temperature isotherm T sep . As this evolution is due to quasi 2D temperature diffusion in the cavity, we recover a square root dependence with time (except for shorter times before 1 s, where we observe the signature of the 3D thermal diffusion). Nevertheless the direct comparison of r out (t) with the temperature profile evolution is tricky since a ± 1 o C variation gives an uncertainty of ± 500 µm on the radial position. The higher the voltage (and the heat injected in the system), the faster the isotherm propagates. The upper limit r out = 2.5 mm corresponds to the accessible visual window. At longer times, the temperature profile reaches a stationary state and r out tends to a constant (this regime is not displayed).

B. Flow profile in the cavity

In order to understand why the droplets of regions II and III are driven in opposite directions, it is necessary to tackle the 3D structure of the flow. This is possible using confocal microscopy (Leica DMi8 with scanning laser head TCS SP8) [START_REF] Dgal Aarts | Confocal scanning laser microscopy on fluid-fluid demixing colloid-polymer mixtures[END_REF] allowing direct visualization in a cross-section of the cavity (see Supplemental Movie S4). Fluorescein (Sigma-Aldrich) is added at 0.1 g.L -1 to the 25wt% IL solution. The microscope records the fluorescence of excited fluorescein within the IL-rich phase, while the water-rich phase is dark. Fig. 5(a)-(d) displays fluorescent images of the same cross-section in the cavity at different times. The front of the phase separation propagates (Fig. 5(a)), IL-rich droplets nucleate, grow in size and sediment (as the denser phase) (Fig. 5(b)). Their complete spreading on the bottom gives birth to a micrometer-thick wetting layer which thickness h grows rapidly to yield a value of 6 ± 2 µm throughout region III (Fig. 5(b)-(c)). Some IL-rich droplets are conveyed above the film toward the center (Fig. 5(c)-(d)) and meet with the IL-rich central drop expanding (Fig. 5(d)). Fig. 5(e) summarizes this 3D flow sketching the role of the film in region III: as the surface tension increases with temperature, a thermocapillary stress drives the interface of the bottom IL film toward the center of the cavity. Thanks to momentum diffusion, this interfacial transport drags the water-rich phase as well as the IL-rich droplets located just above. The intake of IL-rich phase from the film accumulates at the center where a single IL-rich drop grows in size (region IV ). The central drop profile can be sessile (Fig. 3(b)-(d)) or wetting-disk type (Fig. 5(d)). We believe that the sessile profile is out of equilibrium and is sustained by thermal interfacial stresses since the IL is completely wetting. Moreover a sessile drop could not exist in the cavity since the capillary length l c exceeds the confinement. When the apex of the sessile drop makes contact with the upper wall, the drop rearranges in a wetting disk configuration bridging cavity lower and upper walls. By mass conservation, the water-rich phase converging to the center is sent back outwards and pushes aside the cloud of droplets. We now show that it is possible to rationalize this scenario and find quantitative agreement between our measures and the model. Experimentally the velocity field is radial and, as the vertical length scales h and H are much smaller than r c , only the variation along z is considered. The dependence on r is contained in the interfacial stress ∂ r γ. Then the flow is assumed to follow the 2D Stokes equation in the lubrication approximation in a plan (r, z) as h H, see Appendix C. Region III is split in two domains to solve the equation: domain 1 refers to the IL-rich wetting film at the bottom, domain 2 refers to the upper phase enriched in water (Fig. 5(e)insets). The Stokes equation in domain 1, η IL ∂ 2 z v 1 = 0, is solved using v 1 (0) = 0 and the interfacial stress continuity at z = h: η IL (∂ z v 1 ) z=h -η w (∂ z v 2 ) z=h = ∂ r γ. In this domain, we neglect the radial pressure term in the above Stokes equation: as h H the velocity profile is well approximated by a linear Couette flow. Since the viscosity of the IL-rich phase is 5 times the viscosity of the water-rich phase: η IL ≈ 5η w , and the film thickness is 10 times smaller than the cavity thickness, we have η IL (∂ z v 1 ) z=h η w (∂ z v 2 ) z=h . As such, the flow field in domain 1 yields:

v 1 (∂ r γ, z) = ∂ r γ η IL z (1)
It is not possible to measure this velocity profile directly, nevertheless the droplets located just above the film are conveyed at a velocity with same order of magnitude thanks to viscous diffusion of momentum. These droplets can serve as tracers, noting that they move slower than the interface, until they eventually merge with the film. The temperature gradient range is ∂ r T ∈ [0.5 2] × 10 4 K.m -1 , which gives the expected interfacial velocities v 1 (h) ∈ [150 600] µm.s -1 , with ∂ T γ = 2.5.10 -5 N.m -1 .K -1 , η IL = 5.10 -3 Pa.s and h = 6 µm. We plot on Fig. 6 the droplets velocities measured by PIV for 5 successive times [START_REF] Thielicke | Pivlab-towards user-friendly, affordable and accurate digital particle image velocimetry in matlab[END_REF]. The maximum speed reaches 300 µm.s -1 at shorter times, showing good agreement with the order of magnitude of the calculated interfacial velocity. Flows stemming from buoyancy contribution are of typical velocity 0.008H 3 g∂ r ρ/η w ≈ 5 µm.s -1 and are thus found negligible [START_REF] Rivière | Convection flows driven by laser heating of a liquid layer[END_REF][START_REF] Selva | Solutal convection in confined geometries: Enhancement of colloidal transport[END_REF].

The linear distribution of the droplets velocities at each time is difficult to rationnalize since: 1) the droplets sediment throughout time and shall not keep the same distance from the film dragging them, 2) they are also submitted to thermocapillary action opposite to their direction of propagation and 3) they shrink in size while going up the temperature gradient because of composition equilibration (water is expelled from the IL-rich droplet). The sedimentation brings droplets closer to the film and should accelerate them even more. The contributions of thermocapillary action and droplet's size diminution should decrease the droplets speed. These contributions may balance each other since the thermocapillary force is proportionnal to R∂ r T (with R the droplet radius): ∂ r T increases as the droplet comes closer to the center but simultaneously R decreases. We do not model these effects analytically in this work. Inspired by the work of Roché et. al. on interfacial Marangoni flows [START_REF] Roché | Marangoni flow of soluble amphiphiles[END_REF], the inset on Fig. 6 shows the rescaled velocity profiles v r /v max as a function of the reduced radial coordinate (r in -r)/(r in -r c ). The collapse of the five profiles testifies that the droplets migration obeys the same mechanism and the above cited effects keep the same balance throughout time. In domain 2 of region III, the water-rich phase swept to the center by the shear flow has no option but to turn back when it reaches the central drop, due to axial symmetry and mass flux conservation. This counter Poiseuille flow adds up with the thermocapillary effect to push the cloud of region II outward (Fig. 5(e)). Considering the same assumptions as in domain 1, the flow in domain 2 is described by the Stokes equation:

η w ∂ 2 z v 2 = ∂ r p, which is solved using v 2 (H) = 0, v 1 (h) = v 2 (h) and the flux conservation h 0 v 1 (z)dz + H h v 2 (z)dz = 0, leading to: v 2 (∂ r γ, z) = ∂ r γ η IL h(H -z) (H -h) 1 - 3H(z -h) (H -h) 2 (2)
Then the average velocity of the Poiseuille flow v av 2 can be safely calculated.

C. Pattern dynamics: rin(t) and rc(t)

Consequently, the cloud inner radius r in is expected to move at a velocity which results from the addition of this Poiseuille flow to the thermocapillary migration, given by v T cap = R∂ T γ∂ r T 3η w (1 + 3η IL /2η w ) [START_REF] Chen | Surfactant-induced retardation of the thermocapillary migration of a droplet[END_REF]:

∂ t r in (t) = v av 2 (t) + v T cap (t) (3)
Thereby the temporal dependence of ∂ t r in is mainly carried by ∂ r γ(r = r in (t)). The confocal imaging allows us to estimate h 3 µm at r = r in and R 10 µm for the cloud droplets radii, which we set as constants over time (see Appendix C). Given these values, Fig. 7(a) displays the calculated Poiseuille contribution as a dashed line, and the sum of the Poiseuille and the thermocapillary migration as a solid line. Remarkably, this model reproduces the experimental data plotted as dark crosses showing the relevance of our model. In order to evaluate the sensitivity of the velocities on h and R, a variation of 30% is represented as lighter blue zones in the plots. Finally we explain the dynamics of the central drop radius r c plotted on Fig. 7(b). This drop is assumed to be a flat cylinder of volume V c = πr 2 c H which is filled by the flux coming from the IL-rich wetting film. The mass conservation leads to ∂ t V c = 2πr c h 0 ∂rγ η IL zdz. Assuming that the temperature gradient is inversely proportional to r, ∂ r T = ∆T /r (cf. Fig. 7(a)inset, this feature is discussed in Appendix A), we get:

r c (t) = ∂ T γ∆T h 2 Hη IL 1/2 t 1/2 = (ξt) 1/2 (4)
The inset of Fig. 7(b) compares the experimental and calculated values of the prefactor ξ for which we find good agreement without fitting parameter. Given the uncertainties yielded by ∆T and h, the confidence interval for ξ is within 20% of its value. As a whole, our model supports the scenario described previously. The data shown here correspond to a Voltage of 7 Volts. The measurements obtained for other voltages are gathered in Appendix B.

D. Late stage of the dynamics

With r in being propelled by both the Poiseuille flow and the thermocapillary migration, ∂ t r in is driven by a different mechanism than ∂ t r out . Hence the inner radius of the toroidal cloud can propagate faster than the T sep isotherm, and r in may overtake r out . It occurs after 10 to 100 seconds depending on the room temperature: the colder it is, the sooner r out starts to reach steady-state and the sooner r in catches up. When it happens the cloud vanishes gradually, the number of phase-separated IL-rich droplets diminishes drastically and the wetting layer suffers from a supply shortage in IL. The continuous drainage to the center thins the wetting film and triggers a periodic destabilization: the film configuration switches into several fingers (see Fig. 8). Along a finger the interfacial shear flow keeps dragging material from region I toward the central region. By doing so, the material starts to phase separate as the temperature rises, producing a visible darker plume composed of IL-rich droplets superimposed to the wetting film finger (see Supplemental Movie S5). This digitation pattern is maintained as long as the isotherm of phase separation T sep (i.e. r out ) keeps on propagating, it can last a few minutes. When T sep becomes static the fingers gradually disappear and we end up with the final state of the dynamics: the IL-rich wetting phase has accumulated at the center above the heating resistor while the water-rich non-wetting phase is distributed all around. The radius r out of the whole pattern is given by the position of T sep . The complete study of this instability is out of the scope of the paper. When r out exceeds the radius of the cavity, all the liquid in the cavity is phase separated. Increasing even more the temperature induces further concentration of both phases in their respective majority constituents (according to the phase diagram in Fig. 1(b)).

E. Lutidine-water system

In order to tackle the reproducibility of the demixing pattern regarding the role of the wetting phase, we performed the same experiments using another LCST binary mixture widely employed in the literature: the lutidine-water system. To do so, a binary solution with a weight fraction of 40% in Lutidine (T sep = 34 o C) is injected in the oxygen plasma treated cavity, such that water becomes the dispersed phase expected to develop a wetting film on the hydrophilic walls [START_REF] Beysens | Wetting-induced aggregation of colloids[END_REF]. In both cases the picture is taken when the wetting film has destabilized to form fingers. Qualitatively, the higher separation temperature of our lutidine-water mixture implies a slower propagation of r out compared to the IL-water experiments (the higher the separation temperature, the slower its isotherm propagates) and the destabilization of the wetting film happens at shorter times (the propagation pace of r in is tuned by the temperature gradient: a greater difference between room and resistor temperature implies a steeper gradient). Nevertheless the two patterns on Fig. 9 look very similar. As expected the water-rich phase behaves like the IL-rich phase discussed previously: the digitations cross the surrounding lutidine-rich phase and water is accumulated above the heating resistor. These results comfort the universality, in term of the wetting properties, of the demixing scenario.

IV. CONCLUSION

To conclude, we investigated the influence of a temperature gradient on the phase separation of LCST binary mixtures under confinement. Same as the experiments carried with homogeneous heating, the volume fraction and wetting behavior of both constituents drive the dynamics. The emergence of a micrometric wetting film submitted to thermal interfacial tension gradients is responsible for strong flows directed toward the warmer region. We rationalized the 3D complex flow generated by the separation and found good quantitative agreement with experimental measures. More importantly, the wetting phase carried in the film is entirely accumulated at the warmer side. Thus, tuning the wall surface energy allows to select which component shall be concentrated and eventually recovered. This behavior should be universal to all LCST binary mixtures. The present paper paves a way in binary mixture recycling. The impact of UCST behavior and spatial patterning in the cavity will be the object of future works [START_REF] Pascual | Wettability patterning in microfluidic devices using thermally-enhanced hydrophobic recovery of pdms[END_REF][START_REF] Nandyala | Design, fabrication, and analysis of a capillary diode for potential application in water-oil separation[END_REF][START_REF] Das | Surface-directed spinodal decomposition on chemically patterned substrates[END_REF][START_REF] Das | Surface-directed spinodal decomposition on morphologically patterned substrates[END_REF].

FIG. 1 .

 1 FIG. 1. (a) Top view of the microfluidic cavity 1 cm in diameter. The gold connectors are in dark grey, and the chromium resistor is in red (50x500 µm 2 ). (b) Phase diagram of the IL-water (blue dots) and lutidine-water systems (orange circles).The two sketches show the homogeneous and separated states of the mixture. The IL-rich is denser and colored with a blue dye.

FIG. 2 .

 2 FIG. 2. (a)Interfacial tension between the IL-rich (lutidine-rich) and the water-rich phases as a function of the temperature. The solid line gives ∂T γ = 2.5 × 10 -5 N.m -1 .K -1 for the IL-water system, the dashed line gives ∂T γ = 3.0 × 10 -5 N.m -1 .K -1 for the lutidine-water system (adapted from ref[START_REF] Grattoni | Lower critical solution coexistence curve and physical properties (density, viscosity, surface tension, and interfacial tension) of 2, 6-lutidine+ water[END_REF]). Inset: picture of the water-rich rising drop embed in a thermostated IL-rich bath. (b) Temperature profile in the cavity for six different times. The radial coordinate is the distance to the resistor center. The black dashed horizontal line indicates Tsep. Inset: temperature profile with the radial coordinate rescaled by a thermal diffusion lengthscale. The applied voltage is 7 Volt (80 mW).

FIG. 3 .

 3 FIG. 3. (a)-(d) Phase separation timelapse of the IL-water solution at 7 Volts (80 mW). The mass fraction in IL is 25% and the cavity height is H = 60 µm. (c) Definition of the four regions within which the flows are rationalized: I) IL-water non-separated mixture, II) Separation of the two phases, the droplets are mostly pushed outwards, III) some IL-rich droplets are dragged inward across the water-rich phase, IV) IL-rich sessile drop. Inset: Zoom on the droplets moving from the cloud to the center drop. (d) Definition of rc, rin and rout, corresponding to the central drop radius, along with the cloud inner and outer radii.

FIG. 4 .

 4 FIG.[START_REF] Douglas R Macfarlane | New dimensions in salt-solvent mixtures: a 4th evolution of ionic liquids[END_REF]. Position of the cloud outer radius rout versus the square root of time. Voltages applied are 7, 7.9, 8.6 and 9.2 Volts (R = 620 Ω). Cavity Height is H = 60 µm. IL mass fraction is 25%.

FIG. 5 .

 5 FIG. 5. (a)-(d) Confocal imaging of the phase separation along the height of the cavity at different times for 8 Volts (100 mW). The central drop seen on (d) is bridging top and bottom cavity walls. Scale bar is 40 µm. Cavity height is H = 120 µm. (e) Cross-section sketch of the phase separation dynamics. The tread-milling wetting film induces a radial Couette-Poiseuille flow. The regions I, II, III and IV delimit respectively the non-separated solution, the droplet cloud, the Couette-Poiseuille flow induced by the film, and the central IL-rich drop. The red rectangle respresents the heating resistor. Inset: within region III, domain 1 indicates the IL-rich wetting film and domain 2 the water-rich phase above.

1 FIG. 6 .

 16 FIG.[START_REF] Ohno | Functional design of ionic liquids: Unprecedented liquids that contribute to energy technology, bioscience, and materials sciences[END_REF]. Velocity vr of the droplets coming back to the center versus the radial coordinate, at five successive times: 5, 10, 15, 20 and 25 s. The mass fraction in IL is 25%, the cavity height is H = 60 µm and the voltage is 7 Volts. Inset: rescaled velocity versus the reduced spatial coordinate. All profiles collapse on a line with a slope of 1.

FIG. 7 .

 7 FIG. 7. (a) Measured velocity of the cloud inner radius ∂trin versus time, at 7 Volt (black crosses). The blue dashed line represents the average velocity of the Poiseuille contribution eq.(2). The blue solid line is the sum of the Poiseuille and thermocapillary contributions eq.(3). The blue shaded areas give a confidence interval related to a 30% variation in h and in R. Inset: Temperature gradient evolution in the cavity at 5, 10, 15, 20 and 25 seconds after switch-on, derived from the temperature profiles. The black dashed line is a 1/r fit. (b) Growth dynamics of the central drop radius rc = (ξt) 1/2 at four voltages. Inset: Comparison between calculated ξ (red circles) and experimental one (black crosses), see eq.(4).

FIG. 8 .

 8 FIG. 8. Destabilisation of the wetting film into periodic digitations as rin catches up rout. The central IL-rich drop is wetting both cavity floor and ceiling. The applied voltage is 8 Volt (100 mW) and the cavity height is H = 80 µm.

FIG. 9 .

 9 FIG. 9. Phase separation patterns of: (a) IL-water, (b) lutidine-water mixtures in a hydrophilic cavity. Mass fraction in IL and lutidine are respectively 25% and 40%: in both cases the wetting phase is the dispersed component. Images are taken respectively 55 and 10 seconds after switch-on. The applied voltage is 8 Volt (100 mW) and the cavity height is H = 80 µm. In both cases the cloud has vanished and the wetting film already destabilised to form digitations. On the left the central drop is the IL-rich phase (ILW ), while it is the water-rich phase (WLut) on the right. Scale bars are 300 µm.

Fig. 9

 9 Fig.9compares the demixing patterns of our two systems: IL-water on the left and lutidine-water on the right. In both cases the picture is taken when the wetting film has destabilized to form fingers. Qualitatively, the higher separation temperature of our lutidine-water mixture implies a slower propagation of r out compared to the IL-water experiments (the higher the separation temperature, the slower its isotherm propagates) and the destabilization of the wetting film happens at shorter times (the propagation pace of r in is tuned by the temperature gradient: a greater difference between room and resistor temperature implies a steeper gradient). Nevertheless the two patterns on Fig.9look very similar. As expected the water-rich phase behaves like the IL-rich phase discussed previously:

FIG. 10

 10 FIG. 10. (a) Velocity vr of the droplets coming back to the center versus the radial coordinate, at five successive times 5, 10, 15, 20 and 25 s, for three voltages: 7.9, 8.6 and 9.2 Volt. The mass fraction in IL is 25%, the cavity height is H = 60 µm. Inset: rescaled velocity versus the reduced spatial coordinate. All profiles collapse on a line with a slope of 1. (b) Measured velocity of the cloud inner radius ∂trin versus time, at 7.9, 8.6 and 9.2 Volt (black crosses). The blue dashed line represents the average velocity of the Poiseuille contribution eq.(2). The blue solid line is the sum of the Poiseuille and thermocapillary contributions eq.(3). The blue shaded areas give a confidence interval related to a 30% variation in h and in R. The grey shaded zone on the right is out of the observation window (r > 2500 µm). The mass fraction in IL is 25%, the cavity height is H = 60 µm.

FIG. 11 . 44 FIG. 12 .

 114412 FIG. 11. Phase separation at three consecutive times (12, 18 and 26 s) under monochromatic illumination (λ = 546 nm). The four concentric fringes due to the film are pointed out by the black hatched arcs. The blue and red hatched arcs indicate rc and rin respectively. The cavity height is H = 80 µm.

ACKNOWLEDGMENTS

The authors are grateful to L. Bocquet for driving them towards this subject, to E. Martin for his help with the micromilling device, and wish to thank M. Kerdraon, A. Mansur, L. Keiser, J. T. Stockmann, J. D. McGraw, D. Beysens and L. Leibler for fruitful discussions. This work was supported by CNRS, ESPCI Paris, Agence Nationale de la Recherche (ANR) under the grant ANR-18-CE09-0029, IPGG (Equipex ANR-10-EQPX-34 and Labex ANR-10-LABX-31) and PSL (Idex ANR-10-IDEX-0001-02).

APPENDIX A: TEMPERATURE PROFILE IN THE CAVITY

We legitimize here the use of ∂ r γ = ∆T /r in the paper. A simple model to estimate the dependence of T is to consider the heat diffusion equation between two concentric cylinders of radii r c and r in > r c , held at two temperatures T c and T in . Since r c and r in both follow a square-root dependence with time, we argue that T c and T in are rather constants and their value is determined by the y-axis values: T c = T (r c (t)/(α T t) 1/2 ) and T in = T (r in (t)/(α T t) 1/2 ) on Fig. 2(b)inset. Then the heat diffusion equation between moving boundaries r c (t) and r in (t) is stationary and we have:

which gives after integration:

So that the temperature gradient writes:

The uncertainty on T c and T in being related to the measure of r c and r in , we get a ±1.5 o C confidence interval on their values.

APPENDIX B: VELOCITIES MEASURED FOR OTHER VOLTAGES

We show here the droplets velocities v r measured by PIV (Fig. 10(a)) and the inner cloud radius propagating speed ∂ t r in (Fig. 10(b)) for three other voltages: 7.9, 8.6 and 9.2 Volts. At a constant room temperature, the higher the voltage applied, the higher the temperature gradient, and the higher the droplets velocities. Same as in Fig. 6, for each voltage the velocity profile is attenuated as the distance to the

APPENDIX C: INTERFEROMETRIC DETECTION OF THE WETTING FILM

The thickness variation of the wetting film is difficult to quantify with confocal experiments, but interferometric methods allow us to obtain at least one relative variation in height between two points [START_REF] Keiser | Marangoni bursting: evaporation-induced emulsification of binary mixtures on a liquid layer[END_REF]. We repeated the separation experiment with quasi-monochromatic illumination (mercury lamp filtered at λ = 546 nm) and a magnification x10 (against x5 usually). By playing with the contrast of the recorded movies, the interference fringes present at the liquidliquid interface of the film become visible. Fig. 11 shows three successive stages of separation under monochromatic illumination. Four dark fringes are visible and propagate radially following the same dynamics as the separation pattern. The inter-fringe distance decreases by 20% between the first and the third image. The difference in film thickness between two dark fringes is given by the formula:

with n f ilm the optical index of the liquid forming the wetting film. We measured independently and at room temperature the optical index of our ionic liquid solutions using a pocket refractometer (ATAGO 3850 PAL-RI). The measurements are shown in figure 12. Assuming the composition of the IL-rich wetting film is about 60 wt%, we use n f ilm ≈ 1.40 to calculate the thickness variation:

Thus the film sees its thickness vary by ±800 nm along the radial coordinate. The wetting film is not completely flat but this micrometric variation of the thickness over 1 mm in length shows the very small curvature of the interface


CHARACTERIZATION OF THE FRENCH RABBIT BREED FAUVE-DE-BOURGOGNE IN AN INTENSIVE SYSTEM

Keywords: Genetic resources, local breed, biodiversity, Oryctolagus cuniculus

A characterization of the French local breed Fauve-de-Bourgogne was realized on a population of 48 rabbits (11 males and 37 females) gathered from five different amateur farms located in the French regions of Alsace, Lorraine and Bourgogne. We checked the growth of future breeders, the female reproductive performances and their feed intake during the first 10 days of lactation, as well as the kit survival and growth. Fauve-de-Bourgogne female rabbits have an adult weight of about 4.3 (±0.43) kg and reached 84% of the adult weight around 5 months old. Under a reproductive rhythm of 42 days, reproductive performances were low. Fertility rates averaged 60% and litter sizes at birth averaged 4.3 (±2.7) newborn. On average, females weaned (at 35 days) 3.4 (±2.4) kits weighing 720 (±170) g. In the absence of antibiotics supplementation, kit survival was as high as 83% and growing animals reached 1649 (±192) g at 65 days old.

INTRODUCTION

Together with the increase of public concern to improve animal welfare, intensive farming faces the challenge of raising animals with the minimal use of antibiotics as possible. One strategy to reduce antibiotic dependence is to keep a herd of diseases resistant individuals. According to [START_REF] Hamilton | Sexual reproduction as an adaptation to resist parasites (a review)[END_REF], to resist numerous parasites, hosts species should preserve an array of genotypes (i.e. high genetic diversity). However, artificial selection tends to erode genetic diversity, and this is the case for the domestic rabbit. First because most rabbit selection programs used a limited genetic background as the base population (New Zealand White and California), and secondly because selection herds are managed in a close population with no introduction of foreign individuals [START_REF] Garreau | Génétique et sélection[END_REF]. The burden of such strategy is a reduced effective population size, the accumulation of inbreeding and a degraded fitness in the selection herd [START_REF] Pekkala | The effect of inbreeding rate on fitness, inbreeding depression and heterosis over a range of inbreeding coefficients[END_REF]. In addition to the erosion of genetic diversity, the use of antibiotics to sustain performance and health is a common practice extended in almost every selection and production farms since the advent of professional animal production [START_REF] Kirchhelle | Pharming animals: a global history of antibiotics in food production (1935-2017[END_REF]. The artificial selection (loss of genetic variety and fitness) coupled with a systematic use of antibiotics results in a population that is dependent on the use of chemical treatments to function properly. In this context, the use of local breeds raised in a variety of antibiotic 'free' environments together with commercial populations may help to increase the array of genotypes needed to avoid pathogens affecting intensive production systems. Another strategy is to cross commercial and local populations to boost genetic diversity, increasing thus the population adaptive response [START_REF] Spielman | Does inbreeding and loss of genetic diversity decrease disease resistance?[END_REF], while benefiting from the achievements of breeding programs. The obtained outbreed individuals are expect to better resist infections and to perform well at different set of environmental conditions [START_REF] Kargo | Short communication: Is crossbreeding only beneficial in herds with low management level?[END_REF]. In France, there is at least 10 local rabbit breeds (FAO, 2015) with a population size big enough to allow their multiplication and use under intensive farming systems. One of such breed is the Fauve-de-Bourgogne, a medium-size breed that presents a reasonable prolificacy and growth rate [START_REF] Bolet | Evaluation of the reproductive performance of eight rabbit breeds on experimental farms[END_REF], being also renowned among amateurs farmers as a robust breed. However, there is still a lack of scientific information concerning growth and the reproductive potential of using this breed under intensive conditions to increase the genetic array of a herd (i.e. mixed breed population). In this sense, we characterized a population of the French rabbit breed Fauve-de-Bourgogne, raised under intensive farming conditions, to be potentially used as a pure breed or as a crossbred with commercial rabbit lines in systems promoting an augmentation of the genetic diversity at the herd level.

MATERIALS AND METHODS

The French Committee no. 115 for Ethics, Science and Animal Health approved all procedures.

Origin of Fauve-de-Bourgogne rabbits

We gathered a population of 48 Fauve-de-Bourgogne rabbits (11 males and 37 females) from five different farms located in the French regions of Alsace (n = 24), Lorraine (n = 17) and Bourgogne (n = 7). Animals were born between April and June 2018 and most individuals had between 78 and 94 days at their arrival at our experimental farm (n = 38). Ten animals had between 107 and 152 days old. They are sons and daughters of 14 males and 19 females. Sires and grand-sires of our animals were not related.

Management practices and measures

From September 2018 to May 2019, each rabbit lived indoors in wire cages (W×L×H: 62×68×50 cm). At all times, the daylight program was set to a 16/8h light/dark cycle with indoor temperatures set to vary between 15 and 28 °C. All animals had free access to water and to a commercial diet containing 12.4 MJ of DE per kg of DM, 17.6% of CP, 2.5% of EE, 31.9% of NDF, 16.5% of ADF, and 5.1% of ADL on a DM basis. Natural mattings occurred every 42 days (three consecutive attempts) and weaning at 35 days. Weaned kits were raised until 65 days of age. At parturition, females having zero born alive and those that did not produce milk adopted no kits. We individually recorded the female's live weight, reproductive performance and feed intake for the first 10 days of lactations. On males, we recorded their live weight gain. We checked the litter weight at birth and at 16 days, and recorded individual live weight of kits at 35, 50 and 65 days of age. Individual mortality was also recorded. Growing kits were housed in wire cages (W×L×H: 46×76×30 cm) to a maximum of five animals per cage with room temperatures set to vary between 15 and 28 °C. To avoid digestive troubles, growing kits received 50 g of a commercial diet at 35 days, then 90 g per day from 36 to 42 days old, 110 g per day from 43 to 49 days old and 130 g per day from 50 to 56 days old. From day 57 onwards, feed was freely available. The commercial diet offered to growing kits contained 11.3 MJ of DE per kg of DM, 15.4% of CP, 1.9% EE, 37.5% of NDF, 20.5% of ADF and 6.4% of ADL on a DM basis, but no antibiotics. At all times, growing kits had free access to fresh water.

Statistical Analyses

We used the R-software, version 3.6.0 (R core Team, 2019) to analyse our data. We used a general linear model for litter traits and kits live weight data, a mixed model (including the individual as a mixed effect) for female feed intake data, and a logistic regression model for female fertility and kits survival data. Female parity (1, 2 or 3) was the dependent variable of all models.

RESULTS AND DISCUSSION

Live weight of Fauve-de-Bourgogne rabbits of both sexes aged between 78 and 343 days are in Figure 1. At 149 days old (5 months), female rabbits weighed 3.6 (±0.44) kg and had a stable weight of 4.3 (±0.43) kg around 9 months. It indicates that Fauve-de-Bourgogne female rabbits could be mated as soon as they reach ≥ 3.6 kg (~80% of adult weight). We did not observed a live weight plateau in our male rabbit population. Main reproductive traits of Fauve-de-Bourgogne females at parturition 1, 2 and 3 are in Table 1. Although not significantly, fertility rate at 2nd parity was numerically superior to values observed at 1st and at 3rd parity (+13.2 and +19.1 points, respectively). These values are in line with those reported by [START_REF] Bolet | Evaluation of the reproductive performance of eight rabbit breeds on experimental farms[END_REF] for this same breed, but falls far below the fertility reported for a commercial Spanish crossbreed line (85.0%; Martinez-Paredes et al., 2018). The average number of kits born alive was 4.3 (±2.7) and it seems to be superior at 3rd parity respect to the 1st and 2nd parities (+2.0 kits; P<0.10). The number of stillborn and weaned kits were constant among parities. Kits survival during lactation dropped between the 1st and the 3rd parity from 83 to 39% (P<0.05). This drop is partly explained by the reduced number of females raising a litter (n = 6). In fact, one female weaned none of the seven kits it adopted and two others, raising nine kits, weaned only two. The average birth weight was 53.3 g (range: 26.2 to 72.5 g), being constant among parities. Although kits weight at mid-lactation (16 days) was higher in the 1st parity than in the following ones (+68.0 g; P<0.05), their weaning weight was lower with respect of the 2nd (-262 g) and the 3rd (-132 g) parities. Weaning weight of kits from the 1st parity was very low (584 g), but the values observed in the subsequent mattings (around 780 g) were close to those reported by [START_REF] Paës | Onset of feed intake of the suckling rabbit and evidence of dietary preferences according to pellet physical properties[END_REF] for kits raised by primiparous females of the French hybrid line PS19 (on average 816 g) in the same facilities. Feed intake of females during the first 10 days of lactation of parities 1, 2 and 3 are in Figure 2.

Figure 2: Feed intake (g/day) of female rabbits during the first 10 days of lactation 1, 2 and 3. Red dots represents non-lactating females and blue dots lactating females. Size of the raised litters are represented by the size of the dots (small for zero kits, medium for litters between 4 and 6 kits and big for litters of 8 or 9 kits). Lines represented the number of litters raised per female. No lines no litters, dotted lines 1 litter, dashed lines 2 litters and solid lines 3 litters.

At each lactation, feed intake of nursing females was higher than no lactating females (+137.5, +92.8 and +82.8 g/day for parity 1, 2 and 3 respectively; P<0.01). Among nursing females, and independently from the size of the nursed litter (range 4 to 9), the average feed intake was similar at lactations 1, 2 and 3 (272, 254 and 213 g/day, respectively). Nine females raised zero litters, 18 raised 1, 5 raised 2s and only 1 female raised 3 litters.

Performance traits of growing rabbit kits are in Table2. Live weight of growing kits at 65 days from the 2nd and the 3rd parity was, on average, 105 g higher than values of growing kit from the 1st parity (P<0.05). The average daily gain (between 35 and 65 days) of growing rabbits from the 3rd parity was 2.6 g/day higher (P<0.05) than values of kits from the 1st and 2nd parity. Those values were lower (less 7.1 g/day) than those observed for the French crossbreed PS19 line raised in the same facilities (38.4 g/day; [START_REF] Paës | Onset of feed intake of the suckling rabbit and evidence of dietary preferences according to pellet physical properties[END_REF]. Survival rate of growing kits from the 1st, 2nd and the 3rd parity were 82.2%, 77.5% and 100%, respectively.

CONCLUSIONS

Under intensive farming system, the reproductive performances of Fauve-de-Bourgogne female rabbits are low. The average daily gain observed and the high survival during growing period (96 kits alive at 65 days of 114 weaned kits at 35 days), in the absence of any antibiotics treatments, makes this breed an interesting genetic material to be considered in crossbreed schemes with prolific pure lines to benefit of the complementary traits of these genetics.

Figure 1 :

 1 Figure 1: Individual live weight of Fauvede-Bourgogne rabbits of both sexes in function of age. Black curves represents the estimated live weight in function of age (non-parametric local polynomial regression fitting: loess) and the shadow grey area the 95% confidence interval around the fitted curve. Dashed black segments represents the weight of female rabbits (3.6 kg) at a median age of 149 days (5 months).

Table 1 :

 1 Reproductive traits of Fauve-de-Bourgogne female rabbits at 1st, 2nd and 3rd parity. Means (SE). Means of a variable followed by distinct letters differs at P<0.05. †Average litter size raised by 11, 14 or 6 females at first, second and third matting, respectively

	Reproductive traits

ABC

Table 2 :

 2 Growth and survival of Fauve-de-Bourgogne growing rabbits from first, second and third parity. Means (SE).

	Performance traits	First	Female parity Second	Third
	Live weight (g)
	at 35 days	584 a (18.2)	847 b (17.4)	710 c (26.6)
	at 50 days	1074 a (26.6) 1261 b (25.9) 1170 ab (36.2)
	at 65 days	1581 a (30.7) 1705 b (30.3) 1667 ab (40.7)
	Average daily gain (g/day)
	35 to 50 days	30.0 (0.95)	29.6 (0.90)	30.7 (1.20)
	50 to 65 days	34.6 a (1.12) 30.5 b (1.09)	35.5 a (1.45)
	35 to 65 days	30.8 a (0.75) 30.0 a (0.74)	33.0 b (0.98)
	Survival 35 to 65 days (%)	82.2 (5.7)	77.5 (6.0)	100 (0.0)
	abc Means of a variable followed by distinct letters differs at P<0.05.

ACKNOWLEDGEMENTS

Authors acknowledges the Department PHASE of INRAE for the economic support and A. Raulain for gathering and providing the rabbits studied.