Order-Disorder Structural Transitions in Mazes Built by Evaporating Drops.

We show that the evaporation of surfactant solutions confined in quasi-two-dimensional porous media creates micron-sized labyrinthine patterns composing the walls of a centimeter-sized maze. These walls are made of solid deposits formed during drying via a sequence of individual Haines jumps occurring at the pore scale. We rationalize this process driven by simple iterative rules with a cellular automaton that acts as a maze generator. This model well describes the formation dynamics and final structure of an experimental maze as functions of the wettability heterogeneities of a porous medium and its geometry. Also, our findings unveil the crucial role of two geometric dimensionless quantities that control the structural order of a maze.

Path selection rules for droplet trains in single-lane microfluidic networks.

We investigate the transport of periodic trains of droplets through microfluidic networks having one inlet, one outlet, and nodes consisting of T junctions. Variations of the dilution of the trains, i.e., the distance between drops, reveal the existence of various hydrodynamic regimes characterized by the number of preferential paths taken by the drops. As the dilution increases, this number continuously decreases until only one path remains explored. Building on a continuous approach used to treat droplet traffic through a single asymmetric loop, we determine selection rules for the paths taken by the drops and we predict the variations of the fraction of droplets taking these paths with the parameters at play including the dilution. Our results show that as dilution decreases, the paths are selected according to the ascending order of their hydrodynamic resistance in the absence of droplets. The dynamics of these systems controlled by time-delayed feedback is complex: We observe a succession of periodic regimes separated by a wealth of bifurcations as the dilution is varied. In contrast to droplet traffic in single asymmetric loops, the dynamical behavior in networks of loops is sensitive to initial conditions because of extra degrees of freedom.

Towards high throughput production of artificial egg oocytes using microfluidics.

The production of micron-size droplets using microfluidic tools offers new opportunities to carry out biological assays in a controlled environment. We apply these strategies by using a flow-focusing microfluidic device to encapsulate Xenopus egg extracts, a biological system recapitulating key events of eukaryotic cell functions in vitro. We present a method to generate monodisperse egg extract-in-oil droplets and use high-speed imaging to characterize the droplet pinch-off dynamics leading to the production of trains of droplets. We use fluorescence microscopy to show that our method does not affect the biological activity of the encapsulated egg extract by observing the self-organization of microtubules and actin filaments, two main biopolymers of the cell cytoskeleton, encapsulated in the produced droplets. We anticipate that this assay might be useful for quantitative studies of biological systems in a confined environment as well as high throughput screenings for drug discovery.

Complex dynamics of droplet traffic in a bifurcating microfluidic channel: periodicity, multistability, and selection rules.

The binary path selection of droplets reaching a T junction is regulated by time-delayed feedback and nonlinear couplings. Such mechanisms result in complex dynamics of droplet partitioning: numerous discrete bifurcations between periodic regimes are observed. We introduce a model based on an approximation that makes this problem tractable. This allows us to derive analytical formulae that predict the occurrence of the bifurcations between consecutive regimes, establish selection rules for the period of a regime, and describe the evolutions of the period and complexity of droplet pattern in a cycle with the key parameters of the system. We discuss the validity and limitations of our model which describes semiquantitatively both numerical simulations and microfluidic experiments.

Droplet motion in microfluidic networks: Hydrodynamic interactions and pressure-drop measurements.

We present experimental, numerical, and theoretical studies of droplet flows in hydrodynamic networks. Using both millifluidic and microfluidic devices, we study the partitioning of monodisperse droplets in an asymmetric loop. In both cases, we show that droplet traffic results from the hydrodynamic feedback due to the presence of droplets in the outlet channels. We develop a recently-introduced phenomenological model [W. Engl, Phys. Rev. Lett. 95, 208304 (2005)] and successfully confront its predictions to our experimental results. This approach offers a simple way to measure the excess hydrodynamic resistance of a channel filled with droplets. We discuss the traffic behavior and the variations in the corresponding hydrodynamic resistance length L_{d} and of the droplet mobility beta , as a function of droplet interdistance and confinement for channels having circular or rectangular cross sections.

Dynamics of wetting: from inertial spreading to viscous imbibition.

We report the influence of the nature of boundaries on the dynamics of wetting. We review some work recently published and highlight new experimental observations. Our paper begins with the spreading of drops on substrates and demonstrates how the exponents of the spreading laws are affected either by the surface chemistry or by the droplet shape. We then discuss the imbibition of completely and partially wetting fluids into channels and over microtextured surfaces. Starting with the one-dimensional imbibition of completely wetting liquids in tubes and surface textures, we show that (i) shape variations of channels change the power-law response of the imbibition and (ii) the geometrical parameters of a surface roughness change the spreading behavior. For partially wetting fluids, we observe directionally dependent spreading: polygonal wetted domains can be obtained. We conclude with a tabular summary of our findings, allowing us to draw connections between the different systems investigated, and shed light on open questions that remain to be addressed.

Slow relaxation mode in concentrated oil-in-water microemulsions consisting of repulsive droplets.

The present contribution reports on the observation of two diffusive relaxation modes in a concentrated microemulsion made of repulsive droplets. These two modes can be interpreted in the frame of Weissman's and Pusey's theoretical pioneering works. The fast mode is associated to the collective diffusion of droplets whereas the slow one corresponds to the relaxation of droplet concentration fluctuations associated with composition and/or size. We show that (i) repulsive interactions considerably slow down the latter and (ii) a generalized Stokes Einstein relationship between its coefficient of diffusion and the Newtonian viscosity of the solutions, similar to the Walden's rule for electrolytes, holds for concentrated microemulsion systems made of repulsive droplets.

Study and formation of vesicle systems with low polydispersity index by ultrasound method.

The formation of liposomes with low polydispersity index by application of ultrasounds was investigated considering methodology specifications such as sonication time and sonication power. Phosphatidylcholine (PC) liposomes were formed by the evaporation-hydration method. The vesicles were sonicated using several sonication conditions. The liposomes were then characterized by dynamic light scattering (DLS) and freeze-fracture electron microscopy (FFEM). Correlation functions from DLS were treated by cumulants method and GENDIST to obtain the mean radius and polydispersity index. These calculations allowed to fix an optimal sonication time (3000 s) and a useful interval of ultrasound power between 39 and 91 W. DLS and FFEM results confirmed that vesicle size, lamellarity and the polydispersity index decreased with the increase of sonication power. Thus, we propose a systematic method to form liposomes in which the physical characteristics of the vesicles may be controlled as a function of sonication time and power.

Structural steady states and relaxation oscillations in a two-phase fluid under shear flow: experiments and phenomenological model.

By means of several rheophysics techniques, we report on an extensive study of the couplings between flow and microstructures in a two-phase fluid made of lamellar (L(alpha)) and sponge (L(3)) phases. Depending on the nature of the imposed dynamical parameter (stress or shear rate) and on the experimental conditions (brine salinity or temperature), we observe several different structural steady states consisting of either multilamellar droplets (with or without a long range order) or elongated (L(3)) phase domains. Two different astonishing phenomena, shear-induced phase inversion and relaxation oscillations, are observed. We show that (i) phase inversion is related to a shear-induced topological change between monodisperse multilamellar droplets and elongated structures and (ii) droplet size relaxation oscillations result from a shear-induced change of the surface tension between both coexisting (L(alpha)) and (L(3)) phases. To explain these relaxation oscillations, we present a phenomenological model and compare its numerical predictions to our experimental results.

Can a droplet break up under flow without elongating? Fragmentation of smectic monodisperse droplets.

We study the fragmentation under shear flow of smectic monodisperse droplets at high volume fraction. Using small angle light scattering and optical microscopy, we reveal the existence of a break-up mechanism for which the droplets burst into daughter droplets of the same size. Surprisingly, this fragmentation process, which is strain controlled and occurs homogeneously in the cell, does not require any transient elongation of the droplets. Systematic experiments as a function of the initial droplet size and the applied shear rate show that the rupture is triggered by an instability of the inner droplet structure.

Shear-induced formation of vesicles in membrane phases: kinetics and size selection mechanisms, elasticity versus surface tension.

Multilamellar vesicles can be formed upon shearing lamellar phases (L(alpha)) and phase-separated lamellar-sponge (L(alpha)/L(3)) mixtures. In the first case, the vesicle volume fraction is always 100% and the vesicle size is monitored by elasticity ("onion textures"). In the second system the vesicle volume fraction can be tuned from 0 to 100% and the mean size results from a balance between capillary and viscous forces ("Taylor droplets"). However, despite these differences, in both systems we show that the formation of vesicles is a strain-controlled process monitored by a universal primary buckling instability of the lamellae.

Instability of a lamellar phase under shear flow: formation of multilamellar vesicles.

The formation of closed-compact multilamellar vesicles (referred to in the literature as the "onion texture") obtained upon shearing lamellar phases is studied using small-angle light scattering and cross-polarized microscopy. By varying the shear rate gamma;, the gap cell D, and the smectic distance d, we show that: (i) the formation of this structure occurs homogeneously in the cell at a well-defined wave vector q(i), via a strain-controlled process, and (ii) the value of q(i) varies as (dgamma;/D)(1/3). These results strongly suggest that formation of multilamellar vesicles may be monitored by an undulation (buckling) instability of the membranes, as expected from theory.