Search

We have developed a poly(dimethylsiloxane) (PDMS) microfluidic chip to study the directional drying of a colloidal dispersion confined in a channel. Our measurements on a dispersion of silica nanoparticles once again revealed the phenomenology commonly observed for such systems: the formation of a porous solid with linear growth in the channel at short times, slowing down at longer times as the evaporation rate decreases. The growth of the solid is also accompanied by mechanical stresses that are released by the delamination of the solid from the channel walls and the formation of cracks. In addition to these observations, we report original measurements using hydrophilic filler in the PDMS formulation used (Sylgard-184). When the PDMS matrix is in contact with water, water molecules pool around these hydrophilic sites, resulting in the formation of microscopic water clusters whose size depends on the water potential $\psi$. In our work, we have used these water clusters to estimate the water potential profile in the channel as the porous solid grows. Using a transport model that also takes into account solid delamination in the channel, we then linked these water potential measurements to the hydraulic permeability of the porous solid. These measurements finally enabled us to show that the slowdown in the evaporation rate is due to the invasion of the porous solid by air/water nanomenisci at a critical capillary pressure $\psi_\text{cap}$.

We have developed a microfluidic tool to measure the diffusion coefficient $D$ of solutes in an aqueous solution, by following the temporal relaxation of an initially steep concentration gradient in a microchannel. Our chip exploits multilayer soft lithography and the opening of a pneumatic microvalve to trigger the interdiffusion of pure water and the solution initially separated in the channel by the valve, the so-called free interface diffusion technique. Another microvalve at a distance from the diffusion zone closes the channel and thus suppresses convection. Using this chip, we have measured diffusion coefficients of solutes in water with a broad size range, from small molecules to polymers and colloids, with values in the range $D \in [10^{-13}- 10^{-9}]$~m$^2$/s. The same experiments but with added colloidal tracers also revealed diffusio-phoresis and diffusio-osmosis phenomena due to the presence of the solute concentration gradient. We nevertheless show that these interfacial-driven transport phenomena do not affect the measurements of the solute diffusion coefficients in the explored concentration range., Comment: 12 pages, 11 figures

We show, using a model coupling mass transport and liquid theory calculations for a charge-stabilized colloidal dispersion, that diffusion significantly limits measurement times of its Equation Of State (EOS), osmotic pressure vs composition, using the osmotic compression technique. Following this result, we present a microfluidic chip allowing one to measure the entire EOS of a charged dispersion at the nanoliter scale in a few hours. We also show that time-resolved analyses of relaxation to equilibrium in this microfluidic experiment lead to direct estimates of the collective diffusion coefficient of the dispersion in Donnan equilibrium with a salt reservoir., Comment: 7 pages, 4 figures

We theoretically investigate the role of solutal free convection on the diffusion of a buoyant solute at the microfluidic scales, $\simeq 5$--$500~\mu$m. We first consider a horizontal microfluidic slit, one half of which initially filled with a binary solution (solute and solvent), and the other half with pure solvent. The buoyant forces generate a gravity current that couples to the diffusion of the solute. We perform numerical resolutions of the 2D model describing the transport of the solute in the slit. This study allows us to highlight different regimes as a function of a single parameter, the Rayleigh number $\text{Ra}$ which compares gravity-induced advection to solute diffusion. We then derive asymptotic analytical solutions to quantify the width of the mixing zone as a function of time in each regime and establish a diagram that makes it possible to identify the range of $\text{Ra}$ and times for which buoyancy does not impact diffusion. In a second step, we present numerical resolutions of the same model but for a 3D microfluidic channel with a square cross-section. We observe the same regimes as in the 2D case, and focus on the dispersion regime at long time scales. We then derive the expression of the 1D dispersion coefficient for a channel with a rectangular section, and analyse the role of the transverse flow in the particular case of a square section. Finally, we show that the impact of this transverse flow on the solute transport can be neglected for most of the microfluidic experimental configurations., Comment: 38 pages, 15 figures

In the present work, we use Mach-Zehnder interferometry to thoroughly investigate the drying dynamics of a 2D confined drop of a charged colloidal dispersion. This technique makes it possible to measure the colloid concentration field during the drying of the drop at a high accuracy (about 0.5%) and with a high temporal and spatial resolution (about 1 frame/s and 5 $\mu$m/pixel). These features allow us to probe mass transport of the charged dispersion in this out-of-equilibrium situation. In particular, our experiments provide the evidence that mass transport within the drop can be described by a purely diffusive process for some range of parameters for which the buoyancy-driven convection is negligible. We are then able to extract from these experiments the collective diffusion coefficient of the dispersion $D(\varphi)$ over a wide concentration range $\varphi=0.24$-$0.5$, i.e. from the liquid dispersed state to the solid glass regime, with a high accuracy. The measured values of $D(\varphi)\simeq 5$-$12 D_0$ are significantly larger than the simple estimate $D_0$ given by the Stokes-Einstein relation, thus highlighting the important role played by the colloidal interactions in such dispersions.

We investigate the impact of buoyancy on the solute mass transport in an evaporating liquid mixture (non-volatile solute $+$ solvent) confined in a slit perpendicular to the gravity. Solvent evaporation at one end of the slit induces a solute concentration gradient which in turn drives free convection due to the difference between the densities of the solutes and the solvent. From the complete model coupling mass transport and hydrodynamics, we first use a standard Taylor-like approach to derive a one dimensional non-linear advection-dispersion equation describing the solute concentration process for a dilute mixture. We then perform a complete analysis of the expected regimes using both scaling analysis and asymptotic solutions of this equation. The validity of this approach is confirmed using a thorough comparison with the numerical resolution of both the complete model and the 1D advection-dispersion equation. Our results show that buoyancy-driven free convection always impacts solute mass transport at long time scales, dispersing solutes in a steadily increasing length scale along the slit. Beyond this confined drying configuration, our work also provides an easy way for evaluating the relevance of buoyancy on mass transport in any other microfluidic configuration involving concentration gradients., Comment: 12 pages, 5 figures

We present a microfluidic method leading to accurate measurements of the mutual diffusion coefficient of a liquid binary mixture over the whole solute concentration range in a single experiment. This method fully exploits solvent pervaporation through a poly(dimethylsiloxane) (PDMS) membrane to obtain a steady concentration gradient within a microfluidic channel. Our method is applicable for solutes which cannot permeate through PDMS, and requires the activity and the density over the full concentration range as input parameters. We demonstrate the accuracy of our methodology by measuring the mutual diffusion coefficient of the water (1) $+$ glycerol (2) mixture, from measurements of the concentration gradient using Raman confocal spectroscopy and the pervaporation-induced flow using particle tracking velocimetry., Comment: 9 pages, 8 figures

We investigated theoretically water evaporation from concentrated supramolecular mixtures, such as solutions of polymers or amphiphilic molecules, using numerical resolutions of a one dimensional model based on mass transport equations. Solvent evaporation leads to the formation of a concentrated solute layer at the drying interface, which slows down evaporation in a long-time scale regime. In this regime, often referred to as the falling rate period, evaporation is dominated by diffusive mass transport within the solution, as already known. However, we demonstrate that, in this regime, the rate of evaporation does not also depend on the ambient humidity for many molecular complex fluids. Using analytical solutions in some limiting cases, we first demonstrate that a sharp decrease of the water chemical activity at high solute concentration, leads to evaporation rates which depend weakly on the humidity, as the solute concentration at the drying interface slightly depends on the humidity. However, we also show that a strong decrease of the mutual diffusion coefficient of the solution enhances considerably this effect, leading to nearly independent evaporation rates over a wide range of humidity. The decrease of the mutual diffusion coefficient indeed induces strong concentration gradients at the drying interface, which shield the concentration profiles from humidity variations, except in a very thin region close to the drying interface., Comment: 13 pages, 10 figures

We performed a thorough investigation of the drying dynamics of a charged colloidal dispersion drop in a confined geometry. We developed an original methodology based on Raman micro-spectroscopy to measure spatially-resolved colloids concentration profiles during the drying of the drop. These measurements lead, for the first time, to estimates of the collective diffusion coefficient of the dispersion over a wide range of concentration. The collective diffusion coefficient is one order of magnitude higher than the Stokes-Einstein estimate showing the importance of the electrostatic interactions for the relaxation of concentration gradients. At the same time, we also performed fluorescence imaging of tracers embedded within the dispersion during the drying of the drop, which reveals two distinct regimes. At early stages, concentration gradients along the drop lead to buoyancy-induced flows. Strikingly, these flows do not influence the colloidal concentration gradients that generate them, as the mass transport remains dominated by diffusion. At longer time scales, the tracers trajectories reveal the formation of a gel which dries quasi homogeneously. For such a gel, we show using linear poro-elastic modeling, that the drying dynamics is still described by the same transport equations as for the liquid dispersion. However, the collective diffusion coefficient follows a modified generalized Stokes-Einstein relation, as also demonstrated in the context of unidirectional consolidation by Style et al. [Crust formation in drying colloidal suspensions, Style et al., Proc. R. Soc. A 467, 174 (2011)]., Comment: 11 pages, 7 figures

Hierarchical self-assembly arranges nanostructures at different length scales. It gradually becomes an effective method of fabricating artificial metamaterials from composite nanostructures tailored for a particular response. Hierarchical self-assembly overcomes shortcomings of "top-down" methods by significantly reducing fabrication time and making it possible to form bulk materials. Here we report an application of hierarchical self-assembly of metal nanoparticles for the creation of the first isotropic optical metamaterial with strong artificial magnetism in blue light. We have used colloidal self-assembly to create artificial "nanomolecules" that generate the desired magnetic response and microfluidic self-assembly to produce a bulk metastructure. We demonstrate that the magnetic response of the final material is accurately described by an isotropic magnetic permeability that satisfies the principle of locality. Our approach unlocks the fabrication of large volumes of composite nanomaterials. Moreover, the spatial disorder inherent to this "bottom-up" method holds the key to solving the non-locality problem. The technique can be readily extended to the future generations of low-loss optical metamaterials made of dielectric nano-blocks to bypass the limitations of optical losses associated with plasmonic resonances in noble metals., Comment: Main article:10 pages, 4 figures. Supplementary information: 11 pages, 7 figures

X-ray Photon Correlation Spectroscopy (XPCS) has emerged as a unique technique allowing the measurement of dynamics in materials on mesoscopic lengthscales. In particular, applications in soft matter physics cover a broad range of topics which include, but are not limited to, nanostructured materials such as colloidal suspensions or polymers, dynamics at liquid surfaces, membranes and interfaces, and the glass or gel transition. One of the most common problems associated with the use of bright X-ray beams with soft materials is beam induced radiation damage, and this is likely to become an even more limiting factor at future synchrotron and free electron laser sources. Flowing the sample during data acquisition is one of the simplest method allowing to limit the radiation damage. In addition to distributing the dose over many different scatterers, the method also enables new functionalities such as time-resolved studies in mixing cells. Here, we further develop an experimental technique that was recently proposed combining XPCS and continuously flowing samples. More specifically, we use a model system to show how the macroscopic advective response to flow and the microscopic dissipative dynamics (diffusion) can be quantified from the X-ray data. The method has many potential applications, e.g. dynamics of glasses and gels under continuous shear/flow, protein aggregations processes, the interplay between dynamics and rheology in complex fluids., Comment: 11 pages, 5 figures

We consider a situation commonly encountered in microfluidics: two streams of miscible liquids are brought at a junction to flow side by side within a microchannel, allowing solutes to diffuse from one stream to the other and possibly react. We focus on two model problems: (i) the transverse transport of a single solute from a stream into the adjacent one, (ii) the transport of the product of a diffusion-controlled chemical reaction between solutes originating from the two streams. Our description is made general through a non-dimensionalized formulation that incorporates both the parabolic Poiseuille velocity profile along the channel and thermal diffusion in the transverse direction. Numerical analysis over a wide range of the streamwise coordinate $x$ reveal different regimes. Close to the top and the bottom walls of the microchannel, the extent of the diffusive zone follows three distinct power law regimes as $x$ is increased, characterized respectively by the exponents 1/2, 1/3 and 1/2. Simple analytical arguments are proposed to account for these results.

We have developed an original setup using microfluidic tools allowing one to produce continuously monodisperse microreactors ($\approx 100$ nL), and to control their temperatures as they flow in the microdevice. With a specific microchannels geometry, we are able to apply large temperature quenches to droplets containing a KNO$_3$ solution (up to 50$^{\circ}$C in 10 s), and then to follow nucleation kinetics at high supersaturations. By measuring the probability of crystal presence in the droplets as a function of time, we estimate the nucleation rate for different supersaturations, and confront our results to the classical nucleation theory.

We present an experimental study of the flow dynamics of a lamellar phase sheared in the Couette geometry. High-frequency ultrasonic pulses at 36 MHz are used to measure time-resolved velocity profiles. Oscillations of the viscosity occur in the vicinity of a shear-induced transition between a high-viscosity disordered fluid and a low-viscosity ordered fluid. The phase coexistence shows up as shear bands on the velocity profiles. We show that the dynamics of the rheological data result from two different processes: (i) fluctuations of slip velocities at the two walls and (ii) flow dynamics in the bulk of the lamellar phase. The bulk dynamics are shown to be related to the displacement of the interface between the two differently sheared regions in the gap of the Couette cell. Two different dynamical regimes are investigated under applied shear stress: one of small amplitude oscillations of the viscosity ($\delta\eta/\eta\simeq 3$%) and one of large oscillations ($\delta\eta/\eta\simeq 25$%). A phenomenological model is proposed that may account for the observed spatio-temporal dynamics, Comment: 16 pages, 17 figures, submitted to Eur. Phys. J. E

Experimental observations of droplet size sustained oscillations are reported in a two-phase flow between a lamellar and a sponge phase. Under shear flow, this system presents two different steady states made of monodisperse multilamellar droplets, separated by a shear-thinning transition. At low and high shear rates, the droplet size results from a balance between surface tension and viscous stress whereas for intermediate shear rates, it becomes a periodic function of time. A possible mechanism for such kind of oscillations is discussed.

Using Dynamic Light Scattering in heterodyne mode, we measure velocity profiles in a much studied system of wormlike micelles (CPCl/NaSal) known to exhibit both shear-banding and stress plateau behavior. Our data provide evidence for the simplest shear-banding scenario, according to which the effective viscosity drop in the system is due to the nucleation and growth of a highly sheared band in the gap, whose thickness linearly increases with the imposed shear rate. We discuss various details of the velocity profiles in all the regions of the flow curve and emphasize on the complex, non-Newtonian nature of the flow in the highly sheared band., Comment: 4 pages, 5 figures, submitted to Phys. Rev. Lett

We describe an optical fiber based interferometer to measure velocity profiles in sheared complex fluids using Dynamic Light Scattering (DLS). After a review of the theoretical problem of DLS under shear, a detailed description of the setup is given. We outline the various experimental difficulties induced by refraction when using a Couette cell. We also show that homodyne DLS is not well suited to measure quantitative velocity profiles in narrow-gap Couette geometries. On the other hand, the heterodyne technique allows us to determine the velocity field inside the gap of a Couette cell. All the technical features of the setup, namely its spatial resolution ($\approx 50$--$100 \mu$m) and its temporal resolution ($\approx 1$ s per point, $\approx 1$ min per profile) are discussed, as well as the calibration procedure with a Newtonian fluid. As briefly shown on oil-in-water emulsions, such a setup permits one to record both velocity profiles and rheological data simultaneously, Comment: 13 pages, 16 figures, Submitted to Eur. Phys. J. AP

We present local velocity measurements in emulsions under shear using heterodyne Dynamic Light Scattering. Two emulsions are studied: a dilute system of volume fraction $\phi=20$ % and a concentrated system with $\phi=75$ %. Velocity profiles in both systems clearly show the presence of wall slip. We investigate the evolution of slip velocities as a function of shear stress and discuss the validity of the corrections for wall slip classically used in rheology. Focussing on the bulk flow, we show that the dilute system is Newtonian and that the concentrated emulsion is shear-thinning. In the latter case, the curvature of the velocity profiles is compatible with a shear-thinning exponent of 0.4 consistent with global rheological data. However, even if individual profiles can be accounted for by a power-law fluid (with or without a yield stress), we could not find a fixed set of parameters that would fit the whole range of applied shear rates. Our data thus raise the question of the definition of a global flow curve for such a concentrated system. These results show that local measurements are a crucial complement to standard rheological tools. They are discussed in light of recent works on soft glassy materials., Comment: 13 pages, 21 figures, submitted to Eur. Phys. J. E