Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions.

The venerable theory of electrokinetic phenomena rests on the hypothesis of a dilute solution of point-like ions in quasi-equilibrium with a weakly charged surface, whose potential relative to the bulk is of order the thermal voltage (kT/e approximately 25 mV at room temperature). In nonlinear electrokinetic phenomena, such as AC or induced-charge electro-osmosis (ACEO, ICEO) and induced-charge electrophoresis (ICEP), several V approximately 100 kT/e are applied to polarizable surfaces in microscopic geometries, and the resulting electric fields and induced surface charges are large enough to violate the assumptions of the classical theory. In this article, we review the experimental and theoretical literatures, highlight discrepancies between theory and experiment, introduce possible modifications of the theory, and analyze their consequences.

Kinetic theory of plastic flow in soft glassy materials.

A kinetic model for the elastoplastic dynamics of a jammed material is proposed, which takes the form of a nonlocal--Boltzmann-like--kinetic equation for the stress distribution function. Coarse graining this equation yields a nonlocal constitutive law for the flow, exhibiting as a key dynamic quantity the local rate of plastic events. This quantity, interpreted as a local fluidity, is spatially correlated with a correlation length diverging in the quasistatic limit, i.

Suppression of instabilities in multiphase flow by geometric confinement.

We investigate the effect of confinement on drop formation in microfluidic devices. The presence or absence of drop formation is studied for two immiscible coflowing liquids in a microfluidic channel, where the channel width is considerably larger than the channel height. We show that stability of the inner fluid thread depends on the channel geometry: when the width of the inner fluid is comparable to or larger than the channel height, hydrodynamic instabilities are suppressed, and a stable jet that does not break into drops results; otherwise, the inner fluid breaks into drops, in either a dripping or jetting regime.

Stochastic low Reynolds number swimmers.

As technological advances allow us to fabricate smaller autonomous self-propelled devices, it is clear that at some point directed propulsion could not come from pre-specified deterministic periodic deformation of the swimmer's body and we need to develop strategies for extracting a net directed motion from a series of random transitions in the conformation space of the swimmer. We present a theoretical formulation for describing the 'stochastic motor' that drives the motion of low Reynolds number swimmers based on this concept, and use it to study the propulsion of a simple low Reynolds number swimmer, namely, the three-sphere swimmer model. When the detailed balanced is broken and the motor is driven out of equilibrium, it can propel the swimmer in the required direction.

Stability of a jet in confined pressure-driven biphasic flows at low Reynolds number in various geometries.

We adress the question of the stability of a confined coflowing jet at low Reynolds number in various geometries. Our study is motivated by recent experiments in microfluidic devices. When immiscible fluids flow in microchannels, either monodisperse droplets or parallel flows are obtained depending upon the flow rate of the aqueous phase and the oil phase.

Analytic results for the three-sphere swimmer at low Reynolds number.

The simple model of a low Reynolds number swimmer made from three spheres that are connected by two arms is considered in its general form and analyzed. The swimming velocity, force-velocity response, power consumption, and efficiency of the swimmer are calculated both for general deformations and also for specific model prescriptions. The role of noise and coherence in the stroke cycle is also discussed.

Droplet traffic in microfluidic networks: a simple model for understanding and designing.

We propose a simple model to analyze the traffic of droplets in microfluidic "dual networks." Such functional networks which consist of two types of channels, namely, those accessible or forbidden to droplets, often display a complex behavior characteristic of dynamical systems. By focusing on three recently proposed configurations, we offer an explanation for their remarkable behavior.

Mechanical response of a small swimmer driven by conformational transitions.

A conformation space kinetic model is constructed to drive the deformation cycle of a three-sphere swimmer to achieve propulsion at low Reynolds number. We analyze the effect of an external load on the performance of this kinetic swimmer and show that it depends sensitively on where the force is exerted, so that there is no general force-velocity relation. We discuss how the conformational cycle of such swimmers should be designed to increase their performance in resisting forces applied at specific points.

Stability of a jet in confined pressure-driven biphasic flows at low reynolds numbers.

Motivated by its importance for microfluidic applications, we study the stability of jets formed by pressure-driven concentric biphasic flows in cylindrical capillaries. The specificity of this variant of the classical Rayleigh-Plateau instability is the role of the geometry which imposes confinement and Poiseuille flow profiles. We experimentally evidence a transition between situations where the flow takes the form of a jet and regimes where drops are produced.

Building up longitudinal concentration gradients in shallow microchannels.

We demonstrate a compact and low consumption (60 nL) method for generating concentration gradients along microchannels with shallow parabolic cross-sections. The regimes of dispersion at work in such systems and the resulting concentration fields are described theoretically and experimentally. Experiments are performed in PDMS (polydimethylsiloxane) microchannels actuated by integrated valves.

Imbibition by polygonal spreading on microdecorated surfaces.

Micropatterned surfaces have been studied extensively as model systems to understand influences of topographic or chemical heterogeneities on wetting phenomena. Such surfaces yield specific wetting or hydrodynamic effects, for example, ultrahydrophobic surfaces, 'fakir' droplets, tunable electrowetting, slip in the presence of surface heterogeneities and so on. In addition, chemical patterns allow control of the locus, size and shape of droplets by pinning the contact lines at predetermined locations.

Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson-Nernst-Planck equations.

In situations involving large potentials or surface charges, the Poisson-Boltzman (PB) equation has shortcomings because it neglects ion-ion interactions and steric effects. This has been widely recognized by the electrochemistry community, leading to the development of various alternative models resulting in different sets "modified PB equations," which have had at least qualitative success in predicting equilibrium ion distributions. On the other hand, the literature is scarce in terms of descriptions of concentration dynamics in these regimes.

Steric effects in the dynamics of electrolytes at large applied voltages. I. Double-layer charging.

The classical Poisson-Boltzmann (PB) theory of electrolytes assumes a dilute solution of point charges with mean-field electrostatic forces. Even for very dilute solutions, however, it predicts absurdly large ion concentrations (exceeding close packing) for surface potentials of only a few tenths of a volt, which are often exceeded, e.g.

Impact dynamics for elastic membranes.

We study the dynamic response of stretched thin polymeric films following an impact by a rigid sphere. We vary the sphere radius, the impact velocity, and the film tension, and measure the contact time and the maximum deflection of the film during the impact. The response is sensitive to nonlinearities associated with the additional tension provided by the deformation.

Experimental characterization of hydrodynamic dispersion in shallow microchannels.

Hydrodynamic dispersion in shallow microchannels with almost parabolic cross-sectional shapes and with heights much less than their widths is studied experimentally. Both long serpentine channels and rotary mixers are used. The experimental results demonstrate that the dispersion depends on the width rather than the height of the channel.

ac electrokinetic micropumps: the effect of geometrical confinement, Faradaic current injection, and nonlinear surface capacitance.

Recent experiments have demonstrated that ac electrokinetic micropumps permit integrable, local, and fast pumping (velocities approximately mm/s) with low driving voltage of a few volts only. However, they also displayed many quantitative and qualitative discrepancies with existing theories. We therefore extend the latter theories to account for three experimentally relevant effects: (i) vertical confinement of the pumping channel, (ii) Faradaic currents from electrochemical reactions at the electrodes, and (iii) nonlinear surface capacitance of the Debye layer.

Thin double layer approximation to describe streaming current fields in complex geometries: analytical framework and applications to microfluidics.

We set up an analytical framework that allows one to describe and compute streaming effects and electro-osmosis on an equal footing. This framework relies on the thin double layer approximation commonly used for description of electroosmotic flows, but rarely used for streaming problems. Using this framework we quantitatively assess the induction of bulk streaming current patterns by topographic or charge heterogeneities on surfaces.

Stable modification of PDMS surface properties by plasma polymerization: application to the formation of double emulsions in microfluidic systems.

We describe a method based on plasma polymerization for the modification and control of the surface properties of poly(dimethylsiloxane) (PDMS) surfaces. By depositing plasma polymerized acrylic acid coatings on PDMS, we succeeded to fabricate stable (several days) hydrophilic and patterned hydrophobic/hydrophilic surfaces. We used this approach to generate direct and (for the first time in this material) double emulsions in PDMS microchannels.

Giant amplification of interfacially driven transport by hydrodynamic slip: diffusio-osmosis and beyond.

We demonstrate that "moderate" departures from the no-slip hydrodynamic boundary condition (hydrodynamic slip lengths in the nanometer range) can result in a very large enhancement--up to 2 orders of magnitude--of most interfacially driven transport phenomena. We study analytically and numerically the case of neutral solute diffusio-osmosis in a slab geometry to account for nontrivial couplings between interfacial structure and hydrodynamic slip. Possible outcomes are fast transport of particles in externally applied or self-generated gradient, and flow enhancement in nano- or microfluidic geometries.

Microevaporators for kinetic exploration of phase diagrams.

We use pervaporation-based microfluidic devices to concentrate species in aqueous solutions with spatial and temporal control of the process. Using experiments and modeling, we quantitatively describe the advection-diffusion behavior of the concentration field of various solutions (electrolytes, colloids, etc.) and demonstrate the potential of these devices as universal tools for the kinetic exploration of the phases and textures that form upon concentration.

Hydrodynamic dispersion in shallow microchannels: the effect of cross-sectional shape.

We highlight the fact that hydrodynamic dispersion in shallow microchannels is in most cases controlled by the width of the cross section rather than by the much thinner height of the channel. We identify the relevant time scales that separate the various regimes involved. Using the lubrication approximation, we provide simple formulas that permit a quantitative evaluation of dispersion for most shallow cross-sectional shapes in the "long-time" Taylor regime, which is effectively diffusive.

Droplet traffic at a simple junction at low capillary numbers.

We report that, when a train of confined droplets flowing through a channel reaches a junction, the droplets either are alternately distributed between the different outlets or all collect into the shortest one. We argue that this behavior is due to the hydrodynamic feedback of droplets in the different outlets on the selection process occurring at the junction. A "mean field" model, yielding semiquantitative results, offers a first guide to predict droplet traffic in branched networks.

Aging and nonlinear rheology in suspensions of polyethylene oxide-protected silica particles.

In an attempt to establish connections between classical rheology and aging in paste colloidal suspensions, we report in this paper a large set of experimental results on a given system. We have studied suspensions of polyethylene oxide-protected silica particles and performed classical rheology experiments that exhibit a very nonlinear behavior. We have then evidenced aging through stress relaxation as observed in various glassy systems, and finally show other manifestations of aging through various rheological experiments.