For a microchamber filled with a binary electrolyte and containing a flat un-biased center electrode at one wall, we employ three numerical models to study the strength of the resulting induced-charge electro-osmotic (ICEO) flow rolls: (i) a full nonlinear continuum model resolving the double layer, (ii) a linear slip-velocity model not resolving the double layer and without tangential charge transport inside this layer, and (iii) a nonlinear slip-velocity model extending the linear model by including the tangential charge transport inside the double layer. We show that compared to the full model, the slip-velocity models significantly overestimate the ICEO flow. This provides a partial explanation of the quantitative discrepancy between observed and calculated ICEO velocities reported in the literature. The discrepancy increases significantly for increasing Debye length relative to the electrode size, i.e. for nanofluidic systems. However, even for electrode dimensions in the micrometer range, the discrepancies in velocity due to the finite Debye length can be more than 10% for an electrode of zero height and more than 100% for electrode heights comparable to the Debye length.
The microchannel corner is a common inherent component of most planar microfluidic systems and thus its influence on the channel flow is of significant interest. Application of an alternating current electric field enables quantification of the non-linear induced-charge electro-osmosis (ICEO) ejection flow effect by isolating it from linear electro-osmotic background flow which is present under dc forcing. The hydrodynamic flow in the vicinity of a sharp channel corner is analyzed using experimental micro-particle-image-velocimetry (PIV) and numerical simulations for different buffer concentra…
We analyze the AC electro-osmotic motion of a 1:1 aqueous solution, taking into account the difference in mobilities and diffusion coefficients between positive and negative ions. This model serves to understand the behavior of common systems as a solution of NaCl in water. We pay special attention to two cases. First, the case of slightly different mobilities, that can model a KCl solution. Second, the case of a strongly asymmetric solution, with an almost vanishing mobility, applicable to the case of a salt where the negative ion is much more massive than the positive one. For all the cases,…
Nonlinear behavior of electro-osmosis in dilute non-adsorbing polymer solutions with low salinity is investigated with Brownian dynamics simulations and a kinetic theory. In the Brownian simulations, the hydrodynamic interaction between the polymers and a no-slip wall is considered with Rotne-Prager approximation of Blake tensor. In a plug flow under a sufficiently strong applied electric field, the polymer migrates toward the bulk, forming a depletion layer thicker than the equilibrium one. Consequently, the electro-osmotic mobility increases nonlinearly with the electric field and gets satur…
Electro-osmosis (EO) is a powerful tool to manipulate liquids in micro and nanofluidic systems. While EO has been studied extensively at liquid-solid interfaces, the case of liquid-vapor interfaces, found e.g. in foam films and bubbles, remains to be explored. Here we perform molecular dynamics (MD) simulations of EO in a film of aqueous electrolyte covered with fluid layers of ionic surfactants and surrounded by gas. Following the experimental procedure, we compute the zeta potential from the EO velocity, defined as the velocity difference between the middle of the liquid film and the surroun…
We consider laminar flow of incompressible electrolytes in long, straight channels driven by pressure and electro-osmosis. We use a Hilbert space eigenfunction expansion to address the general problem of an arbitrary cross section and obtain general results in linear-response theory for the mass and charge transport coefficients which satisfy Onsager relations. In the limit of non-overlapping Debye layers the transport coefficients are simply expressed in terms of parameters of the electrolyte as well as the hydraulic radius R=2A/P with A and P being the cross-sectional area and perimeter, res…
We give a general theoretical description of electro-osmotic flow at striped super-hydrophobic surfaces in a thin double layer limit, and derive a relation between the electro-osmotic mobility and hydrodynamic slip-length tensors. Our analysis demonstrates that electro-osmotic flow shows a very rich behavior controlled by slip length and charge at the gas sectors. In case of uncharged liquid-gas interface, the flow is the same or inhibited relative to flow in homogeneous channel with zero interfacial slip. By contrast, it can be amplified by several orders of magnitude provided slip regions ar…
A model is constructed to describe the arbitrary deformation of a drop or vesicle that contains and is embedded in an electrolyte solution, where the deformation is caused by an applied electric field. The applied field produces an electrokinetic flow or induced charge electro-osmosis. The model is based on the coupled Poisson-Nernst-Planck and Stokes equations. These are reduced or simplified by forming the limit of strong electrolytes, for which ion densities are relatively large, together with the limit of thin Debye layers. Debye layers of opposite polarity form on either side of the drop …
We describe the general phenomenon of `induced-charge electro-osmosis' (ICEO) -- the nonlinear electro-osmotic slip that occurs when an applied field acts on the ionic charge it {\sl induces} around a polarizable surface. Motivated by a simple physical picture, we calculate ICEO flows around conducting cylinders in steady (DC), oscillatory (AC), and suddenly-applied electric fields. This picture, and these systems, represent perhaps the clearest example of nonlinear electrokinetic phenomena. We complement and verify this physically-motivated approach using a matched asymptotic expansion to the…
Since its prediction fifteen years ago, electro-osmotic instability has been attributed to non-equilibrium electro-osmosis related to the extended space charge which develops at the limiting current in the course of concentration polarization at a charge-selective interface. This attribution had a double basis. Firstly, it has been recognized that equilibrium electro-osmosis cannot yield instability for a perfectly charge-selective solid. Secondly, it has been shown that non-equilibrium electro-osmosis can. First theoretical studies in which electro-osmotic instability was predicted and analyz…
Analytic expressions for the speed, flux, microrotation, stress, and couple stress in a micropolar fluid exhibiting steady, symmetric and one-dimensional electro-osmotic flow in a uniform cylindrical microcapillary were derived under the constraint of the Debye-Hueckel approximation, which is applicable when the cross-sectional radius of the microcapillary exceeds the Debye length, provided that the zeta potential is sufficiently small in magnitude. As the aciculate particles in a micropolar fluid can rotate without translation, micropolarity influences fluid speed, fluid flux, and one of the …
We give a general, physical description of ``induced-charge electro-osmosis'' (ICEO), the nonlinear electrokinetic slip at a polarizable surface, in the context of some new techniques for microfluidic pumping and mixing. ICEO generalizes ``AC electro-osmosis'' at micro-electrode arrays to various dielectric and conducting structures in weak DC or AC electric fields. The basic effect produces micro-vortices to enhance mixing in microfluidic devices, while various broken symmetries -- controlled potential, irregular shape, non-uniform surface properties, and field gradients -- can be exploited t…
Induced-charge electro-osmosis (ICEO) is shown to control the length scale of the diffusion layer (DL), which in turn, affects the diffusion limited ion transport through the microchannel-Nafion membrane system. The ICEO vortices form at an interdigitated floating electrode array embedded within a microchannel interfacing a Nafion membrane and stir the fluid, arresting the diffusive growth of the depletion layer. By varying the spacing between the array and the membrane we are able to control the length of the DL. Activating the electrodes results in further enhancement of the fluid stirring d…
We study the deformation and breakup of an axisymmetric electrolyte drop which is freely suspended in an infinite dielectric medium and subjected to an imposed electric field. The electric potential in the drop phase is assumed small, so that its governing equation is approximated by a linearized Poisson-Boltzmann or modified Helmholtz equation (the Debye-Hückel regime). An accurate and efficient boundary integral method is developed to solve the low-Reynolds-number flow problem for the time-dependent drop deformation, in the case of arbitrary Debye layer thickness. Extensive numerical results…
We report that an electro-osmotic instability of concentration enrichment in curved geometries for an aqueous electrolyte, as opposed to the well-known one, is initiated exclusively at the enriched interface (anode), rather than at the depleted one (cathode). For this instability, the limitation of unrealistically high material Peclet number in planar geometry is eliminated by the strong electric field arising from the line charge singularity. In a model setup of concentric circular electrodes, we show by stability analysis, numerical simulation, and experimental visualization that instability…
We investigate the possibility that electrically neutral porous spheres electrophorese in electrolyte solutions with asymmetric affinity of ions to spheres on the basis of electrohydrodynamics and the Poisson-Boltzmann and Debye-Bueche-Brinkman theories. Assuming a weak electric field and ignoring the double-layer polarization, we obtain analytical expressions for electrostatic potential, electrophoretic mobility, and flow field. In the equilibrium state, the Galvani potential forms across the interface of the spheres. Under a weak electric field, the spheres show finite mobility with the same…
