Rubinstein-Zaltzman Instability in Micro- and Nano-Channels (original) (raw)
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Electro-osmotic slip and electroconvective instability
Journal of Fluid Mechanics, 2007
Electric conduction from an electrolyte solution into a charge selective solid, such as ion exchange membrane or electrode, becomes unstable when the electrolyte concentration near the interface approaches zero owing to diffusion limitation. The sequence of events leading to instability is as follows: upon the decrease of the interface concentration, the electric double layer at the interface transforms from its common quasi-equilibrium structure to a different, non-equilibrium one. The key feature of this new structure is an extended space charge added to the usual one of the quasi-equilibrium electric double layer. The non-equilibrium electro-osmotic slip related to this extended space charge renders the quiescent conductance unstable. A unified asymptotic picture of the electric double-layer undercurrent, encompassing all regimes from quasi-equilibrium to the extreme non-equilibrium one, is developed and employed for derivation of a universal electro-osmotic slip formula. This formula is used for a linear stability study of quiescent electric conduction, yielding the precise parameter range of instability, compared with that in the full electroconvective formulation. The physical mechanism of instability is traced both kinematically, in terms of non-equilibrium electro-osmotic slip, and dynamically, in terms of forces acting in the electric double layer.
Electroconvective instability in concentration polarization and nonequilibrium electro-osmotic slip
Physical Review E, 2005
This paper concerns the comparison of electroconvective instability in concentration polarization at an ion-selective membrane with previously reported nonequilibrium electro-osmotic instability. Electro-osmotic formulation represents an asymptotic limit case of the electroconvective one. An improved nonequilibrium electro-osmotic slip formula is derived. Linear stability analysis for various nonequilibrium electro-osmotic formulations is carried out, including the analytic studies of the short-and long-wave limits. The obtained results are compared with those for a full electroconvective formulation. It is observed that the shortwave singularity typical for the nonequilibrium electro-osmotic instability is removed in the full electroconvective formulation. The effect of ionic diffusivities ratio on stability is discussed.
Electrokinetic microflow instability with conductivity gradients
2003
We have experimentally identified and quantified an electrokinetic flow instability that occurs in DC-electric-field driven microfluidic channels with significant conductivity gradients. We have, for the first time, developed a physical model for this instability which captures the interactions between bulk charge accumulation, electromigration, convection, and diffusion. A linear stability analysis based on this model captures key physics of this convective instability with a threshold electric field, The model and experiments show conductivity gradients and their associated bulk charge accumulation are crucial for such instabilities.
Convective instability of electrokinetic flows in a cross-shaped microchannel
2006
We present a parametric experimental study of convective electrokinetic instability (EKI) in an isotropically etched, cross-shaped microchannel using quantitative epifluorescence imaging. The base state is a three-inlet, one-outlet electrokinetic focusing flow configuration where the centre sample stream and sheath flows have mismatched ionic conductivities. Electrokinetic flows with conductivity gradients become unstable when the electroviscous stretching and folding of conductivity interfaces grows faster than the dissipative effect of molecular diffusion. Scalar images, critical applied fields required for instability, and temporal and spatial scalar energy are presented for flows with a wide range of applied d.c. electric field and centre-tosheath conductivity ratios. These parameters impose variations of the electric Rayleigh number across four orders of magnitude. We introduce a scaling for charge density in the bulk fluid as a function of local maximum conductivity gradients in the flow. This scaling shows that the flow becomes unstable at a critical electric Rayleigh number (Ra e, = 205) and applies to a wide range of applied field and centre-tosheath conductivity ratios. This work is relevant to on-chip electrokinetic flows with conductivity gradients such as field amplified sample stacking, flow at the intersections of multi-dimensional assays, electrokinetic control and separation of sample streams with poorly specified chemistry, and low-Reynolds number micromixing. † Present address:
Electrokinetic instabilities in thin microchannels
2005
An important class of electrokinetic, microfluidic devices aims to pump and control electrolyte working liquids that have spatial gradients in conductivity. These high-gradient flows can become unstable under the application of a sufficiently strong electric field. In many of these designs, flow channels are thin in the direction orthogonal to the main flow and the conductivity gradient. Viscous stresses due to the presence of these walls introduce a stabilizing force that plays a major role in determining the overall instability. A thin channel model for fluid flow is developed and shown to provide good agreement with a complete three-dimensional model for channel aspect ratios Շ0.1.
Physical Review Fluids, 2017
Equilibrium electroconvective instability at a perfectly charge-selective solid, such as ion-exchange membrane or metal electrode, previously deemed impossible, is possible if one takes into account finite electrical conductivity of the solid. A simple model of electroconvective diffusion of ions in the depleted diffusion layer in this system predicts a supercritical transition to instability in the vicinity of the limiting current, as opposed to the subcritical transition for the previously studied nonequilibrium instability related to the extended space charge. The linear stability analysis in this model yields the division of the parameter space into domains in which each instability mechanism with its characteristic signatures dominates. Identification of the particular instability mechanism for a given system requires a detailed experimental study of the vicinity of the instability threshold in terms of both the voltage versus current dependence and flow visualization.
Equilibrium Electro-osmotic Instability
Since its prediction 15 years ago, hydrodynamic instability in concentration polarization at a chargeselective interface has been attributed to nonequilibrium electro-osmosis related to the extended space charge which develops at the limiting current. This attribution had a double basis. On the one hand, it has been recognized that neither equilibrium electro-osmosis nor bulk electroconvection can yield instability for a perfectly charge-selective solid. On the other hand, it has been shown that nonequilibrium electroosmosis can. The first theoretical studies in which electro-osmotic instability was predicted and analyzed employed the assumption of perfect charge selectivity for the sake of simplicity and so did the subsequent studies of various time-dependent and nonlinear features of electro-osmotic instability. In this Letter, we show that relaxing the assumption of perfect charge selectivity (tantamount to fixing the electrochemical potential of counterions in the solid) allows for the equilibrium electroconvective instability. In addition, we suggest a simple experimental test for determining the true, either equilibrium or nonequilibrium, origin of instability in concentration polarization.
Instability of Electrokinetic Microchannel Flows With Conductivity Gradients
2004
Electrokinetic flow is leveraged in a variety of applications, and is a key enabler of on-chip electrophoresis systems. An important sub-class of electrokinetic devices aim to pump and control electrolyte working liquids with spatial gradients in conductivity. These high-gradient flows can become unstable under the application of a sufficiently strong electric field. In this work the instability physics is explored using theoretical and numerical analyses, as well as experimental observations. The flow in a long, rectangular-cross-section channel is considered. A conductivity gradient is assumed to be orthogonal to the main flow direction, and an electric field is applied in the streamwise direction. It is found that such a system exhibits a critical electric field above which the flow is highly unstable, resulting in fluctuating velocities and rapid stirring. Modeling results compare well with experimental observations. The model indicates that the fluid forces associated with the thin dimension of the channel ͑transverse to both the conductivity gradient and the main flow direction͒ tends to stabilize the flow. These results have application to the design and control of on-chip assays that require high conductivity gradients, and provides a rapid mixing mechanism for low Reynolds number flows in microchannels.
Interfacial electrokinetic effect on the microchannel flow linear stability
TRANSACTIONS-AMERICAN SOCIETY OF …, 2004
The electrostatic double layer (EDL) effect on the linear hydrodynamic stability of microchannel flows is investigated. It is shown that the EDL destabilizes the Poiseuille flow considerably. The critical Reynolds number decreases by a factor five when the nondimensional Debye-Huckel parameter is around ten. Thus, the transition may be quite rapid for microchannels of a couple of microns heights in particular when the liquid contains a very small number of ions. The EDL effect disappears quickly for у150 corresponding typically to channels of heights 400 m or larger. These results may explain why significantly low critical Reynolds numbers have been encountered in some experiments dealing with microchannel flows.