Two-dimensional numerical simulation of microscale thermoelectrokinetic instability

Two-dimensional direct numerical simulation of thermoelectrokinetic instability in electrolyte bounded by semiselective surfaces was conducted for the first time. The results of numerical experiments show that the convective motion in the electrolyte takes place due to the stability loss of one-dimensional steady state solution. This motion manifested itself in two-dimensional structures similar to electroconvective rolls. What fundamentally differs is formation of thin lines connecting the membranes, where the salt concentration reaches its maximum value. Electric current in the system, obviously, will firstly flow through these lines

Two-dimensional numerical simulation of microscale thermoelectrokinetic instability

Two-dimensional direct numerical simulation of thermoelectrokinetic instability in electrolyte bounded by semiselective surfaces was conducted for the first time. The results of numerical experiments show that the convective motion in the electrolyte takes place due to the stability loss of one-dimensional steady state solution. This motion manifested itself in two-dimensional structures similar to electroconvective rolls. What fundamentally differs is formation of thin lines connecting the membranes, where the salt concentration reaches its maximum value. Electric current in the system, obviously, will firstly flow through these lines

Transitions and Instabilities in Imperfect Ion-Selective Membranes

Numerical investigation of the underlimiting, limiting, and overlimiting current modes and their transitions in imperfect ion-selective membranes with fluid flow through permitted through the membrane is presented. The system is treated as a three layer composite system of electrolyte-porous membrane-electrolyte where the Nernst–Planck–Poisson–Stokes system of equations is used in the electrolyte, and the Darcy–Brinkman approach is employed in the nanoporous membrane. In order to resolve thin Debye and Darcy layers, quasi-spectral methods are applied using Chebyshev polynomials for their accumulation of zeros and, hence, best resolution in the layers. The boundary between underlimiting and overlimiting current regimes is subject of linear stability analysis, where the transition to overlimiting current is assumed due to the electrokinetic instability of the one-dimensional quiescent state. However, the well-developed overlimiting current is inherently a problem of nonlinear stability and is subject of the direct numerical simulation of the full system of equations. Both high and low fixed charge density membranes (low- and high concentration electrolyte solutions), acting respectively as (nearly) perfect or imperfect membranes, are considered. The perfect membrane is adequately described by a one-layer model while the imperfect membrane has a more sophisticated response. In particular, the direct transition from underlimiting to overlimiting currents, bypassing the limiting currents, is found to be possible for imperfect membranes (high-concentration electrolyte). The transition to the overlimiting currents for the low-concentration electrolyte solutions is monotonic, while for the high-concentration solutions it is oscillatory. Despite the fact that velocities in the porous membrane are much smaller than in the electrolyte region, it is further demonstrated that they can dramatically influence the nature and transition to the overlimiting regimes. A map of the bifurcations, transitions, and regimes is constructed in coordinates of the fixed membrane charge and the Darcy number

Two layer dielectric-electrolyte micro-flow with pressure gradient

The present work considers stability of two-phase dielectric/electrolyte system, consisting of two immiscible liquids in microchannel. The system is set in motion by the constant external electric field, which causes the electroosmotic flow in the electrolyte, and by the pressure driving force. The investigation of its linear stability has shown that there are two types of instability in the system: short-wave and long-wave instability. The short-wave instability occurs for a stronger external field than the long-wave instability but the growth rate of the short-wave instability is much higher than that of the long-wave instability

Two layer dielectric-electrolyte micro-flow with pressure gradient

The present work considers stability of two-phase dielectric/electrolyte system, consisting of two immiscible liquids in microchannel. The system is set in motion by the constant external electric field, which causes the electroosmotic flow in the electrolyte, and by the pressure driving force. The investigation of its linear stability has shown that there are two types of instability in the system: short-wave and long-wave instability. The short-wave instability occurs for a stronger external field than the long-wave instability but the growth rate of the short-wave instability is much higher than that of the long-wave instability

Instabilities, bifurcations and transition to chaos in electrophoresis of charge-selective microparticle

Electro-hydrodynamic instabilities near a cation-exchange microgranule in an electrolyte solution under an external electric field are studiednumerically. Despite the smallness of the particle and practically zero Reynolds numbers, in the vicinity of the particle, several sophisticatedflow regimes can be realized, including chaotic ones. The obtained results are analyzed from the viewpoint of hydrodynamic stability andbifurcation theory. It is shown that a steady-state uniform solution is a non-unique one; an extra solution with a characteristic microvortex,caused by non-linear coupling of the hydrodynamics and electrostatics, in the region of incoming ions is found. Implementation of oneof these solutions is subject to the initial conditions. For sufficiently strong fields, the steady-state solutions lose their stability via the Hopfbifurcation and limit cycles are born: a system of waves grows and propagates from the left pole,θ= 180○, toward the angleθ=θ0≈60○. Furtherbifurcations for these solutions are different. With the increase in the amplitude of the external field, the first cycle undergoes multiple perioddoubling bifurcation, which leads to the chaotic behavior. The second cycle transforms into a homoclinic orbit with the eventual chaotic modevia Shilnikov’s bifurcation. Santiago’s instability [Chenet al., “Convective and absolute electrokinetic instability with conductivity gradients,”J. Fluid Mech.524, 263 (2005)], the third kind of instability, was then highlighted: an electroneutral extended jet of high salt concentrationis formed at the right pole (region of outgoing ions,θ= 0○). For a large enough electric field, this jet becomes unstable; the perturbations areregular for a small supercriticality, and they acquire a chaotic character for a large supercriticality. The loss of stability of the concentrationjet significantly affects the hydrodynamics in this area. In particular, the Dukhin–Mishchuk vortex, anchored to the microgranule atθ≈60○,under the influence of the jet oscillations loses its stationarity and separates from the microgranule, forming a chain of vortices moving off thegranule. This phenomenon strongly reminds the Kármán vortices behind a sphere but has another physical mechanism to implement. Besidesthe fundamental importance of the results, the instabilities found in the present work can be a key factor limiting the robust performance ofcomplex electrokinetic bio-analytical systems. On the other hand, these instabilities can be exploited for rapid mixing and flow control ofnanoscale and microscale device

Electrokinetic instability of liquid micro- and nanofilms with a mobile charge

The instability of ultra-thin films of an electrolyte bordering a dielectric gas in an external tangential electric field is scrutinized. The solid wall is assumed to be either a conducting or charged dielectric surface. The problem has a steady one-dimensional solution. The theoretical results for a plug-like velocity profile are successfully compared with available experimental data. The linear stability of the steady-state flow is investigated analytically and numerically. Asymptotic long-wave expansion has a triple-zero singularity for a dielectric wall and a quadruple-zero singularity for a conducting wall, and four (for a conducting wall) or three (for a charged dielectric wall) different eigenfunctions. For infinitely small wave numbers, these eigenfunctions have a clear physical meaning: perturbations of the film thickness, of the surface charge, of the bulk conductivity, and of the bulk charge. The numerical analysis provides an important result: the appearance of a strong short-wave instability. At increasing Debye numbers, the short-wave instability region becomes isolated and eventually disappears. For infinitely large Weber numbers, the long-wave instability disappears, while the short-wave instability persists. The linear stability analysis is complemented by a nonlinear direct numerical simulation. The perturbations evolve into coherent structures; for a relatively small external electric field, these are large-amplitude surface solitary pulses, while for a sufficiently strong electric field, these are short-wave inner coherent structures, which do not disturb the surface

Maxwell stress generated long wave instabilities in a thin aqueous film under time-dependent electro-osmotic flow

In this study the dynamics and stability of thin and electrically conductive aqueous films under the influence of a time-periodic electric field are explored. With the help of analytical linear stability analysis for long wavelength disturbances, the stability threshold of the system as a function of various electrochemical parameters and transport coefficients is presented. The contributions of parameters like surface tension, disjoining pressure, electric double layer (Debye length and interfacial zeta potential), and unsteady Maxwell and viscous stresses are highlighted with the help of appropriate dimensionless groups. The physical mechanisms affecting the stability of thin films are detailed with the above-mentioned forces and parametric dependence of stability trends is discussed