Linear and nonlinear evolution and diffusion layer selection in electrokinetic instability

Abstract

In the present work, four nontrivial stages of electrokinetic instability are identified by direct numerical simulation (DNS) of the full Nernst-Planck-Poisson-Stokes system: (i) a stage of the influence of the initial conditions (milliseconds); (ii) one-dimensional (1D) self-similar evolution (milliseconds-seconds); (iii) a primary instability of the self-similar solution (seconds); (iv) a nonlinear stage with secondary instabilities. The self-similar character of evolution at moderately large times is confirmed. Rubinstein and Zaltzman instability and noise-driven nonlinear evolution toward overlimiting regimes in ion-exchange membranes are numerically simulated and compared with theoretical and experimental predictions. The primary instability which happens during this stage is found to arrest a self-similar growth of the diffusion layer. It also specifies its characteristic length as was first experimentally predicted by Yossifon and Chang [G. Yossifon and H.-C. Chang, Phys. Rev. Lett. 101, 254501 (2008)]. A novel principle for the characteristic wave-number selection from the broadband initial noise is established.

Helical vortex formation in three-dimensional electrochemical systems with ion-selective membranes

“…In order to limit excessive grid refinement near membrane surfaces, the equations were solved with a dimensionless Debye length, λ = 10 −3 , far larger than a physically realistic value (i.e., ∼10 −4 ). Other studies [6,7,[15][16][17][18] employ similar dimensionless Debye length values, and as shown below, the simulation results are clearly qualitatively similar to the realistic phenomenon observed in the experiment.…”

“…2, we show simulated (SIM) and measured (EXP) ion concentrations at the outlet and on the symmetry plane of a system with aspect ratio w/d = 1. Note that there is a good match between simulation and experiment, and that the results lead to two conclusions: (1) In the Ohmic and limiting regimes, there is little concentration variation in the width (z) direction, indicating only minor 3D effects; (2) in the overlimiting regime, however, the concentration profile in the width direction exhibits characteristic features of electrokinetic instability (also known as "Rubinstein and Zaltzman" instability [7], often found in 2D quiescent solutions) [7,12,13,15,16]. In particular, there appear to be side-by-side vortex pairs spanning the channel cross section, as shown in Fig.…”

“…the channel, and on a lateral cross section. In the earlier studies in quiescent solution, instability vortices develop in time from small seed vortices to pairs of big vortices, though a merging process [7,12,15,16]. However, the size selection criteria for the maximum vortex size was rather arbitrary (determined by the boundary condition); therefore it was not easy to employ the insight gained in a realistic membrane system.…”

“…Every aspect of the problem is more complicated in three dimensions: generalizing the analytical techniques is not straightforward; experimentally observing system behavior in the third dimension is technologically challenging; and extending recently developed 2D numerical simulation [15,16] to 3D proved to be computationally challenging [16]. Regardless, three-dimensional effects are far from inconsequential.…”

Two layer dielectric-electrolyte micro-flow with pressure gradient

“…Upon a tangential electric field, these charges produce a Coulomb force and cause a movement of the liquid; experimental evidence for an electroosmotic flow at the liquid-liquid interface and in the liquid bulk is given in [2]. In spite of almost zero Reynolds numbers (negligible inertia effects), the electrohydrodynamics of liquid flows at micro-and nanoscales includes complicated instabilities [3] and bifurcations [4], and even chaotic motion at micro-and nanoscales, which is named as microturbulence.…”