Linear and Nonlinear Evolution and Diffusion Layer Selection in Electrokinetic Instability

Abstract

In the present work fournontrivial stages of electrokinetic instability are identified by direct numerical simulation (DNS) of the full Nernst-Planck-Poisson-Stokes (NPPS) system: i) The stage of the influence of the initial conditions (milliseconds); ii) 1D self-similar evolution (milliseconds-seconds); iii) The primary instability of the self-similar solution (seconds); iv) The nonlinear stage with secondary instabilities. The self-similar character of evolution at intermediately large times is confirmed. Rubinstein and Zaltzman instability and noise-driven nonlinear evolution to over-limiting 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 self-similar growth of the diffusion layer and specifies its characteristic length as was first experimentally predicted by Yossifon and Chang (PRL 101, 254501 (2008)). A novel principle for the characteristic wave number selection from the broadbanded initial noise is established.

13 pages, 8 figures

Cited by in corpus (8)

• Direct Numerical Simulation of Electrokinetic Instability and Transition to Chaotic Motion
• Three-dimensional Coherent Structures of Electrokinetic Instability
• A coupled finite-volume solver for numerical simulation of electrically-driven flows
• Electrokinetic Instability near Charge-Selective Hydrophobic Surfaces
• Effect of Couette Flow on Electroconvective Vortices
• Transient electrohydrodynamic flow with concentration dependent fluid properties: modelling and energy-stable numerical schemes
• Suppression of Electroconvective and Morphological Instabilities by an Imposed Cross Flow of the Electrolyte
• Electrohydrodynamic channeling effects in narrow fractures and pores