Ganchenko G S, Kalaydin E N, Schiffbauer J, Demekhin E A
Laboratory of Micro- and Nanoscale Electro- and Hydrodynamics, Financial University, Krasnodar 350051, Russian Federation.
Department of Mathematics and Informatics, Financial University, Krasnodar 350051, Russian Federation.
Phys Rev E. 2016 Dec;94(6-1):063106. doi: 10.1103/PhysRevE.94.063106. Epub 2016 Dec 12.
The direct transition to overlimiting current bypassing the stage of limiting currents is considered for imperfect membranes. Instability of the quiescent steady-state one-dimensional solution, which is the result of a balance of diffusion and electromigration, is investigated on the basis of the full Nernst-Planck-Poisson-Stokes system and a simplified quasielectroneutral system. A three-layer geometry, electrolyte-porous membrane-electrolyte, is considered. The usual assumption of a constant electrochemical potential along the membrane surface is removed from consideration. The effect of bulk and surface effects on the instability and transition to the overlimiting currents is evaluated for a different membrane selectivity. It becomes clear that for sufficiently small fixed charge concentration (large ion concentration in the electrolyte), the monotonic instability is replaced by an oscillatory one. The dependence of instability on the membrane porosity is found to be weak.
对于不完美的膜，考虑绕过极限电流阶段直接过渡到过极限电流。基于完整的能斯特 - 普朗克 - 泊松 - 斯托克斯系统和简化的准电中性系统，研究了作为扩散和电迁移平衡结果的静态稳态一维解的不稳定性。考虑了三层几何结构，即电解质 - 多孔膜 - 电解质。不再考虑沿膜表面电化学势恒定这一通常假设。针对不同的膜选择性，评估了体相和表面效应对不稳定性以及向过极限电流转变的影响。很明显，对于足够小的固定电荷浓度（电解质中离子浓度大），单调不稳定性被振荡不稳定性所取代。发现不稳定性对膜孔隙率的依赖性较弱。
