title: Modes of electrokinetic instability for imperfect electric membranes.
abstract: 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.
authors.affiliation: Laboratory of Micro- and Nanoscale Electro- and Hydrodynamics, Financial University, Krasnodar 350051, Russian Federation.
authors.forename: G S
authors.initials: GS
authors.lastname: Ganchenko
authors.affiliation: Department of Mathematics and Informatics, Financial University, Krasnodar 350051, Russian Federation.
authors.forename: E N
authors.initials: EN
authors.lastname: Kalaydin
authors.affiliation: University of Notre Dame, Notre Dame, Indiana 46556, USA.
authors.forename: J
authors.initials: J
authors.lastname: Schiffbauer
authors.affiliation: 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.|Laboratory of General Aeromechanics, Institute of Mechanics, Moscow State University, Moscow 119192, Russian Federation.
authors.forename: E A
authors.initials: EA
authors.lastname: Demekhin