Eur. Phys. J. E (2018) 41: 40
https://doi.org/10.1140/epje/i2018-11650-7

Regular Article

Stability of the electroosmotic flow of a two-layer electrolyte-dielectric system with external pressure gradient^⋆

¹ Kuban State University, 149 Stavropolskaya St., 350040, Krasnodar, Russia
² Financial University under the Government of the Russian Federation, 32 sh. Neftyanikov St., 350000, Krasnodar, Russia
³ Laboratory of General Aeromechanics, Institute of Mechanics, Moscow State University, 119192, Moscow, Russia

^* e-mail: ganchenko.ru@gmail.com

Received: 17 August 2017
Accepted: 13 March 2018
Published online: 27 March 2018

Abstract

The stability of the electroosmotic flow of electrolyte-dielectric viscous liquids under the influence of the DC and AC electric fields along with the external pressure gradient is studied theoretically. Liquids are bounded by two infinite parallel plates. The lower wall bordering the electrolyte is assumed to be a charged surface, and the upper wall is electrically isolated. The charge at the lower boundary is assumed to be immobile, while the surface charge at the free surface is assumed to be mobile. In this paper, we study the micro- and nanosized liquid layers. The mathematical model is described by a nonlinear system of the Nernst-Planck-Poisson-Stokes partial differential equations with the appropriate boundary conditions on the solid surface, the electrolyte/dielectric interface, and on the upper wall. The pressure gradient is highly important for the stability of the flow. For the DC case, the external pressure could either stabilize and destabilize the flow depending on the relative directions of the electroosmotic flow and the pressure-driven flow. For the AC case, the dependence on the value of the external pressure is not monotonous for different wave numbers of perturbations, but, as a rule, the external pressure destabilizes the flow. As the frequency of the electric field increases, the one-dimensional solution of the problem becomes stable.