Electrohydrodynamics of conductive micro- and nanofilms under DC electric field

Abstract

The present paper considers a two-phase micro/nanoflow system of conductive (electrolyte) and non-conductive (dielectric) viscous liquids bounded by two solid walls in an external electric field. The charge near the solid body is immobile, but the surface charge is mobile. Electrostatic attraction then creates an excess of counter ions within the electrolyte solution next to the solid surface or interface, thereby forming electric Debye layers near both surfaces. We study both the micro- and nanoscale electrolyte layers. In the latter case Debye layers in the electrolyte aren’t overlapped. Related two-layer Couette-Poiseuille flow of viscous liquids has been thoroughly studied using asymptotic and numerical analysis of the Orr-Sommerfeld equation. These studies revealed existence of two types of instabilities: short and long-wave instabilities related to inertia and viscous effects. In this work the problem is described by the Nernst-Planck-Poisson-Stokes system in the liquid-electrolyte phase; the Laplace-Stokes system in the liquid-dielectric phase; and appropriate boundary conditions on the solid-electrolyte, the solid-dielectric, and the liquid-liquid interfaces. The problem has 1D steady-state answer: equilibrium between solution and a plug-like velocity profile.