Long-wave interfacial instabilities in a thin electrolyte film undergoing coupled electrokinetic flows: a nonlinear analysis

Abstract

Spatiotemporal deformations of the free charged surface of a thin electrolyte film undergoing a coupled electrokinetic flow composed of an electroosmotic flow (EOF) on a charged solid substrate and an electrophoretic flow (EPF) at its free surface are explored through linear stability analysis and the long-wave nonlinear simulations. The nonlinear evolution equation for the deforming surface is derived by considering both the Maxwell’s stresses and the hydrodynamic stresses. The electric potential across the film is obtained from the Poisson–Boltzmann equation under the Debye–Huckel approximation. The simulations show that at the charged electrolyte–air interface, the applied electric field generates an EPF similar to that of a large charged particle. The EOF near the solid–electrolyte interface and the EPF at the electrolyte–air interface are in the same (or opposite) directions when the zeta potentials at the two interfaces are of the opposite (or same) signs. The linear and nonlinear analyses of the evolution equation predict the presence of travelling waves, which is strongly modulated by the applied electric field and the magnitude/sign of the interface zeta potentials. The time and length scales of the unstable modes reduce as the sign of zeta potential at the two interfaces is varied from being opposite to same and also with the increasing applied electric field. The increased destabilization is caused by a reverse EPF near the free surface when the interfaces bear the same sign of zeta potentials. Flow reversal by EPF at the free surface occurs at smaller zeta potential of the free surface when the film is thicker because of less influence of the EOF arising at the solid–electrolyte boundary. The amplitude of the surface waves is found to be smaller when the unstable waves travel at a faster speed. The films can undergo pseudo-dewetting when the free surface is almost stationary under the combined influences of EPF and EOF. The free surface instability of the coupled EOF and EPF has some interesting implications in the development of micro/nano fluidic devices involving a free surface.