Nonlinear Dynamics and Wall Touch-Up in Unstably Stratified Multilayer Flows in Horizontal Channels under the Action of Electric Fields

Abstract

This study considers the nonlinear dynamics of stratified immiscible fluids when an electric field acts perpendicular to the direction of gravity. A particular setup is investigated in detail, namely, two stratified fluids inside a horizontal channel of infinite extent. The fluids are taken to be perfect dielectrics, and a constant horizontal field is imposed along the channel. The sharp interface separating the two fluids may or may not support surface tension, and the Rayleigh--Taylor instability is typically present when the heavier fluid is on top. A novel system of partial differential equations that describe the interfacial position and the leading order horizontal velocity in the fluid layers is studied analytically and computationally. The system is valid in the asymptotic limit of one layer being asymptotically thin compared to the second fluid layer, and as a result nonlocal electrostatic terms arise due to the multiscale nature of the physical setup. The initial value problem on spatially perio...