Effective zero-thickness model for a conductive membrane driven by an electric field

TL;DR

This paper develops a simplified zero-thickness model for conductive membranes in electric fields, capturing electro-mechanical interactions and fluid flows, and compares predictions with experimental results.

Contribution

It introduces a novel zero-thickness boundary condition model that simplifies analysis while accurately describing electro-mechanical effects in conductive membranes.

Findings

Model predicts membrane undulation instability due to capacitive effects.

Flow analysis reveals similarities with induced charge electro-osmosis.

Model aligns well with recent experimental observations.

Abstract

The behavior of a conductive membrane in a static (DC) electric field is investigated theoretically. An effective zero-thickness model is constructed based on a Robin-type boundary condition for the electric potential at the membrane, originally developed for electrochemical systems. Within such a framework, corrections to the elastic moduli of the membrane are obtained, which arise from charge accumulation in the Debye layers due to capacitive effects and electric currents through the membrane and can lead to an undulation instability of the membrane. The fluid flow surrounding the membrane is also calculated, which clarifies issues regarding these flows sharing many similarities with flows produced by induced charge electro-osmosis (ICEO). Non-equilibrium steady states of the membrane and of the fluid can be effectively described by this method. It is both simpler, due to the zero thickness approximation which is widely used in the literature on fluid membranes, and more general than previous approaches. The predictions of this model are compared to recent experiments on supported membranes in an electric field.