Fluctuations of a driven membrane in an electrolyte

TL;DR

This paper models the behavior of a driven membrane in an electrolyte under out-of-equilibrium conditions, revealing new instability mechanisms due to electric fields and ion flow.

Contribution

It introduces a novel membrane equation of motion accounting for out-of-equilibrium effects in electrolyte environments.

Findings

Out-of-equilibrium conditions modify membrane tension and bending modulus.

New terms in the membrane equation lead to potential instabilities.

Charge accumulation near the membrane influences membrane dynamics.

Abstract

We develop a model for a driven cell- or artificial membrane in an electrolyte. The system is kept far from equilibrium by the application of a DC electric field or by concentration gradients, which causes ions to flow through specific ion-conducting units (representing pumps, channels or natural pores). We consider the case of planar geometry and Debye-H\"{u}ckel regime, and obtain the membrane equation of motion within Stokes hydrodynamics. At steady state, the applied field causes an accumulation of charges close to the membrane, which, similarly to the equilibrium case, can be described with renormalized membrane tension and bending modulus. However, as opposed to the equilibrium situation, we find new terms in the membrane equation of motion, which arise specifically in the out-of-equilibrium case. We show that these terms lead in certain conditions to instabilities.