Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane

TL;DR

This paper investigates how electrostatic and electrokinetic effects, especially induced-charge electro-osmosis, influence the elastic properties of membranes under DC electric fields, revealing destabilizing mechanisms and flow behaviors.

Contribution

It extends previous models by providing a physical explanation for destabilizing electrokinetic effects and predicting reverse ICEO flows around driven membranes.

Findings

Electrostatic effects modify membrane elastic moduli in electrolyte under DC fields.

Induced-charge electro-osmosis (ICEO) causes destabilizing fluctuations in membranes.

Reverse ICEO flows enhance membrane protrusions due to curvature-induced tangential fields.

Abstract

We discuss the electrostatic contribution to the elastic moduli of a cell or artificial membrane placed in an electrolyte and driven by a DC electric field. The field drives ion currents across the membrane, through specific channels, pumps or natural pores. In steady state, charges accumulate in the Debye layers close to the membrane, modifying the membrane elastic moduli. We first study a model of a membrane of zero thickness, later generalizing this treatment to allow for a finite thickness and finite dielectric constant. Our results clarify and extend the results presented in [D. Lacoste, M. Cosentino Lagomarsino, and J. F. Joanny, Europhys. Lett., {\bf 77}, 18006 (2007)], by providing a physical explanation for a destabilizing term proportional to $\kps^3$ in the fluctuation spectrum, which we relate to a nonlinear ($E^2$) electro-kinetic effect called induced-charge electro-osmosis (ICEO). Recent studies of ICEO have focused on electrodes and polarizable particles, where an applied bulk field is perturbed by capacitive charging of the double layer and drives flow along the field axis toward surface protrusions; in contrast, we predict "reverse" ICEO flows around driven membranes, due to curvature-induced tangential fields within a non-equilibrium double layer, which hydrodynamically enhance protrusions. We also consider the effect of incorporating the dynamics of a spatially dependent concentration field for the ion channels.