Eur. Phys. J. E (2009) 28: 243-264
https://doi.org/10.1140/epje/i2008-10433-1

Regular Article

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

¹ Laboratoire de Physico-Chimie Théorique, UMR 7083, ESPCI, 10 rue Vauquelin, 75231, Paris Cedex 05, France
² The Institute of Mathematical Sciences, C.I.T Campus, 600 113, Chennai, India
³ Department of Mathematics, Massachusetts Institute of Technology, 02139, Cambridge Massachusetts, USA
⁴ Institut Curie, UMR 168, 26 rue d’Ulm, 75005, Paris, France

^* e-mail: david@turner.pct.espci.fr

Received: 26 June 2008
Revised: 27 October 2008
Accepted: 8 December 2008
Published online: 28 January 2009

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 by D. Lacoste, M. Cosentino Lagomarsino, and J.F. Joanny (EPL 77, 18006 (2007)), by providing a physical explanation for a destabilizing term proportional to k _⊥ ³ in the fluctuation spectrum, which we relate to a nonlinear (E²) electrokinetic 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 the 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 nonequilibrium 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.