Nonlinear Dynamics of Lipid Films under Electric Forces

Abstract

We study the dynamics and rupture of lipid films perturbed in the symmetric mode squeezing through an electrohydrodynamical approach. The lipid phase and the two surrounding aqueous phases are considered as incompressible Newtonian viscous fluids submitted to van der Waals, steric, and electric body forces. A nonlinear evolution equation for the film thickness, at the long-wavelength limit, is obtained for two symmetric cases: a film with equally charged surfaces with no potential drop and a neutral film submitted to an external electric field. At the long-wavelength limit, the electric term only influences the film evolution when the electric field inside the film is nonvanishing. We solve numerically, as an initial value problem with periodic boundary conditions, the nonlinear evolution equation. The rupture time is obtained and compared with analytical estimates. Sufficiently strong steric forces prevent the film from narrowing beyond a minimum thickness leading the film to a steady state different from the planar one consistently with the nonlinear analytical approach. The presence of a transmembrane electric potential destabilizes the perturbed film as predicted by the linear and nonlinear approaches; however, as expected, destabilization is not relevant at physiological values of the potential drop.