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.

Long-Scale Evolution of Thin Liquid Films Bounded by a Viscous Phase with Diffusing Charged Surfactants

“…We follow basically the same numerical methodology employed previously (7). Equation [1] is solved as an initial value problem considering spatially periodic boundary conditions (PBC).…”

“…In the past decade some progress has been made on the description of pattern formation in thin liquid films since such a concept appeared (2). By numerical analysis, morphological patterns were demonstrated in 2D thin films subjected to antagonistic forces (3)(4)(5)(6)(7). An analytical proof of pattern formation in 2D thin aqueous films delimited by a fixed substrate and a gaseous phase with constant tension was given (8): morphological patterns become possible whenever there is a competition between external attractive and repulsive forces.…”