Repulsive stabilization in black lipid membranes. A hydrodynamic model

A linear stability analysis is performed for a black lipid membrane. The hydrodynamic model consists of a viscous hydrocarbon film sandwiched between two aqueous phases. Attractive forces (van der Waals and electrical) and repulsive forces (steric) are expressed as body forces in the equations of fluid motion in the three phases. The steric repulsion due to overlap of the hydrocarbon chains of the lipids at small film thicknesses is described via an exponentially decaying interaction potential. The dispersion equation displays two modes of vibrations: the bending mode with the two Film surfaces transversely in phase, and the squeezing mode with the two surfaces 180 degrees out of phase. For symmetrical films, these two modes are uncoupled, and the squeezing mode (with thickness variations) is stabilized by the repulsive interactions. For nonsymmetrical films (different surface tensions, surface charges, etc.). these two modes are coupled and the asymmetry induces a shift of the marginal stability curve to shorter wavelengths.