Pressure effects on the equilibrium configurations of bilayer lipid membranes

Planar bilayer lipid membranes (BLMs) are currently employed to construct many bio-inspired material systems and structures. In order to characterize the pressure effects on the equilibrium configurations of these biological membranes, a novel continuum model is proposed. The BLM is assumed to be a two-layer smectic A liquid crystal. The mean orientation of the amphiphilic molecules comprising the membrane is postulated to be perpendicular to the layers and each layer is idealized as a two-dimensional liquid. Moreover, the BLM is modeled as a simply supported plate undergoing small deformations. It is subjected to a pressure load that acts perpendicularly to the layers. The equilibrium equations and boundary conditions are derived from the bulk elastic energy for smectic A liquid crystals as described by de Gennes and Prost (1993 The Physics of Liquid Crystals 2nd edn (Oxford Science Publications)) by using variational methods. The resulting fourth-order linear partial differential equation is solved by employing cylindrical functions and the series solution is proved to be convergent. The solution is numerically computed for values of the model parameters that are reported in the literature. PACS number: 61.30.Cz