Boundary element method for membranes

Motivated by recent experiments on the dynamics of colloidal membranes, we employ the boundary element method to determine the evolution of a fluid membrane in a viscous solvent sagging under its own weight. The membrane velocities are expressed using the boundary integral formulation in terms of a distribution of Green's functions on the membrane. We assume the associated force densities to be a combination of gravitational forces, surface tension, and bending stiffness. A surface incompressibility constraint is used to maintain the experimentally observed conservation of membrane area. This model recovers and recapitulates the experimentally observed neck and pendant-like drop formation.