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Phase field calculus, curvature-dependent energies, and vesicle membranes

Lipid bilayer vesicles are membranes formed spontaneously in aqueous environments under suitable conditions. They have been extensively studied in literature as a simple model of cell membranes. In this work, we discuss some recent developments in the phase field modeling and simulations of vesicles. We describe how the equilibrium and dynamic properties of the vesicles can be effectively described by the phase field calculus which is a natural translation of the energy variations with respect to the vesicle geometry to the variations of the corresponding diffuse interfacial energy with respect to the phase field functions. We also illustrate how phase field techniques can be generalized to model a multi-component vesicle, a vesicle interacting with a surrounding fluid and the adhesion of a vesicle to a substrate.