Finite element simulation of multi‐component vesicle morphologies undergoing phase separation

Abstract

Morphological changes in lipid bilayer vesicles are due to phase transitions and surface deformations occurring in unison. We present a dynamic chemo-mechanical finite element model to study such changes. This is achieved by coupling two fourth order partial differential equations (PDEs): The Cahn-Hilliard [2] mass balance equation based on irreversible thermodynamics, and the Kirchhoff-Love [1] rotation free thin shell equation. The Helmholtz free energy consists of Helfrich energy to model elastic bending, and also includes in-plane elastic energy with a finite shear modulus for the purpose of regularization. The geometry is discretized by C1-continuous NURBS shape functions. An implicit second order accurate generalized-α scheme is used for time integration. Newton-Raphson iterations are utilized to solve the resulting linearized weak form monolithically. The proposed formulation is illustrated by a numerical example.