Stochastic and Multiscale Modeling and Computation Seminar with Shuwang Li: Phase Field Modeling and Computation of Vesicle Growth and Shrinkage

Speaker: Shuwang Li, Department of Applied Mathematics, Illinois Institute of Technology

 Title: Phase Field Modeling and Computation of Vesicle Growth and Shrinkage

Abstract: We study a phase field model for vesicle growth or shrinkage based on osmotic pressure that arises due to a chemical potential gradient. The model consists of an Allen-Cahn-like equation, which describes the phase field evolution, a Cahn-Hilliard-like equation, which simulates the fluid concentration, and a Stokes-like equation, which models the fluid flow. It is mass conserved and surface area constrained during the membrane deformation. Conditions for vesicle growth or shrinkage are analyzed via the common tangent construction. The numerical computing is in two-dimensional space using a nonlinear multigrid method consisting of a FAS method for the PDE system. Convergence test suggests that the global error is of first order in time and of second order in space.  Numerical results are demonstrated under no flux boundary conditions and with boundary-driven shear flow respectively. 

Stochastic and Multiscale Modeling and Computation Seminar