Dynamics of Biomembranes: Effect of the Bulk Fluid

¹ Department of Mathematics, Texas A&M University, College Station, Texas, USA
² Department of Mathematics, University of Maryland, College Park, Maryland, USA

^⋆ Corresponding author. E-mail: bonito@math.tamu.edu

Abstract

We derive a biomembrane model consisting of a fluid enclosed by a lipid membrane. The membrane is characterized by its Canham-Helfrich energy (Willmore energy with area constraint) and acts as a boundary force on the Navier-Stokes system modeling an incompressible fluid. We give a concise description of the model and of the associated numerical scheme. We provide numerical simulations with emphasis on the comparisons between different types of flow: the geometric model which does not take into account the bulk fluid and the biomembrane model for two different regimes of parameters.