A Diffuse Interface Model For Electrowetting
Ricardo H. Nochetto
Department of Mathematics and
Institute for Physical Science and Technology
University of Maryland
College Park, MD 20742

We present three models of biomembranes along with their numerical simulation and analysis. The first one is purely geometric since the equilibrium shapes are the minimizers of the Willmore (or bending) energy under area and volume constraints. The second model incorporates the effect of the inside (bulk) viscous incompressible fluid and leads to more physical dynamics. The third model describes the interaction of a director field with a membrane, giving rise to an induced spontaneous curvature.

We propose a parametric finite element method for the discretization of these models and examine crucial numerical issues such as dealing with curvature and length constraints within a variational framework. We show several simulations describing the dynamics of purely geometric flows, membrane-fluid interaction, and the dramatic effect of defects of the director field on membrane shape.

This work is joint with S. Bartels, A. Bonito, G. Dolzmann, and M.S. Pauletti.