Curvature Driven Flows: Electrowetting on Dielectrics and Biomembranes

Monday, July 15, 2013 - 3:30pm - 4:30pm
Keller 3-180
Andrea Bonito (Texas A & M University)
We present a general framework for the numerical resolution of processes
driven by geometric components such as the curvature of the domain boundary.
In this context, the Laplace-Beltrami operator plays a crucial role.
Two applications are discussed: Electrowetting on dielectric (EWOD) and
the simulation of Biomembranes.

The former refers to a parallel-plate
micro-device that moves fluid droplets through electrically
actuated surface tension effects. These devices have potential
applications in biomedical `lab-on-a-chip' devices (such as automated DNA
testing and cell separation) and controlled micro-fluidic transport
(e.g. mixing and concentration control).
We model the fluid
dynamics using Hele-Shaw type equations (in 2-D) with a focus on
including the relevant boundary phenomena. Specifically, we model contact
line pinning as a static (Coulombic) friction effect that effectively
becomes a variational inequality for the motion of
the liquid-gas interface.
We analyze this approach, present simulations and compare them to
experimental videos of EWOD driven droplets.

The latter applies to 2 mono-molecular forming an encapsulating bag called
vesicle. Equilibrium shapes are obtained via the minimization of the
Willmore energy under area and volume constraints. Physical dynamics are
obtained by taking into account the effect of the inside (bulk) fluid.
Forth order, highly nonlinear arising problems are solved using an
adaptive mixed finite element method.
Two and three dimensional simulations are presented.
In particular, typical biconcave shape specific to red blood cells are

This presentation is based on joint works with R. Nochetto, M. Pauletti, and S. Walker.