Title: Surface Tension Driven Motion of Microfluid Droplets Actuated by Electric Fields

Author: Prof. Ricardo Nochetto (Department of Mathematics, University of Maryland at College Park)

Dr. Nochetto is a highly regarded numerical analyst working on adaptive methods. His other research interests include free boundary problems and phase transitions: finite element methods, PDE issues.

Abstract:

Electrowetting on dielectric (EWOD) 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 (automated DNA testing, cell separation) and controlled micro-fluidic transport (e.g. mixing and concentration control). Their design and control are of paramount importance in engineering. This requires a flexible and robust fluid model to account for contact line pinning, a critical boundary effect leading to hysteresis, and an efficient and reliable numerical method, including space-time adaptivity, to simulate the dynamics. The latter involves large droplet deformations, splitting and merging.

We model the fluid dynamics using Hele-Shaw type equations (in 2-D), and contact line pinning as a static (Coulombic) friction effect that effectively becomes a variational inequality for the motion of the liquid-gas interface. We propose a numerical scheme consisting of mixed finite elements for space discretization and a semi-implicit time discretization. We discuss the variational computation of curvature, based on a natural finite element representation of the interface, as well as an Uzawa method for solving the variational inequality. We also present a hybrid approach to topological changes, which combines one step of the level set method with a variational method to handle the interface motion, and a variational geodesic active contour method to adjust the mesh and make it conforming.

We analyze this approach, present several simulations, and compare them to experimental videos of EWOD driven droplets. The model contains just one parameter to account for hysteresis and leads to remarkable agreement between simulations and experiments, both in space and time. This is joint work with S. Walker, A. Bonito, and B. Shapiro.