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Fluid Dynamics Seminar

Monday, October 27th, 2008, 4:00 PM
Cullimore Lecture Hall, Room 611
New Jersey Institute of Technology

Modeling, Analysis, and Simulation for Electrowetting Driven Hele-Shaw Flow with Contact Line Friction

Shawn Walker

Courant Institute of Mathematical Sciences, New York University

Abstract

Electrowetting On Dielectric (EWOD) refers to a parallel-plate 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). The fluid dynamics are modeled 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 and becomes an inequality constraint for the motion of the liquid-gas interface that accounts for the `sticking' effect of the interface. The model is presented in a mixed variational framework and is discretized using Finite Elements. Both the semi-(time)discrete and fully discrete methods are shown to be well-posed. The curvature/surface tension is discretized in a semi-implicit way for accuracy using an explicit representation of the interface. The contact line friction is captured by a variational inequality. Finally, simulations are presented and compared to experimental videos of EWOD driven droplets. These experiments exhibit droplet pinching and merging events and are reasonably captured by our simulations.