Mixed finite element method for electrowetting on dielectric with contact line pinning

  • Shawn W. Walker

    Louisiana State University, Baton Rouge, USA
  • Andrea Bonito

    Texas A&M University, College Station, USA
  • Ricardo H. Nochetto

    University of Maryland, College Park, USA


We present a mixed finite element method for a model of the flow in a Hele-Shaw cell of 2-D fluid droplets surrounded by air driven by surface tension and actuated by an electric field. The application of interest regards a micro-fluidic device called ElectroWetting on Dielectric (EWOD). Our analysis first focuses on the time discrete (continuous in space) problem and is presented in a mixed variational framework, which incorporates curvature as a natural boundary condition. The model includes a viscous damping term for interface motion, as well as contact line pinning (sticking of the interface) and is captured in our formulation by a variational inequality. The semi-discrete problem uses a semiimplicit time discretization of curvature. We prove the well-posedness of the semi-discrete problem and fully discrete problem when discretized with iso-parametric finite elements. We derive a priori error estimates for the space discretization. We also prove the convergence of an Uzawa algorithm for solving the semi-discrete EWOD system with inequality constraint. We conclude with a discussion about experimental orders of convergence.

Cite this article

Shawn W. Walker, Andrea Bonito, Ricardo H. Nochetto, Mixed finite element method for electrowetting on dielectric with contact line pinning. Interfaces Free Bound. 12 (2010), no. 1, pp. 85–119

DOI 10.4171/IFB/228