Geodesic
Mixed finite element method for electrowetting on dielectric with contact line pinning
Shawn W. Walker1 ; Andrea Bonito2 orcid ; Ricardo H. Nochetto3 orcid
1Louisiana State University, Baton Rouge, USA
2Texas A&M University, College Station, USA
3University of Maryland, College Park, USA
Interfaces and free boundaries, Tome 12 (2010) no. 1, pp. 85-119

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DOI

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.
DOI : 10.4171/ifb/228
Classification : 35-XX, 65-XX, 76-XX, 92-XX

Shawn W. Walker  1   ; Andrea Bonito  2   ; Ricardo H. Nochetto  3

1 Louisiana State University, Baton Rouge, USA
2 Texas A&M University, College Station, USA
3 University of Maryland, College Park, USA 
Shawn W. Walker; Andrea Bonito; Ricardo H. Nochetto. Mixed finite element method for electrowetting on dielectric with contact line pinning. Interfaces and free boundaries, Tome 12 (2010) no. 1, pp. 85-119. doi: 10.4171/ifb/228
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     title = {Mixed finite element method for electrowetting on dielectric with contact line pinning},
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     pages = {85--119},
     year = {2010},
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     number = {1},
     doi = {10.4171/ifb/228},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/228/}
}
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