Geodesic
Electrowetting of a 3D drop : numerical modelling with electrostatic vector fields
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 44 (2010) no. 4, pp. 647-670

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The electrowetting process is commonly used to handle very small amounts of liquid on a solid surface. This process can be modelled mathematically with the help of the shape optimization theory. However, solving numerically the resulting shape optimization problem is a very complex issue, even for reduced models that occur in simplified geometries. Recently, the second author obtained convincing results in the 2D axisymmetric case. In this paper, we propose and analyze a method that is suitable for the full 3D case.

DOI : 10.1051/m2an/2010014
Classification : 65N12, 65N30, 49Q10
Keywords: electrowetting, energy minimization, contact angle, error estimates 
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     title = {Electrowetting of a {3D} drop : numerical modelling with electrostatic vector fields},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {647--670},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {4},
     year = {2010},
     doi = {10.1051/m2an/2010014},
     mrnumber = {2683577},
     zbl = {1193.78029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010014/}
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Ciarlet Jr., Patrick; Scheid, Claire. Electrowetting of a 3D drop : numerical modelling with electrostatic vector fields. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 44 (2010) no. 4, pp. 647-670. doi: 10.1051/m2an/2010014

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