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.
@article{M2AN_2010__44_4_647_0,
author = {Ciarlet Jr., Patrick and Scheid, Claire},
title = {Electrowetting of a 3D drop : numerical modelling with electrostatic vector fields},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {44},
year = {2010},
pages = {647-670},
doi = {10.1051/m2an/2010014},
mrnumber = {2683577},
zbl = {1193.78029},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2010__44_4_647_0}
}
Ciarlet Jr., Patrick; Scheid, Claire. Electrowetting of a 3D drop : numerical modelling with electrostatic vector fields. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 44 (2010) pp. 647-670. doi : 10.1051/m2an/2010014. http://gdmltest.u-ga.fr/item/M2AN_2010__44_4_647_0/
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