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On a phase-field model for electrowetting and other electrokinetic phenomena

Author
Fontelos, M. A.; Grün, G.; Jörres, S.
Entity
UAM. Departamento de Matemáticas
Publisher
Society for Industrial and Applied Mathematics
Date
2011
Citation
10.1137/090779668
SIAM Journal on Mathematical Analysis 43.1 (2011): 527-563
 
 
 
ISSN
0036-1410
DOI
10.1137/090779668
Funded by
This work was supported by DAAD, Ministerio de Educación y Ciencia through the program Acciones Integradas Hispano Alemanas, project D/06/12788, and by Dr. Hertha und Helmut Schmauser-Stiftung.
Editor's Version
http://dx.doi.org/10.1137/090779668
Subjects
Cahn-Hilliard equation; Electrolytes; Electrowetting; Elliptic transmission problem; Existence of weak solutions in three dimensions; Free boundary problem in PDE; Llog L-Orlicz class; Navier-Stokes system; Nernst-Planck equation; Phase-field model; Regularity iteration; Matemáticas
URI
http://hdl.handle.net/10486/669551
Rights
© 2011 by SIAM

Abstract

In three space dimensions, we present existence results for weak solutions to a novel two-phase model for various electrokinetic phenomena, including in particular dynamic electrowetting with electrolytes. The model is thermodynamically consistent. It combines Navier-Stokes- and Cahn-Hilliard-type phase-field equations with Nernst-Planck equations for ion density-evolution and with an elliptic transmission problem for the electrostatic potential. As physical energy estimates guarantee only boundedness of ion densities in the Llog L-Orlicz class uniformly with respect to time, an iteration method is proposed to establish higher regularity and integrability results of these quantities. In an appendix, the derivation of the model is sketched
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