- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:03
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
11
2009
2
On a phase-field model for electrowetting
Christof
Eck
Universität Stuttgart, STUTTGART, GERMANY
M.
Fontelos
Universidad Autónoma de Madrid, MADRID, SPAIN
Günther
Grün
Universität Erlangen-Nünberg, ERLANGEN, GERMANY
F.
Klingbeil
Universität Erlangen-Nünberg, ERLANGEN, GERMANY
O.
Vantzos
Universidad Autónoma de Madrid, MADRID, SPAIN
Electrowetting, phase-field model, Navier–Stokes system, Cahn–Hilliard model, free boundary problem in PDE, existence of weak solutions
The term electrowetting is commonly used for phenomena where shape and wetting behavior of liquid droplets are changed by the application of electric fields. We develop and analyze a model for electrowetting that combines the Navier–Stokes system for fluid flow, a phase-field model of Cahn–Hilliard type for the movement of the interface, a charge transport equation, and the potential equation of electrostatics. The model is derived with the help of a variational principle due to Onsager and conservation laws. A modification of the model with the Stokes system instead of the Navier– Stokes system is also presented. The existence of weak solutions is proved for several cases in two and three space dimensions, either with non-degenerate or with degenerate electric conductivity vanishing in the droplet exterior. Some numerical examples in two space dimensions illustrate the applicability of the model.
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
259
290
10.4171/IFB/211
http://www.ems-ph.org/doi/10.4171/IFB/211