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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on July 6, 2009
The Quarterly Journal of Mechanics and Applied Mathematics 2009 62(4):465-480; doi:10.1093/qjmam/hbp016
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© The author 2009. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

A Variational Approach to Contact Angle Saturation and Contact Line Instability in Static Electrowetting

M. A. Fontelos{dagger}

( Instituto de Ciencias Matemáticas (ICMAT, CSIC-UAM-UCM-UC3M), Consejo Superior de Investigaciones Científicas, C/ Serrano 123, 28006 Madrid, Spain )

U. Kindelán{ddagger}

( Departamento de Matemática Aplicada y Met. Inf., Universidad Politécnica de Madrid, Ríos Rosas 21, 28003 Madrid, Spain )

{dagger} Corresponding author. <marco.fontelos{at}uam.es>

{ddagger} <ultano.kindelan{at}upm.es>

Received 2 February 2009. Revise 24 May 2009. Accepted 6 June 2009.


  Abstract

Drops of a conducting fluid in electrowetting devices tend to spread when a difference of potential V0 is set between the drop and an electrode external to it. The classical Lippmann theory predicts unlimited spreading, with a decrease of the contact angle between drop and solid substrate, as one increases V0. This fact is in contradiction with current experiments, where saturation of the contact angle to a limiting value is found. A further increase of V0 does not lead to further spreading but to the appearance of instabilities in the form of emitted drops at the contact line. We provide an explanation to these two related phenomena based solely on interfacial and electrostatic energies. A local analysis close to the contact line is also provided and an expression for the most unstable mode is deduced.


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