Modeling of electrowetted surface tension for addressable microfluidic systems: dominant physical effects, material dependences, and limiting phenomena

This paper describes the equilibrium shape of a liquid drop under applied fields such as gravity and electrical fields, taking into account material properties such as dielectric constants, resistivities, and surface tension coefficients. The analysis is based on an energy minimization framework, scaling arguments, and on solutions of Maxwell´s electrostatic equations. A rigorous and exact link is provided between the energy function corresponding to any given physical phenomena, and the resulting shape and size dependent force term in the (modified) Young´s equation. It is shown that a dielectric solid and a perfectly conducting liquid is all that is needed to exactly recover the Young-Lippmann equation. A dielectric liquid on a conducting solid gives rise to line tension terms. Finally, a slightly resistive liquid on top of a dielectric, highly resistive solid gives rise to contact angle saturation and accurately predicts the experimental data that we observe in our electrowetting devices.