Equilibrium behavior of sessile drops under surface tension, applied external fields, and material variations

This article 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. 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 Young’s equation. In particular, the framework shows that a physical effect, such as capacitive energy storage in the liquid, will lead to 1/R ‘‘line-tension’’-type terms if and only if the energy of the effect is proportional to the radius of the liquid drop: E}R . The effect of applied electric fields on shape change is analyzed. It is shown that a dielectric solid and a perfectly conducting liquid are 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 matches the experimental data that we observe in our electro-wetting-on-dielectric devices. © 2003 American Institute of Physics. @DOI: 10.1063/1.1563828#