Equilibrium drop surface profiles in electric fields

Electrowetting is becoming a more and more frequently used tool to manipulate liquids in various microfluidic applications. On the scale of the entire drop, the effect of electrowetting is to reduce the apparent contact angle of partially wetting conductive liquids upon application of an external voltage. Microscopically, however, strong electric fields in the vicinity of the three phase contact line give rise to local deformations of the drop surface. We determined the equilibrium surface profile using a combined numerical, analytical, and experimental approach. We find that the local contact angle in electrowetting is equal to Young's angle independent of the applied voltage. Only on the scale of the thickness of the insulator and beyond does the surface slope assume a value consistent with the voltage-dependent apparent contact angle. This behaviour is verified experimentally by determining equilibrium surface profiles for insulators of various thicknesses between 10 and 250 µm. Numerically and analytically, we find that the local surface curvature diverges algebraically upon approaching the contact line with an exponent −1