Electrowetting on thick substrates: A modified Young–Lippmann equation

Electrowetting is a versatile technique for controlling the apparent contact angle of drops on thin insulating films through an externally applied potential. In the light of slide electrification—the spontaneous charging of sliding drops on dielectric substrates—electrowetting has gained new importance. Drops can spontaneously attain kilovolt potentials and undergo spontaneous electrowetting. Often, drop sizes and substrate thicknesses are comparable, violating the assumptions underlying the Young–Lippmann and the plate capacitor equations. In this work, I numerically determine the capacitance of sessile drops on thick substrates and introduce an analytical approximation. I derive a modified Young–Lippmann equation that quantitatively describes electrowetting ranging from thin films to substrate thicknesses many times the drop size.