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.