Past exam of the quantum condensed matter course of the University of Cambridge / 2007 / Section A / A4 / b / Solution

For a smooth homogeneous solid and a partially wetting liquid at equilibrium, tangential balance at the contact line gives Young's equationThe angle is measured through the liquid. Replacing solid-vapour area by solid-liquid plus liquid-vapour area changes free energy by $-S$ per wetted area, where the spreading coefficient isFor partial wetting, $S={\gamma }_{LV}(\cos \theta -1)<0$. Positive $S$ favours a spreading film and zero macroscopic equilibrium contact angle; the finite-angle Young construction cannot be extrapolated to $\cos \theta >1$.