= Solution
For a smooth homogeneous solid and a partially wetting liquid at equilibrium, tangential balance at the <contact line> gives <Young's equation>
$$
\boxed{\gamma_{SV}=\gamma_{SL}+\gamma_{LV}\cos\theta.}
$$
The 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> is
$$
\boxed{S=\gamma_{SV}-\gamma_{SL}-\gamma_{LV}.}
$$
For 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 $\cos\theta>1$.
Back to article page
