Critical Dynamics of Contact Line Depinning

Abstract

The depinning of a contact line is studied as a dynamical critical phenomenon by a functional renormalization group technique. In $D=2-ε$ interface dimensions, the roughness exponent is $ζ=ε/3$ to all orders in perturbation theory. Thus, $ζ=1/3$ for the contact line, equal to the Imry-Ma estimate of Huse for the equilibrium roughness. The dynamical exponent is $z=1-2ε/9+O(ε^2)<1$, resulting in unusual dynamical properties. In particular, a characteristic distortion length of the contact line depinning from a strong defect is predicted to initially increase faster than linearly in time. Some experiments are suggested to probe such dynamics.