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 $D=2-\epsilon$ interface dimensions, the roughness exponent is $\zeta =\epsilon /3$ to all orders in perturbation theory. Thus, $\zeta =1/3$ for the contact line, equal to the Imry-Ma estimate of Huse for the equilibrium roughness. The dynamical exponent is $z=1-2\epsilon /9+O({\epsilon }^2)<1$, 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.

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