Critical Dynamics of Contact Line Depinning

TL;DR

This paper investigates the critical dynamics of contact line depinning using a functional renormalization group approach, revealing universal roughness and dynamical exponents with implications for experimental observation.

Contribution

It provides a theoretical analysis of contact line depinning as a critical phenomenon, deriving universal exponents and predicting unique dynamical behavior.

Findings

Roughness exponent $=1/3$ for contact lines.

Dynamical exponent $z<1$, indicating unusual dynamics.

Predicted initial superlinear growth of depinning length.

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.