Roughness of moving elastic lines - crack and wetting fronts

TL;DR

This paper derives nonlinear equations for propagating elastic lines in disordered media, studying their roughness and revealing a possible universal roughness exponent of 1/2, with implications for wetting and fracture fronts.

Contribution

It provides a first-principles derivation of the equations of motion for crack and wetting fronts and analyzes their roughness behavior using the self-consistent expansion method.

Findings

Possible roughness exponent of 1/2 without irreversibility.

Irreversibility leads to history-dependent propagation.

Experimental results for wetting fronts are close to 0.5, while fracture fronts show higher roughness exponents.

Abstract

We investigate propagating fronts in disordered media that belong to the universality class of wetting contact lines and planar tensile crack fronts. We derive from first principles their nonlinear equations of motion, using the generalized Griffith criterion for crack fronts and three standard mobility laws for contact lines. Then we study their roughness using the self-consistent expansion. When neglecting the irreversibility of fracture and wetting processes, we find a possible dynamic rough phase with a roughness exponent of $\zeta=1/2$ and a dynamic exponent of z=2. When including the irreversibility, we conclude that the front propagation can become history dependent, and thus we consider the value $\zeta=1/2$ as a lower bound for the roughness exponent. Interestingly, for propagating contact line in wetting, where irreversibility is weaker than in fracture, the experimental results are close to 0.5, while for fracture the reported values of 0.55--0.65 are higher.