Can non-linear elasticity explain contact-line roughness at depinning?

TL;DR

This paper investigates whether cubic non-linearities in the elastic energy of a contact line can lead to a different universality class at depinning, potentially explaining the higher roughness exponents observed experimentally.

Contribution

It demonstrates that cubic non-linearities generate a non-local KPZ-type term, leading to a new fixed point with higher roughness exponent, indicating a different universality class.

Findings

A non-local KPZ-type term is generated at depinning.

A fixed point with roughness exponent ~0.45 is identified.

Large cubic terms increase the contact line roughness.

Abstract

We examine whether cubic non-linearities, allowed by symmetry in the elastic energy of a contact line, may result in a different universality class at depinning. Standard linear elasticity predicts a roughness exponent zeta=1/3 (one loop), zeta=0.39 (numerics) while experiments give zeta of about 0.5. Within functional RG we find that a non-local KPZ-type term is generated at depinning and grows under coarse graining. A fixed point with zeta=0.45 (one loop) is identified, showing that large enough cubic terms increase the roughness. This fixed point is unstable, revealing a rough strong-coupling phase. Experimental study of contact angles theta near pi/2, where cubic terms vanish in the energy, is suggested.