Elasticity of a contact-line and avalanche-size distribution at depinning

TL;DR

This paper extends the theoretical understanding of contact line elasticity to arbitrary angles and inclinations, providing exact calculations and predictions for avalanche-size distributions during depinning.

Contribution

It introduces a generalized elastic model for contact lines at various angles and derives exact elastic mode diagonalization, predicting avalanche-size distributions at depinning.

Findings

Elastic modes are exactly diagonalized for arbitrary contact angles.

Predictions for universal avalanche-size distributions are provided.

The ratio of moments of local to global avalanches depends on the elastic kernel.

Abstract

Motivated by recent experiments, we extend the Joanny-deGennes calculation of the elasticity of a contact line to an arbitrary contact angle and an arbitrary plate inclination in presence of gravity. This requires a diagonalization of the elastic modes around the non-linear equilibrium profile, which is carried out exactly. We then make detailed predictions for the avalanche-size distribution at quasi-static depinning: we study how the universal (i.e. short-scale independent) rescaled size distribution and the ratio of moments of local to global avalanches depend on the precise form of the elastic kernel.