Gradient-dynamics model for liquid drops on elastic substrates

TL;DR

This paper introduces a gradient dynamics model for liquid drops on elastic substrates, capturing static and dynamic wetting behaviors and ensemble coarsening, with implications for understanding soft wetting phenomena.

Contribution

A reduced long-wave gradient dynamics model for soft wetting that applies to multiple droplets and captures key static and dynamic features.

Findings

Reproduces the double transition in equilibrium contact angles with substrate softness.

Accurately models the dependence of dynamic contact angle on contact line velocity.

Shows nontrivial changes in coarsening modes with substrate softness.

Abstract

The wetting of soft elastic substrates exhibits many features that have no counterpart on rigid surfaces. Modelling the detailed elastocapillary interactions is challenging, and has so far been limited to single contact lines or single drops. Here we propose a reduced long-wave model that captures the main qualitative features of statics and dynamics of soft wetting, but which can be applied to ensembles of droplets. The model has the form of a gradient dynamics on an underlying free energy that reflects capillarity, wettability and compressional elasticity. With the model we first recover the double transition in the equilibrium contact angles that occurs when increasing substrate softness from ideally rigid towards very soft (i.e., liquid). Second, the spreading of single drops of partially and completely wetting liquids is considered showing that known dependencies of the dynamic contact angle on contact line velocity are well reproduced. Finally, we go beyond the single droplet picture and consider the coarsening for a two-drop system as well as for a large ensemble of drops. It is shown that the dominant coarsening mode changes with substrate softness in a nontrivial way.