Static wetting on deformable substrates, from liquids to soft solids

TL;DR

This paper extends a linear-elastic model to analyze how droplets of various sizes deform soft substrates, revealing a crossover from Young's law to Neumann's prediction and showing size-dependent wetting behavior.

Contribution

It introduces a generalized model for substrate deformation by droplets of arbitrary size, bridging the gap between liquid and solid wetting regimes.

Findings

Large droplets follow Young's law for contact angle.

Small droplets follow Neumann's prediction.

The crossover size depends on surface tension and elastic modulus.

Abstract

Young's law fails on soft solid and liquid substrates where there are substantial deformations near the contact line. On liquid substrates, this is captured by Neumann's classic analysis, which provides a geometrical construction for minimising the interfacial free energy. On soft solids, the total free energy includes an additional contribution from elasticity. A linear-elastic model incorporating an out-of-plane restoring force due to solid surface tension was recently shown to accurately predict the equilibrium shape of a thin elastic film due to a large sessile droplet. Here, we extend this model to find substrate deformations due to droplets of arbitrary size. While the macroscopic contact angle matches Young's law for large droplets, it matches Neumann's prediction for small droplets. The cross-over droplet size is roughly given by the ratio of the solid's surface tension and elastic modulus. At this cross-over, the macroscopic contact angle increases, indicating that the substrate is effectively less wetting. For droplets of all sizes, the microscopic behaviour near the contact line follows the Neumann construction giving local force balance.