Wetting of soft substrates

TL;DR

This paper develops a mean-field theoretical framework to analyze how elastic properties of substrates influence wetting behavior, revealing that substrate elasticity can suppress or alter wetting transitions.

Contribution

It introduces an effective theory for fluid wetting on elastic substrates, incorporating substrate elasticity into the interfacial potential analysis.

Findings

Elasticity can suppress critical wetting transitions.

Substrate elasticity may turn continuous wetting into first-order transitions.

Effective interface potential includes bilinear terms from substrate-fluid interactions.

Abstract

Within mean-field theory we study wetting of elastic substrates. Our analysis is based on a grand canonical free energy functional of the fluid number density and of the substrate displacement field. The substrate is described in terms of the linear theory of elasticity, parametrized by two Lam\'e coefficients. The fluid contribution is of the van der Waals type. Two potentials characterize the interparticle interactions in the system. The long-ranged attraction between the fluid particles is described by a potential $w(r)$, and $v(r)$ characterizes the substrate-fluid interaction. By integrating out the elastic degrees of freedom we obtain an effective theory for the fluid number density alone. Its structure is similar to the one for wetting of an inert substrate. However, the potential $w(r)$ is replaced by an effective potential which, in addition to $w(r)$, contains a term bilinear in $v(r)$. We discuss the corresponding wetting transitions in terms of an effective interface potential $\omega(\ell)$, where $\ell$ denotes the thickness of the wetting layer. We show that in the case of algebraically decaying interactions the elasticity of the substrate may suppress critical wetting transitions, and may even turn them first order.