Wetting transitions on soft substrates

¹ Institute of Theoretical Physics, Faculty of Physics, University of Warsaw - Pasteura 5, 02-093 Warszawa, Poland
² Max-Planck-Institut für Intelligente Systeme - Heisenbergstr. 3, D-70569 Stuttgart, Germany
³ IV. Institut für Theoretische Physik, Universität Stuttgart - Pfaffenwaldring 57, D-70569 Stuttgart, Germany

Received: 5 November 2019
Accepted: 22 January 2020

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 Lamé 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 , and 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 the wetting of an inert substrate. However, the potential is replaced by an effective potential which, in addition to , contains a term bilinear in . We discuss the corresponding wetting transitions in terms of an effective interface potential , where ℓ 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.