Patterns formed in a thin film with spatially homogeneous and non-homogeneous Derjaguin disjoining pressure

TL;DR

This paper analyzes pattern formation in thin films influenced by Derjaguin disjoining pressure and wettability variations, clarifying previous numerical results and exploring bifurcation structures and effects of non-homogeneous pressures.

Contribution

It provides a rigorous theoretical framework for understanding pattern formation in thin films with both homogeneous and non-homogeneous disjoining pressures, extending prior numerical studies.

Findings

Identification of nucleation and metastable regimes in steady states

Analysis of bifurcation structures as film thickness and surface tension vary

Dependence of steady state solutions on wettability contrast

Abstract

We consider patterns formed in a two-dimensional thin film on a planar substrate with a Derjaguin disjoining pressure and periodic wettability stripes. We rigorously clarify some of the results obtained numerically by Honisch et al. and embed them in the general theory of thin-film equations. For the case of constant wettability, we elucidate the change in the global structure of branches of steady state solutions as the average film thickness and the surface tension are varied. Specifically we find, by using methods of local bifurcation theory and the continuation software package AUTO, both nucleation and metastable regimes. We discuss admissible forms of spatially non-homogeneous disjoining pressure, arguing for a form that differs from the one used by Honisch et al. , and study the dependence of the steady state solutions on the wettability contrast in that case.