Stationary solutions of liquid two-layer thin-film models

Jachalski S., Huth R., Kitavtsev G., Peschka D., Wagner B.

SIAM Journal on Applied Mathematics, vol.73, no.3, pp.1183-1202, 2013 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 73 Issue: 3
  • Publication Date: 2013
  • Doi Number: 10.1137/120886613
  • Journal Name: SIAM Journal on Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1183-1202
  • Keywords: Free boundaries, Gamma-convergence, Matched asymptotics, Thin films
  • Middle East Technical University Northern Cyprus Campus Affiliated: No

Abstract

We investigate stationary solutions of a thin-film model for liquid two-layer flows in an energetic formulation that is motivated by its gradient flow structure. The goal is to achieve a rigorous understanding of the contact-angle conditions for such two-layer systems. We pursue this by investigating a corresponding energy that favors the upper liquid to dewet from the lower liquid substrate, leaving behind a layer of thickness h *. After proving existence of stationary solutions for the resulting system of thin-film equations, we focus on the limit h * → 0 via matched asymptotic analysis. This yields a corresponding sharp-interface model and a matched asymptotic solution that includes logarithmic switch-back terms. We compare this with results obtained using G-convergence, where we establish existence and uniqueness of energetic minimizers in that limit. © 2013 Society for Industrial and Applied Mathematics.