Gradient flow perspective on thin-film bilayer flows

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

Journal of Engineering Mathematics, vol.94, no.1, pp.43-61, 2015 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 94 Issue: 1
  • Publication Date: 2015
  • Doi Number: 10.1007/s10665-014-9698-1
  • Journal Name: Journal of Engineering Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.43-61
  • Keywords: Bilayer, Contact line, Gradient flow, Thin-film
  • Middle East Technical University Northern Cyprus Campus Affiliated: No

Abstract

We study gradient flow formulations of thin-film bilayer flows with triple-junctions between liquid/liquid/air phase. First we highlight the gradient structure in the Stokes free-boundary flow and identify its solutions with the well-known PDE with boundary conditions. Next we propose a similar gradient formulation for the corresponding reduced thin-film model and formally identify solutions with those of a PDE problem. A robust numerical algorithm for the thin-film gradient flow structure is then provided. Using this algorithm we compare the sharp triple-junction model with precursor models. For their stationary solutions a rigorous connection is established using (Formula presented.)-convergence. For time-dependent solutions the comparison of numerical solutions shows a good agreement for small and moderate times. Finally we study spreading in the zero-contact angle case, where we compare numerical solutions with asymptotically exact source-type solutions.