Effect of disjoining pressure in a thin film equation with non-uniform forcing

D. E. Moulton, J. Lega

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

We explore the effect of disjoining pressure on a thin film equation in the presence of a non-uniform body force, motivated by a model describing the reverse draining of a magnetic film. To this end, we use a combination of numerical investigations and analytical considerations. The disjoining pressure has a regularizing influence on the evolution of the system and appears to select a single steady-state solution for fixed height boundary conditions; this is in contrast with the existence of a continuum of locally attracting solutions that exist in the absence of disjoining pressure for the same boundary conditions. We numerically implement matched asymptotic expansions to construct equilibrium solutions and also investigate how they behave as the disjoining pressure is sent to zero. Finally, we consider the effect of the competition between forcing and disjoining pressure on the coarsening dynamics of the thin film for fixed contact angle boundary conditions.

Original languageEnglish (US)
Pages (from-to)887-920
Number of pages34
JournalEuropean Journal of Applied Mathematics
Volume24
Issue number6
DOIs
StatePublished - Dec 1 2013

Keywords

  • coarsening
  • evolution equation
  • lubrication approximation
  • magnetic film
  • matched asymptotic expansion

ASJC Scopus subject areas

  • Applied Mathematics

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