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

D. E. Moulton, Joceline C Lega

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 2013

Fingerprint

Thin Film Equation
Forcing
Thin films
Boundary conditions
Magnetic films
Matched Asymptotic Expansions
Contact Angle
Equilibrium Solution
Coarsening
Steady-state Solution
Numerical Investigation
Contact angle
Thin Films
Reverse
Continuum
Zero

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Effect of disjoining pressure in a thin film equation with non-uniform forcing. / Moulton, D. E.; Lega, Joceline C.

In: European Journal of Applied Mathematics, Vol. 24, No. 6, 12.2013, p. 887-920.

Research output: Contribution to journalArticle

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