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

Published online by Cambridge University Press:  02 August 2013

D. E. MOULTON  and
J. LEGA
D. E. MOULTON
Affiliation:
OCCAM, Mathematical Institute, University of Oxford, UK email: moulton@maths.ox.ac.uk Department of Mathematics, University of Arizona, Tucson, AZ, USA email: lega@math.arizona.edu
J. LEGA
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ, USA email: lega@math.arizona.edu
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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.

Keywords

evolution equationlubrication approximationmagnetic filmmatched asymptotic expansioncoarsening
Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 6 , December 2013 , pp. 887 - 920
Copyright
Copyright © Cambridge University Press 2013 

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