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

Type
Article

Authors
MOULTON, D. E.
LEGA, J.

KAUST Grant Number
KUK-C1-013-04

Online Publication Date
2013-08-02

Print Publication Date
2013-12

Date
2013-08-02

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. Copyright © Cambridge University Press 2013.

Citation
MOULTON DE, LEGA J (2013) Effect of disjoining pressure in a thin film equation with non-uniform forcing. European Journal of Applied Mathematics 24: 887–920. Available: http://dx.doi.org/10.1017/S0956792513000235.

Acknowledgements
This paper is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (author DEM). We also thank the reviewers for their helpful comments.

Publisher
Cambridge University Press (CUP)

Journal
European Journal of Applied Mathematics

DOI
10.1017/S0956792513000235

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