The Mathematical Institute, University of Oxford, Eprints Archive

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

Moulton, D. E. and Lega, J. (2012) Effect of disjoining pressure in a thin film equation with
non-uniform forcing.
European Journal of Applied Mathematics . (Submitted)

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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 asymptotics 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.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1627
Deposited By:Peter Hudston
Deposited On:24 Nov 2012 08:58
Last Modified:24 Nov 2012 08:58

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