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

Handle URI:
http://hdl.handle.net/10754/598051
Title:
Effect of disjoining pressure in a thin film equation with non-uniform forcing
Authors:
MOULTON, D. E.; LEGA, J.
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.
Publisher:
Cambridge University Press (CUP)
Journal:
European Journal of Applied Mathematics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
2-Aug-2013
DOI:
10.1017/S0956792513000235
Type:
Article
ISSN:
0956-7925; 1469-4425
Sponsors:
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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorMOULTON, D. E.en
dc.contributor.authorLEGA, J.en
dc.date.accessioned2016-02-25T13:11:44Zen
dc.date.available2016-02-25T13:11:44Zen
dc.date.issued2013-08-02en
dc.identifier.citationMOULTON 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.en
dc.identifier.issn0956-7925en
dc.identifier.issn1469-4425en
dc.identifier.doi10.1017/S0956792513000235en
dc.identifier.urihttp://hdl.handle.net/10754/598051en
dc.description.abstractWe 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.en
dc.description.sponsorshipThis 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.en
dc.publisherCambridge University Press (CUP)en
dc.subjectcoarseningen
dc.subjectevolution equationen
dc.subjectlubrication approximationen
dc.subjectmagnetic filmen
dc.subjectmatched asymptotic expansionen
dc.titleEffect of disjoining pressure in a thin film equation with non-uniform forcingen
dc.typeArticleen
dc.identifier.journalEuropean Journal of Applied Mathematicsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionUniversity of Arizona, Tucson, United Statesen
kaust.grant.numberKUK-C1-013-04en
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