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The slow spreading of a viscous fluid film over a deep viscous pool

The slow spreading of a viscous fluid film over a deep viscous pool
The slow spreading of a viscous fluid film over a deep viscous pool
A model is introduced for the spreading of an isolated viscous foam film over a deep viscous fluid pool. The effects of the bubbles rising in the foam are neglected, but the O(1) alteration to the density and viscosity of the foam due to the bubbles are accounted for. It is assumed that the foam phase is well modelled by the Stokes-flow equations. By exploiting the slenderness of the spreading layer, asymptotic techniques are used to analyse the flow in the foam. It is shown that in this regime the dominant horizontal force balance is between the hydrostatic pressure and the tangential stress induced in the layer by the underlying pool. Boundary-integral techniques are used to determine the form of the flow in the pool and from this an expression for the evolution of the spreading foam is given analytically. In this parameter regime it is found that this expression does not depend upon the viscosity of the foam
0022-0833
393-408
Foster, J.m.
b93acb2c-f981-4d4b-bc01-b1bc8332facf
Please, C.P.
118dffe7-4b38-4787-a972-9feec535839e
Fitt, A.D.
51b348d7-b553-43ac-83f2-3adbea3d69ab
Foster, J.m.
b93acb2c-f981-4d4b-bc01-b1bc8332facf
Please, C.P.
118dffe7-4b38-4787-a972-9feec535839e
Fitt, A.D.
51b348d7-b553-43ac-83f2-3adbea3d69ab

Foster, J.m., Please, C.P. and Fitt, A.D. (2011) The slow spreading of a viscous fluid film over a deep viscous pool. Journal of Engineering Mathematics, 71 (4), 393-408. (doi:10.1007/s10665-011-9460-x).

Record type: Article

Abstract

A model is introduced for the spreading of an isolated viscous foam film over a deep viscous fluid pool. The effects of the bubbles rising in the foam are neglected, but the O(1) alteration to the density and viscosity of the foam due to the bubbles are accounted for. It is assumed that the foam phase is well modelled by the Stokes-flow equations. By exploiting the slenderness of the spreading layer, asymptotic techniques are used to analyse the flow in the foam. It is shown that in this regime the dominant horizontal force balance is between the hydrostatic pressure and the tangential stress induced in the layer by the underlying pool. Boundary-integral techniques are used to determine the form of the flow in the pool and from this an expression for the evolution of the spreading foam is given analytically. In this parameter regime it is found that this expression does not depend upon the viscosity of the foam

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Published date: 27 February 2011
Organisations: Applied Mathematics

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Local EPrints ID: 202959
URI: http://eprints.soton.ac.uk/id/eprint/202959
ISSN: 0022-0833
PURE UUID: e635fa35-fb78-4007-ac82-54ddbcb3e492

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Date deposited: 10 Nov 2011 11:40
Last modified: 14 Mar 2024 04:26

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Contributors

Author: J.m. Foster
Author: C.P. Please
Author: A.D. Fitt

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