The Hele-Shaw injection problem for an extremely shear- thinning power law fluid
The Hele-Shaw injection problem for an extremely shear- thinning power law fluid
We consider Hele-Shaw flows driven by injection of a highly shear-thinning power-law fluid (of exponent n) in the absence of surface tension. We formulate the problem in terms of the streamfunction ?, which satisfies the p-Laplacian equation ?·(|??|p?2??) = 0 (with p = (n+1)/n) and use the method of matched asymptotic expansions in the large n (extreme-shear-thinning) limit to find an approximate solution. The results show that significant flow occurs only in (I) segments of a (single) circle centred on the injection point, whose perimeters comprise the portion of free boundary closest to the injection point and (II) an exponentially small region around the injection point and (III) a transition region to the rest of the fluid: while the flow in the latter is exponentially slow it can be characterised in detail
power law fluids, matched asymptotic expansions, free boundary problems, p-laplace equation
563-594
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
King, John
7d4e166d-4b3c-4440-a472-ef597d7a01f6
September 2015
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
King, John
7d4e166d-4b3c-4440-a472-ef597d7a01f6
Richardson, Giles and King, John
(2015)
The Hele-Shaw injection problem for an extremely shear- thinning power law fluid.
European Journal of Applied Mathematics, 26 (563-594), .
(doi:10.1017/S095679251500039).
Abstract
We consider Hele-Shaw flows driven by injection of a highly shear-thinning power-law fluid (of exponent n) in the absence of surface tension. We formulate the problem in terms of the streamfunction ?, which satisfies the p-Laplacian equation ?·(|??|p?2??) = 0 (with p = (n+1)/n) and use the method of matched asymptotic expansions in the large n (extreme-shear-thinning) limit to find an approximate solution. The results show that significant flow occurs only in (I) segments of a (single) circle centred on the injection point, whose perimeters comprise the portion of free boundary closest to the injection point and (II) an exponentially small region around the injection point and (III) a transition region to the rest of the fluid: while the flow in the latter is exponentially slow it can be characterised in detail
Text
European Journal of Applied Mathematics 2015 RICHARDSON.pdf
- Accepted Manuscript
More information
Accepted/In Press date: 30 June 2015
Published date: September 2015
Keywords:
power law fluids, matched asymptotic expansions, free boundary problems, p-laplace equation
Organisations:
Applied Mathematics
Identifiers
Local EPrints ID: 381660
URI: http://eprints.soton.ac.uk/id/eprint/381660
ISSN: 0956-7925
PURE UUID: 7bad6b98-213a-4c77-a654-b557988041c0
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Date deposited: 12 Oct 2015 12:28
Last modified: 15 Mar 2024 03:33
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Author:
John King
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