Skip Navigation


The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on March 7, 2007
The Quarterly Journal of Mechanics and Applied Mathematics 2007 60(2):161-200; doi:10.1093/qjmam/hbm003
This Article
Right arrow Full Text
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
60/2/161    most recent
hbm003v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Richardson, G
Right arrow Articles by King, J.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Q. Jl Mech. Appl. Math, Vol. 60. No. 2 © The author 2007. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

The Saffman–Taylor problem for an extremely shear-thinning fluid

G Richardson{dagger} and JR King

( Section of Theoretical Mechanics, University of Nottingham, Nottingham NG7 2RD )

{dagger} Giles.Richardson{at}nottingham.ac.uk

Received 2 August 2006. Revise 16 January 2007.
  Abstract

We consider a steady flow driven by pushing a finger of gas into a highly shear-thinning power-law fluid, with exponent n, in a Hele-Shaw channel. We formulate the problem in terms of the streamfunction Formula, which satisfies the p-Laplacian equation Formula (with Formula), and investigate travelling wave solutions in the large-n (extreme shear-thinning) limit. We take a Legendre transform of the free-boundary problem for Formula, which reduces it to a linear problem on a fixed domain. The solution to this problem is found by using matched asymptotic expansions and the resulting shape of the finger deduced (being, to leading order, a semi-infinite strip). The nonlinear problem for the streamfunction is also treated using matched asymptotic expansion in the physical plane. The finger-width selection problem is briefly discussed in terms of our results.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.