Discrete families of Saffman–Taylor fingers with exotic shapes
The mathematical problem of determining the shape of a steadily propagating Saffman–Taylor finger in a rectangular Hele-Shaw cell is known to have a countably infinite number of solutions for each fixed surface tension value. For sufficiently large surface tension values, we find that fingers on higher solution branches are non-convex. The tips of the fingers have increasingly exotic shapes as the branch number increases.
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|Item Type:||Journal Article|
|Keywords:||Hele-Shaw flows, Saffman–Taylor instability, Viscous fingering, surface tension, free boundary problem|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Theoretical and Applied Mechanics (010207)|
|Divisions:||Current > QUT Faculties and Divisions > Science & Engineering Faculty
Past > Schools > Mathematical Sciences
|Copyright Owner:||This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)|
|Copyright Statement:||The CC-BY license allows users to copy, to create extracts, abstracts and new works from the Article, to alter and revise the Article and to make commercial use of the Article (including reuse and/or resale of the Article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made and the licensor is not represented as endorsing the use made of the work. The full details of the license are available at http://creativecommons.org/licenses/by/4.0.|
|Deposited On:||18 May 2015 03:18|
|Last Modified:||22 May 2015 05:23|
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