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ORIGINAL PAPER
The Two-Phase Hell-Shaw Flow: Construction of an Exact Solution
1
Department of Mathematics, Ohio University Athens, OH 45701, USA
Online publication date: 2013-04-19
Publication date: 2013-03-01
International Journal of Applied Mechanics and Engineering 2013;18(1):249-257
KEYWORDS
ABSTRACT
We consider a two-phase Hele-Shaw cell whether or not the gap thickness is time-dependent. We construct an exact solution in terms of the Schwarz function of the interface for the two-phase Hele-Shaw flow. The derivation is based upon the single-valued complex velocity potential instead of the multiple-valued complex potential. As a result, the construction is applicable to the case of the time-dependent gap. In addition, there is no need to introduce branch cuts in the computational domain. Furthermore, the interface evolution in a two-phase problem is closely linked to its counterpart in a one-phase problem
FUNDING
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
CONFLICT OF INTEREST
The authors declare that they have no conflict of interest.
DATA AVAILABILITY
All data generated or analysed during this study are included in this published article.
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| eISSN: | 2353-9003 |
| ISSN: | 1734-4492 |
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