On a Hele-Shaw flow with a time-dependent gap in the presence of surface tension

The introduction of surface tension into a Hele-Shaw problem makes it more realistic from the physical viewpoint, but more difficult from the mathematical viewpoint. In this paper we discuss a Hele-Shaw flow with a time-dependent gap taking into account the surface tension of the free boundary. We u...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2015-03, Vol.48 (12), p.125501-13
Main Authors: Savina, T V, Nepomnyashchy, A A
Format: Article
Language:English
Subjects:
Asymptotic properties
Circles (geometry)
Distortion
Droplets
Free boundaries
Functions (mathematics)
Hele-shaw cell
Mathematical analysis
Schwarz function
Surface tension
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Summary:The introduction of surface tension into a Hele-Shaw problem makes it more realistic from the physical viewpoint, but more difficult from the mathematical viewpoint. In this paper we discuss a Hele-Shaw flow with a time-dependent gap taking into account the surface tension of the free boundary. We use the Schwarz function method to find asymptotic solutions for the interior problem in the case when the initial shape of the droplet is a weakly distorted circle.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/48/12/125501