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Plane Stokes flow driven by capillarity on a free surface. Part 2. Further developments

Published online by Cambridge University Press:  26 April 2006

Robert W. Hopper
Robert W. Hopper
Affiliation:
Chemistry and Materials Science Department, Lawrence Livermore National Laboratory, Livermore, CA, USA
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Abstract

For the free creeping viscous incompressible plane flow of a finite region, bounded by a simple smooth closed curve and driven solely by surface tension, analyzed previously, the shape evolution was described in terms of a time-dependent mapping function z = Ω(ζ,t) of the unit circle, conformal on |ζ| [les ] 1. An equation giving the time evolution of the map, typically in parametric form, was derived. In this article, the flow of the infinite region exterior to a hypotrochoid is given. This includes the elliptic hole, which shrinks at a constant rate with a constant aspect ratio. The theory is extended to a class of semi-infinite regions, mapped from Im ζ [les ] 0, and used to solve the flow in a half-space bounded by a certain groove. The depth of the groove ultimately decays inversely with time.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 230 , September 1991 , pp. 355 - 364
Copyright
© 1991 Cambridge University Press

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References

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