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Numerical experiments on Hele Shaw flow with a sharp interface

Published online by Cambridge University Press:  20 April 2006

Gretar Tryggvason  and
Hassan Aref
Gretar Tryggvason
Affiliation:
Division of Engineering, Brown University, Providence, Rhode Island 02912, USA
Hassan Aref
Affiliation:
Division of Engineering, Brown University, Providence, Rhode Island 02912, USA
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Abstract

The fingering instability of an interface between two immiscible fluids in a Hele Shaw cell is simulated numerically. The algorithm used is based on a transcription of the equations of motion for the interface in which it formally becomes a generalized vortex sheet. The evolution of this sheet is computed using a variant of the vortex-in-cell method. The resulting scheme and code make it possible to follow the collective behaviour of many competing and interacting fingers well into the nonlinear, large-amplitude regime. It is shown that in this regime the evolution is controlled essentially by just one dimensionless parameter, the ratio of fluid viscosities. The effects of varying this parameter are studied and the results compared with experimental investigations. Scaling properties of the average density profile across the evolving mixed layer between the two homogeneous fluid phases are investigated. Many phenomena are observed that must be characterized as collective interactions and thus cannot be understood in terms of flows with just a single finger.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 136 , November 1983 , pp. 1 - 30
Copyright
© 1983 Cambridge University Press

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