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Two-phase displacement in Hele-Shaw cells: experiments on viscously driven instabilities

Published online by Cambridge University Press:  20 April 2006

C.-W. Park ,
S. Gorell  and
G. M. Homsy
C.-W. Park
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305
S. Gorell
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305 Present address: Shell Development Co., Houston, Texas.
G. M. Homsy
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305
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Abstract

Experiments on the instability of the interface in two-phase displacements in Hele-Shaw cells were conducted using air and a viscous oil as the working fluids. The experiments had two objectives: (i) to provide quantitative measurements of the growth constants of the instability which occurs when a less-viscous fluid displaces a more-viscous one, and (ii) to compare the measured dispersion relations with the predictions of the recent theory of Park & Homsy (1984). The experiments were made by analysing the growth characteristics of between 10 and 20 Fourier modes describing the shape of the interface between displaced and displacing fluids, using still photography. For capillary numbers Ca = μU/γ less than approximately 4 × 10−3 the agreement is only fair, owing to substantial edge effects produced by a nearly static contact line near the lateral boundaries of the cell. For 4 × 10−3 < Ca < 1 × 10−2 theory and experiment agree to within the accuracy of the measurements. Location and verification of the behaviour of modes near the predicted cut-off wavenumber give partial verification of the theory of Park & Homsy.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 141 , April 1984 , pp. 275 - 287
Copyright
© 1984 Cambridge University Press

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