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Flow in a differentially rotated cylindrical drop at low Reynolds number

Published online by Cambridge University Press:  20 April 2006

George M. Harriott  and
Robert A. Brown
George M. Harriott
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Robert A. Brown
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
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Abstract

A liquid drop held captive between parallel disks that are differentially rotated is a model for the swirling flows induced by crystal rotation in the floating-zone process for growing semiconductor materials. An asymptotic analysis for a cylindrical drop is presented that elucidates the structure of the axisymmetric cellular motions caused by disk rotation at low Reynolds number. Variations of meniscus shape induced by these flows are described in the limit of small capillary number. Most cellular flow fields break the bifurcation point that corresponds to the Plateau–Rayleigh limit for the length of a static drop into two disjoint shape families and lower the maximum stable drop length. This effect is studied by a singular bifurcation analysis.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 126 , January 1983 , pp. 269 - 285
Copyright
© 1983 Cambridge University Press

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