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Recriprocal theorem for concentric compound drops in arbitrary Stokes flows

Published online by Cambridge University Press:  26 April 2006

H. Haj-Hariri ,
A. Nadim  and
A. Borhan
H. Haj-Hariri
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22901, USA
A. Nadim
Affiliation:
Department of Aerospace and Mechanical Engineering, Boston University, Boston, MA 02215, USA
A. Borhan
Affiliation:
Department of Chemical Engineering, The Pennsylvania State University, University Park, PA 16802, USA
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Abstract

The Lorentz reciprocal theorem is generalized and applied to the study of the quasisteady motion of a concentric spherical (CS) compound drop at zero Reynolds number. Using this result, the migration velocities of a force-free CS compound drop placed in a general ambient Stokes flow, as well as the forces on each drop when subjected to specified migration velocities, are calculated. The latter constitutes a generalization of Faxén's law to the case of a CS compound drop. Also some earlier results on the thermocapillary migration of such drops (Borhan et al. 1992) are rederived more simply and in greater generality.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 252 , July 1993 , pp. 265 - 277
Copyright
© 1993 Cambridge University Press

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