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Particle motion in Stokes flow near a plane fluid-fluid interface. Part 1. Slender body in a quiescent fluid

Published online by Cambridge University Press:  20 April 2006

Seung-Man Yang  and
L. Gary Leal
Seung-Man Yang
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125
L. Gary Leal
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125
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Abstract

The present study examines the motion of a slender body in the presence of a plane fluid–fluid interface with an arbitrary viscosity ratio. The fluids are assumed to be at rest at infinity, and the particle is assumed to have an arbitrary orientation relative to the interface. The method of analysis is slender-body theory for Stokes flow using the fundamental solutions for singularities (i.e. Stokeslets and potential doublets) near a flat interface. We consider translation and rotation, each in three mutually orthogonal directions, thus determining the components of the hydrodynamic resistance tensors which relate the total hydrodynamic force and torque on the particle to its translational and angular velocities for a completely arbitrary translational and angular motion. To illustrate the application of these basic results, we calculate trajectories for a freely rotating particle under the action of an applied force either normal or parallel to a flat interface, which are relevant to particle sedimentation near a flat interface or to the processes of particle capture via drop or bubble flotation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 136 , November 1983 , pp. 393 - 421
Copyright
© 1983 Cambridge University Press

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