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Properties of a bidisperse particle–gas suspension Part 2. Viscous relaxation time small compared with collision time

Published online by Cambridge University Press:  26 April 2006

V. Kumaran  and
Donald L. Koch
V. Kumaran
Affiliation:
School of Chemical Engineering. Cornell University, Ithaca, NY 14853, USA
Donald L. Koch
Affiliation:
School of Chemical Engineering. Cornell University, Ithaca, NY 14853, USA
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Abstract

The properties of a dilute bidisperse particle–gas suspension under low Reynolds number, high Stokes number conditions are studied in the limit τv [Lt ] τc, where τc is the time between successive collisions of a particle, and τv is the viscous relaxation time. In this limit, the particles relax close to their terminal velocity between successive collisions, and we use a perturbation analysis in the small parameter ε, which is proportional to τv/τc, about a base state in which all the particles settle at their terminal velocities. The mean velocities of the two species are O(ε) different from their terminal velocities, and the mean-square velocities are O(ε) smaller than the square of the terminal velocity. The distribution functions for the two species, which incorporate the first effects of collisions between particles settling at their terminal velocities, are derived. The velocity distribution is highly anisotropic in this limit, and the mean-square velocity in the vertical direction is twice that in the horizontal plane. The distribution function for each species is singular at its terminal velocity, and the distributions are non-zero in a finite region in velocity space between the two terminal velocities.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 247 , February 1993 , pp. 643 - 660
Copyright
© 1993 Cambridge University Press

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