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Transverse shear-induced gradient diffusion in a dilute suspension of spheres

Published online by Cambridge University Press:  25 February 1998

Y. WANG
Affiliation:
Levich Institute and Department of Chemical Engineering the City College of CUNY, New York, NY 10031, USA
R. MAURI
Affiliation:
Levich Institute and Department of Chemical Engineering the City College of CUNY, New York, NY 10031, USA
A. ACRIVOS
Affiliation:
Levich Institute and Department of Chemical Engineering the City College of CUNY, New York, NY 10031, USA

Abstract

We study the shear-induced gradient diffusion of particles in an inhomogeneous dilute suspension of neutrally buoyant spherical particles undergoing a simple shearing motion, with all inertia and Brownian motion effects assumed negligible. An expansion is derived for the flux of particles due to a concentration gradient along the directions perpendicular to the ambient flow. This expression involves the average velocity of the particles, which in turn is expressed as an integral over contributions from all possible configurations. The integral is divergent when expressed in terms of three-particle interactions and must be renormalized. For the monolayer case, such a renormalization is achieved by imposing the condition of zero total macroscopic flux in the transverse direction whereas, for the three-dimensional case, the additional constraint of zero total macroscopic pressure gradient is required. Following the scheme of Wang, Mauri & Acrivos (1996), the renormalized integral is evaluated numerically for the case of a monolayer of particles, giving for the gradient diffusion coefficient 0.077γa22, where is the applied shear rate, a the radius of the spheres and their areal fraction.

Type
Research Article
Copyright
© 1998 Cambridge University Press

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