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Longitudinal shear-induced diffusion of spheres in a dilute suspension

Published online by Cambridge University Press:  26 April 2006

A. Acrivos ,
G. K. Batchelor ,
E. J. Hinch ,
D. L. Koch  and
R. Mauri
A. Acrivos
Affiliation:
Levich Institute, T1-M, City College of CUNY, New York, NY 10031, USA
G. K. Batchelor
Affiliation:
Department of Applied Mathematics and Theoretical Physics. University of Cambridge, Silver Street, Cambridge, CB3 9EW, UK
E. J. Hinch
Affiliation:
Department of Applied Mathematics and Theoretical Physics. University of Cambridge, Silver Street, Cambridge, CB3 9EW, UK
D. L. Koch
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853-5201, USA
R. Mauri
Affiliation:
Department of Chemical Engineering, City College of CUNY. New York. NY 10031, USA
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Abstract

We present a calculation of the hydrodynamic self-diffusion coefficient of a tagged particle in a dilute mono-dispersed suspension of small neutrally buoyant spheres undergoing a steady simple shearing motion. The displacement of the tagged particle parallel to the longitudinal or streamwise direction resulting from a ‘collision’ with one other particle is calculated on the assumption that inertia and Brownian motion effects are negligible. Summing over different pairs leads to a logarithmically divergent integral for the diffusivity which is rendered finite by allowing for the cutoff due to the occasional presence of another pair of particles. The longitudinal shearinduced self-diffusion coefficient is thus found to be 0.267a2γ{cln c−1 + O(c)], where γ denotes the applied shear rate, a is the radius of the spheres and c their volume concentration.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 240 , July 1992 , pp. 651 - 657
Copyright
© 1992 Cambridge University Press

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References

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