Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-19T22:50:39.363Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. & Green, J. T. 1972 J. Fluid Mech. 56, 375.
Brady, J. F. & Bossis, G. 1988 Ann. Rev. Fluid Mech. 20, 111.
Eckstein, E. C., Bailey, D. G. & Shapiro, A. H. 1977 J. Fluid Mech. 79, 191.
Leighton, D. & Acrivos, A. 1986 Chem. Engng Sci. 41, 1377.
Leighton, D. & Acrivos, A. 1987a J. Fluid Mech. 177, 109.
Leighton, D. & Acrivos, A. 1987b J. Fluid Mech. 181, 415.