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Self-diffusion of particles in shear flow of a suspension

Published online by Cambridge University Press:  11 April 2006

Eugene C. Eckstein ,
Douglas G. Bailey  and
Ascher H. Shapiro
Eugene C. Eckstein
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge Present address: Biomedical Engineering Program, University of Miami, Coral Gables, Florida 33124.
Douglas G. Bailey
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge Present address: Foster-Miller Associates Inc., Waltham, Massachusetts 02154.
Ascher H. Shapiro
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge
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Abstract

Self-diffusion coefficients were determined experimentally for lateral dispersion of spherical and disk-like particles in linear shear flow of a slurry at very low Reynolds number. Using a concentric-cylinder Couette apparatus, recurrent observations were made of the lateral position of a particular radioactively labelled particle. The self-diffusion coefficient D was calculated by means of random-walk theory, using the ergodic hypothesis. Owing to great experimental difficulties, the calculated values of D are not of high accuracy, but are correct to within a factor of two. In the range 0 < ϕ < 0·2, D/a2ω increases from zero linearly with ϕ up to D/a2ω ≅ 0·02 (where ϕ = volumetric concentration of particles, a = particle radius, ω = mean shear rate of suspending fluid). In the range 0·2 < 0·5, the trend of D/a2ω is not clear because of experimental scatter, but in this range D/a2ω ≅ 0·025 to within a factor of two. Within the experimental accuracy, spheres and disks have the same value of D/a2ω.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 79 , Issue 1 , 20 January 1977 , pp. 191 - 208
Copyright
© 1977 Cambridge University Press

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