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Theory of tracer diffusion in concentrated hard-sphere suspensions

Published online by Cambridge University Press:  15 May 2019

S. S. L. Peppin Open the ORCID record for S. S. L. Peppin [Opens in a new window]
S. S. L. Peppin*
Affiliation:
Mississauga, L5G 2K5 Canada
*
†Email address for correspondence: [email protected]
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Abstract

A phenomenological theory of diffusion and cross-diffusion of tracer particles in concentrated hard-sphere suspensions is developed. Expressions for the diffusion coefficients as functions of the host particle volume fraction are obtained up to the close-packing limit. In concentrated systems the tracer diffusivity decreases because of the reduced pore space available for diffusion. The tracer diffusivity can be modelled by a Stokes–Einstein equation with an effective viscosity that depends on the pore size. Tracer diffusion and segregation during sedimentation cease at a critical trapping volume fraction corresponding to a tracer glass transition. The tracer cross-diffusion coefficient, however, increases near the glass transition and diverges in the close-packed limit.

JFM classification

Complex Fluids: Colloids Low-Reynolds-number flows: Porous media Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 870 , 10 July 2019 , pp. 1105 - 1126
Copyright
© 2019 Cambridge University Press 

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