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Dispersion due to molecular diffusion and macroscopic mixing in flow through a network of capillaries

Published online by Cambridge University Press:  28 March 2006

P. G. Saffman
P. G. Saffman
Affiliation:
Cavendish Laboratory, Cambridge
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Abstract

This paper is concerned with the dispersion of a material quantity in the steady flow of a viscous fluid through a random network of capillaries (which is a useful model of a porous medium), for the case in which molecular diffusion and macroscopic mixing, due to the randomness of the streamlines, are both important. A Lagrangian correlation function is introduced and the longitudinal and lateral effective diffusivities are thereby calculated for all values of Ul/κ less than some large value. Here, l denotes the length of a capillary, U the mean velocity of the fluid, and κ the molecular diffusivity of the material quantity. The theory is compared with experimental observations of dispersion in flow through granular beds.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 7 , Issue 2 , February 1960 , pp. 194 - 208
Copyright
© 1960 Cambridge University Press

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