Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T01:40:31.173Z Has data issue: false hasContentIssue false
  • English
  • Français

Note on the Onsager symmetry of the kinetic coefficients for sedimentation and diffusion in a dilute bidispersion

Published online by Cambridge University Press:  21 April 2006

G. K. Batchelor
G. K. Batchelor
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

The effect of gravity on a statistically homogeneous dispersion of small particles in fluid is to disturb the thermodynamic equilibrium slightly when the Reynolds and Péclet numbers associated with the resulting motion are small. In these circumstances the kinetic coefficients for the sedimentation velocities of two different species of particle should satisfy the Onsager reciprocal relation. It is shown analytically that the explicit expressions for the sedimentation velocities of the two species of spherical particle in a dilute bidispersion at small Péclet number found previously (Batchelor 1982) are in fact consistent with the reciprocal relation. It follows that the known kinetic coefficients for the Brownian diffusion of the particles down concentration gradients in a dilute bidispersion (Batchelor 1983) likewise satisfy the reciprocal relation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 171 , October 1986 , pp. 509 - 517
Copyright
© 1986 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.1976 Brownian diffusion of particles with hydrodynamic interaction. J. Fluid Mech. 74, 1–29.Google Scholar
Batchelor G. K.1982 Sedimentation in a dilute polydisperse system of interacting spheres. Part 1. General theory. J. Fluid Mech. 119, 379–408; and Corrigendum 137, 1983, 467–469. (Paper I).Google Scholar
Batchelor G. K.1983 Diffusion in a dilute polydisperse system of interacting spheres. J. Fluid Mech. 131, 155–175; and Corrigendum 137, 1983, 467–469. (Paper III).Google Scholar
Batchelor G. K.1986 Applications of the Onsager reciprocal relation in colloid science. Proc. XVIIth Symp. on Advanced Problems and Methods in Fluid Mechanics, Poland, Sept. 1985.Google Scholar
Batchelor, G. K. & Wen C.-S.1982 Sedimentation in a dilute polydisperse system of interacting spheres. Part 2. Numerical results. J. Fluid Mech. 124, 495–528; and Corrigendum 137, 1983, 467–469. (Paper II).Google Scholar
de Groot, S. R. & Mazur, P. 1962 Non-equilibrium Thermodynamics. North-Holland.
Onsager L.1931 Reciprocal relations in irreversible processes. Phys. Rev. 37, 405–426 and 38, 2265–2279.Google Scholar