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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
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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

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References

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