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Kinetic theory of diffusion in liquids: A hydrodynamic approximation

Kuščer, I. and Corngold, N. (1976) Kinetic theory of diffusion in liquids: A hydrodynamic approximation. Physica A, 82 (2). pp. 195-220. ISSN 0378-4371. https://resolver.caltech.edu/CaltechAUTHORS:20180522-135447143

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Abstract

Diffusion in simple classical liquids is analyzed in terms of the test-particle phase-space density, with emphasis upon its long-time behavior. The Green's function of the generalized Fokker-Planck equation is used to define auxiliary quantities, in particular the transport mean path that enters solutions of the Chapman-Enskog type. Approximations for the lowest eigenvalues and eigenfunctions of the Fourier- and Laplace-transformed F.-P. operator σ_(ks) are constructed, and an expansion for the resolvent operator (s + ik · v – σ_(ks))^(-1) proposed. With the additional assumption that branch-points on the negative real axis of s are the only singularities of the transformed F.-P. operator, a Laplace inversion is tentatively carried out, so that the general form of the solution is obtained. This is found to agree with the solution derived by hydrodynamic arguments. Only in a limited sense is the latter method equivalent to that of mode-mode coupling.


Item Type:Article
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https://doi.org/10.1016/0378-4371(75)90045-XDOIArticle
Additional Information:© 1976 Published by Elsevier B.V. Received 4 July 1975. Research supported, in part, by the National Science Foundation, under Grant GP 9626. We have learned a great deal through stimulating discussions with Robert Zwanzig, Charles D. Boley and Rashmi C. Desai, who gave us helpful advice and suggestions. One of us (I. K.) wishes to express his gratitude to the Sherman Fairchild Foundation and the National Academy of Sciences for a scholarship, and to the Caltech community for its generous hospitality, which have made participation in this work possible.
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Funding AgencyGrant Number
NSFGP-9626
Sherman Fairchild FoundationUNSPECIFIED
National Academy of SciencesUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20180522-135447143
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180522-135447143
Official Citation:I. Kuščer, N. Corngold, Kinetic theory of diffusion in liquids: A hydrodynamic approximation, Physica A: Statistical Mechanics and its Applications, Volume 82, Issue 2, 1976, Pages 195-220, ISSN 0378-4371, https://doi.org/10.1016/0378-4371(75)90045-X. (http://www.sciencedirect.com/science/article/pii/037843717590045X)
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ID Code:86553
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:24 May 2018 16:44
Last Modified:03 Oct 2019 19:45

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