Eliminating the mean-free-path inconsistency in classical phenomenological model of diffusion for fluids

G.L. Aranovich and M.D. Donohue

Physica A: Statistical Mechanics and its Applications, 2007, vol. 373, issue C, 119-141

Abstract: Classical phenomenological model of diffusion in fluids is based on the concept of the mean-free-path, λ, and density distribution, n(x,t), as a function of coordinate, x, and time, t. Under the assumption that(1)n(x-λ,t)-n(x+λ,t)≈-2λ(∂n/∂x),this model results in the classical diffusion equation,(2)∂n(x,t)∂t=∂∂xD∂n(x,t)∂x,where(3)D=(1/3)V¯λand V¯ is the average velocity of molecules. However, Eq. (3) implies finite λ, but approximation (1) requires the limit of λ→0. Here we show that this (mean-free-path) inconsistency distorts the essential physics; in particular, it results in wrong solutions at finite and large λ (including an incorrect limit for the ideal gas).

Keywords: Classical diffusion model; Mean-free-path inconsistency; Causality problem; Correcting classical equation; Diffusion correlations; Large mean-free-path physics; New diffusion paradigm (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:373:y:2007:i:c:p:119-141

DOI: 10.1016/j.physa.2006.05.056

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