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Anomalous diffusion due to long-range velocity fluctuations in the absence of a mean flow

Koch, Donald L. and Brady, John F. (1989) Anomalous diffusion due to long-range velocity fluctuations in the absence of a mean flow. Physics of Fluids A, 1 (1). pp. 47-51. ISSN 0899-8213. http://resolver.caltech.edu/CaltechAUTHORS:KOCpofa89

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Abstract

The dispersion of a tracer in a heterogeneous medium in which the tracer's velocity has zero mean and a covariance that decays as x^−γ with distance x is studied using nonlocal advection–diffusion theory. If the velocity covariance decays slowly, γ ≤ 2, the tracer's dispersive motion is non-Fickian even at long times after its release. Under these circumstances, it is not possible to predict the dispersion by assuming that the tracer samples the velocity fluctuations primarily by molecular diffusion, even if the fluctuations are weak. Instead, we develop a self-consistent theory in which the tracer samples each velocity fluctuation by the motion resulting from the other fluctuations. It is shown that in cases of anomalous diffusion, the tracer's mean-square displacement grows faster than linearly with time—as t^[4/(2+ γ)] for 0 < γ < 2 and as t(ln t)1/2 for γ = 2 as t→∞.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.857522DOIUNSPECIFIED
http://dx.doi.org/10.1063/1.857522PublisherUNSPECIFIED
Additional Information:© 1989 American Institute of Physics. Received 27 June 1988; accepted 26 September 1988.
Subject Keywords:VELOCITY, FLUCTUATIONS, DIFFUSION, DISORDERED SYSTEMS, MASS TRANSFER, HEAT TRANSFER, PARTICLES, FLUID FLOW, POROUS MATERIALS, PRESSURE GRADIENTS, DISPERSIONS, INHOMOGENEOUS MATERIALS
Record Number:CaltechAUTHORS:KOCpofa89
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:KOCpofa89
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11330
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Aug 2008 18:15
Last Modified:26 Dec 2012 10:12

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