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Title: Diffusion in a heterogeneous medium for low concentrations

Abstract

The equations describing diffusion on a heterogeneous lattice for low concentrations are considered taking into account lattice site blocking. It is shown that lattice site blocking cannot be disregarded in the case of a strongly heterogeneous lattice even for low concentrations. It is established that the equation with a fractional time derivative holds only in a bounded time interval. Anomalous diffusion, which is described by the equation with a fractional time derivative at the initial stage, must be described over long time periods by an ordinary diffusion equation with a concentration-dependent diffusion coefficient.

Authors:
 [1]
  1. National Academy of Sciences of Ukraine, Institute of Surface Chemistry (Ukraine), E-mail: shkilevv@ukr.net
Publication Date:
OSTI Identifier:
21075656
Resource Type:
Journal Article
Journal Name:
Journal of Experimental and Theoretical Physics
Additional Journal Information:
Journal Volume: 105; Journal Issue: 5; Other Information: DOI: 10.1134/S1063776107110180; Copyright (c) 2007 Nauka/Interperiodica; Article Copyright (c) 2007 Pleiades Publishing, Inc; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7761
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIFFUSION; DIFFUSION EQUATIONS; TIME DEPENDENCE

Citation Formats

Shkilev, V. P. Diffusion in a heterogeneous medium for low concentrations. United States: N. p., 2007. Web. doi:10.1134/S1063776107110180.
Shkilev, V. P. Diffusion in a heterogeneous medium for low concentrations. United States. https://doi.org/10.1134/S1063776107110180
Shkilev, V. P. 2007. "Diffusion in a heterogeneous medium for low concentrations". United States. https://doi.org/10.1134/S1063776107110180.
@article{osti_21075656,
title = {Diffusion in a heterogeneous medium for low concentrations},
author = {Shkilev, V. P.},
abstractNote = {The equations describing diffusion on a heterogeneous lattice for low concentrations are considered taking into account lattice site blocking. It is shown that lattice site blocking cannot be disregarded in the case of a strongly heterogeneous lattice even for low concentrations. It is established that the equation with a fractional time derivative holds only in a bounded time interval. Anomalous diffusion, which is described by the equation with a fractional time derivative at the initial stage, must be described over long time periods by an ordinary diffusion equation with a concentration-dependent diffusion coefficient.},
doi = {10.1134/S1063776107110180},
url = {https://www.osti.gov/biblio/21075656}, journal = {Journal of Experimental and Theoretical Physics},
issn = {1063-7761},
number = 5,
volume = 105,
place = {United States},
year = {Thu Nov 15 00:00:00 EST 2007},
month = {Thu Nov 15 00:00:00 EST 2007}
}