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Title: Impurity transport in fractal media in the presence of a degrading diffusion barrier

Abstract

We have analyzed the transport regimes and the asymptotic forms of the impurity concentration in a randomly inhomogeneous fractal medium in the case when an impurity source is surrounded by a weakly permeable degrading barrier. The systematization of transport regimes depends on the relation between the time t{sub 0} of emergence of impurity from the barrier and time t{sub *} corresponding to the beginning of degradation. For t{sub 0} < t{sub *}, degradation processes are immaterial. In the opposite situation, when t{sub 0} > t{sub *}, the results on time intervals t < t{sub *} can be formally reduced to the problem with a stationary barrier. The characteristics of regimes with t{sub *} < t < t{sub 0} depend on the scenario of barrier degradation. For an exponentially fast scenario, the interval t{sub *} < t < t{sub 0} is very narrow, and the transport regime occurring over time intervals t < t{sub *} passes almost jumpwise to the regime of the problem without a barrier. In the slow power-law scenario, the transport over long time interval t{sub *} < t < t{sub 0} occurs in a new regime, which is faster as compared to the problem with a stationarymore » barrier, but slower than in the problem without a barrier. The asymptotic form of the concentration at large distances from the source over time intervals t < t{sub 0} has two steps, while for t > t{sub 0}, it has only one step. The more remote step for t < t{sub 0} and the single step for t > t{sub 0} coincide with the asymptotic form in the problem without a barrier.« less

Authors:
 [1];  [2]
  1. Russian Academy of Sciences, Nuclear Safety Institute (Russian Federation)
  2. State University, Moscow Institute of Physics and Technology (Russian Federation)
Publication Date:
OSTI Identifier:
22756358
Resource Type:
Journal Article
Journal Name:
Journal of Experimental and Theoretical Physics
Additional Journal Information:
Journal Volume: 125; Journal Issue: 2; Other Information: Copyright (c) 2017 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; ABUNDANCE; ASYMPTOTIC SOLUTIONS; CONCENTRATION RATIO; ECOLOGICAL CONCENTRATION; FRACTALS; MATRICES

Citation Formats

Kondratenko, P. S., and Leonov, K. V., E-mail: konstantin.leonov@phystech.edu. Impurity transport in fractal media in the presence of a degrading diffusion barrier. United States: N. p., 2017. Web. doi:10.1134/S1063776117070056.
Kondratenko, P. S., & Leonov, K. V., E-mail: konstantin.leonov@phystech.edu. Impurity transport in fractal media in the presence of a degrading diffusion barrier. United States. doi:10.1134/S1063776117070056.
Kondratenko, P. S., and Leonov, K. V., E-mail: konstantin.leonov@phystech.edu. Tue . "Impurity transport in fractal media in the presence of a degrading diffusion barrier". United States. doi:10.1134/S1063776117070056.
@article{osti_22756358,
title = {Impurity transport in fractal media in the presence of a degrading diffusion barrier},
author = {Kondratenko, P. S. and Leonov, K. V., E-mail: konstantin.leonov@phystech.edu},
abstractNote = {We have analyzed the transport regimes and the asymptotic forms of the impurity concentration in a randomly inhomogeneous fractal medium in the case when an impurity source is surrounded by a weakly permeable degrading barrier. The systematization of transport regimes depends on the relation between the time t{sub 0} of emergence of impurity from the barrier and time t{sub *} corresponding to the beginning of degradation. For t{sub 0} < t{sub *}, degradation processes are immaterial. In the opposite situation, when t{sub 0} > t{sub *}, the results on time intervals t < t{sub *} can be formally reduced to the problem with a stationary barrier. The characteristics of regimes with t{sub *} < t < t{sub 0} depend on the scenario of barrier degradation. For an exponentially fast scenario, the interval t{sub *} < t < t{sub 0} is very narrow, and the transport regime occurring over time intervals t < t{sub *} passes almost jumpwise to the regime of the problem without a barrier. In the slow power-law scenario, the transport over long time interval t{sub *} < t < t{sub 0} occurs in a new regime, which is faster as compared to the problem with a stationary barrier, but slower than in the problem without a barrier. The asymptotic form of the concentration at large distances from the source over time intervals t < t{sub 0} has two steps, while for t > t{sub 0}, it has only one step. The more remote step for t < t{sub 0} and the single step for t > t{sub 0} coincide with the asymptotic form in the problem without a barrier.},
doi = {10.1134/S1063776117070056},
journal = {Journal of Experimental and Theoretical Physics},
issn = {1063-7761},
number = 2,
volume = 125,
place = {United States},
year = {2017},
month = {8}
}