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Title: Diffusion in random networks

Abstract

The ensemble averaging technique is applied to model mass transport by diffusion in random networks. The system consists of an ensemble of random networks, where each network is made of pockets connected by tortuous channels. Inside a channel, fluid transport is assumed to be governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pocket mass density. The so-called dual-porosity model is found to be equivalent to the leading order approximation of the integration kernel when the diffusion time scale inside the channels is small compared to the macroscopic time scale. As a test problem, we consider the one-dimensional mass diffusion in a semi-infinite domain. Because of the required time to establish the linear concentration profile inside a channel, for early times the similarity variable is xt $-$1/4 rather than xt $-$1/2 as in the traditional theory. We found this early time similarity can be explained by random walk theory through the network.

Authors:
;
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1345146
Report Number(s):
LA-UR-16-22197
Journal ID: ISSN 0301-9322
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
International Journal of Multiphase Flow
Additional Journal Information:
Journal Volume: 92; Journal Issue: C; Journal ID: ISSN 0301-9322
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS; 97 MATHEMATICS AND COMPUTING

Citation Formats

Zhang, Duan Z., and Padrino, Juan C. Diffusion in random networks. United States: N. p., 2017. Web. doi:10.1016/j.ijmultiphaseflow.2017.01.019.
Zhang, Duan Z., & Padrino, Juan C. Diffusion in random networks. United States. doi:10.1016/j.ijmultiphaseflow.2017.01.019.
Zhang, Duan Z., and Padrino, Juan C. Thu . "Diffusion in random networks". United States. doi:10.1016/j.ijmultiphaseflow.2017.01.019. https://www.osti.gov/servlets/purl/1345146.
@article{osti_1345146,
title = {Diffusion in random networks},
author = {Zhang, Duan Z. and Padrino, Juan C.},
abstractNote = {The ensemble averaging technique is applied to model mass transport by diffusion in random networks. The system consists of an ensemble of random networks, where each network is made of pockets connected by tortuous channels. Inside a channel, fluid transport is assumed to be governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pocket mass density. The so-called dual-porosity model is found to be equivalent to the leading order approximation of the integration kernel when the diffusion time scale inside the channels is small compared to the macroscopic time scale. As a test problem, we consider the one-dimensional mass diffusion in a semi-infinite domain. Because of the required time to establish the linear concentration profile inside a channel, for early times the similarity variable is xt$-$1/4 rather than xt$-$1/2 as in the traditional theory. We found this early time similarity can be explained by random walk theory through the network.},
doi = {10.1016/j.ijmultiphaseflow.2017.01.019},
journal = {International Journal of Multiphase Flow},
number = C,
volume = 92,
place = {United States},
year = {Thu Jun 01 00:00:00 EDT 2017},
month = {Thu Jun 01 00:00:00 EDT 2017}
}

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