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 onedimensional diffusion equation. Mass balance leads to an integrodifferential equation for the pocket mass density. The socalled dualporosity 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 onedimensional mass diffusion in a semiinfinite 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):
 LAUR1622197
Journal ID: ISSN 03019322
 Grant/Contract Number:
 AC5206NA25396
 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 03019322
 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. 2017.
"Diffusion in random networks". United States.
doi:10.1016/j.ijmultiphaseflow.2017.01.019.
@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 onedimensional diffusion equation. Mass balance leads to an integrodifferential equation for the pocket mass density. The socalled dualporosity 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 onedimensional mass diffusion in a semiinfinite 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 = 2017,
month = 6
}
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