A spatial structural derivative model for the characterization of superfast diffusion/dispersion in porous media

•A local spatial structural derivative diffusion model to depict superfast diffusion in porous media is presented in which the logarithmic function is selected as the structural function.•The fundamental solution is a log-normal distribution and the corresponding mean square displacement is proporti...

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Bibliographic Details
Published in:International journal of heat and mass transfer 2019-08, Vol.139, p.39-45
Main Authors: Xu, Wei, Liang, Yingjie, Chen, Wen, Cushman, John H.
Format: Article
Language:English
Subjects:
Diffusion rate
Dispersion
Heterogeneous media
Normal distribution
Particle migration
Porous media
Structural derivative
Superfast diffusion/dispersion
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Summary:•A local spatial structural derivative diffusion model to depict superfast diffusion in porous media is presented in which the logarithmic function is selected as the structural function.•The fundamental solution is a log-normal distribution and the corresponding mean square displacement is proportional to an exponential function.•The local spatial structural derivative diffusion model is an alternative modeling tool to characterize superfast diffusion. Many theoretical and experimental results show that anomalous diffusion/dispersion occurs in porous media. To exactly solve anomalously fast dispersion, we introduce a structural derivative diffusion model to present superfast diffusion via a logarithmic structural function in space. The fundamental solution of the diffusion model is a form of log-normal distribution, and the corresponding analytical mean squared displacement grows like et/β2, 0
ISSN:0017-9310
1879-2189
DOI:10.1016/j.ijheatmasstransfer.2019.05.001