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Diffusion in anisotropic porous media

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Abstract

An experimental system was constructed in order to measure the two distinct components of the effective diffusivity tensor in transversely isotropic, unconsolidated porous media. Measurements were made for porous media consisting of glass spheres, mica particles, and disks made from mylar sheets. Both the particle geometry and the void fraction of the porous media were determined experimentally, and theoretical calculations for the two components of the effective diffusivity tensor were carried out. The comparison between theory and experiment clearly indicates that the void fraction and particle geometry are insufficient to characterize the process of diffusion in anisotropic porous media.

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Abbreviations

A γκ :

interfacial area between λ- and κ-phases for the macroscopic system, m2

A γe :

area of entrances and exits of the κ-phase for the macroscopic system, m2

A γκ :

interfacial area contained within the averaging volume, m2

a :

characteristic length of a particle, m

b :

average thickness of a particle, m

c A :

concentration of species A, moles/m3

c o :

reference concentration of species A, moles/m3

〈c A〉γ :

intrinsic phase average concentration of species A, moles/m3

≈c a :

c A−〈c A〉γ, spatial deviation concentration of species A, moles/m3

C :

〈c A〉γ/c 0, dimensionless concentration of species A

⊥:

binary molecular diffusion coefficient, m2/s

D eff :

effective diffusivity tensor, m2/s

D xx :

component of the effective diffusivity tensor associated with diffusion parallel to the bedding plane, m2/s

D yy :

component of the effective diffusivity tensor associated with diffusion perpendicular to the bedding plane, m2/s

D eff :

effective diffusivity for isotropic systems, m2/s

f :

vector field that maps ∇〈c A〉γ on to ≈c a , m

h :

depth of the mixing chamber, m

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Author notes

  1. Jin-Hwan Kim

    Present address: Department of Chemical Engineering, Chonnam National University, Korea

Authors and Affiliations

  1. Department of Chemical Engineering, University of California at Davis, 95616, Davis, CA, USA

    Jin-Hwan Kim, J. Alberto Ochoa & Stephen Whitaker

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  1. Jin-Hwan Kim
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  2. J. Alberto Ochoa
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Kim, JH., Ochoa, J.A. & Whitaker, S. Diffusion in anisotropic porous media. Transp Porous Med 2, 327–356 (1987). https://doi.org/10.1007/BF00136440

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