Abstract
The method of spatial averaging is applied to derive a macroscopic form of Fick's law for unsteady diffusion through a rigid porous medium. The validity of this form is found to be restricted by the requirements that diffusion is quasi-steady on a pore scale and that interphase mass transfer rates depend at most linearly upon concentration. Under these conditions the effective diffusivity of the porous medium involves the product of the molecular diffusivity and a dimensionless “intrinsic conductivity” of the porous medium, which is found to be a symmetric and positive definite second order tensor. A reciprocal theorem plays a key role in achieving the macroscopization of Fick's law.
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