Effective diffusivity in porous media

Description

A porous medium (or a porous material) is a material containing pores (voids). The skeletal portion of the material is often called the “matrix” or “frame”. The pores are typically filled with a fluid (liquid or gas). The skeletal material is usually a solid, but structures like foams are often also usefully analyzed using concept of porous media. A porous medium is most often characterised by its porosity.
The effective diffusion coefficient describes diffusion through the pore space of porous media. It is macroscopic in nature, because it is not individual pores but the entire pore space that needs to be considered. The effective diffusion coefficient for transport through the pores, De, is depended on the porosity available for the transport, the constrictivity and the tortuosity of the medium.
(The transport-available porosity equals the total porosity less the pores which, due to their size, are not accessible to the diffusing particles, and less dead-end and blind pores (i.e., pores without being connected to the rest of the pore system). The constrictivity describes the slowing down of diffusion by increasing the viscosity in narrow pores as a result of greater proximity to the average pore wall. It is a function of pore diameter and the size of the diffusing particles.)

Related formulas

Variables

DeEffective diffusivity (m2/s)
DThe diffusion coefficient in gas or liquid filling the pores (m2/s)
ϕtThe porosity available for the transport (dimensionless)
δThe constrictivity (dimensionless)
τThe tortuosity (dimensionless)