Orientational distribution functions, tortuosity

More general models for the porous structure have also been developed by Johnson and Stewart [60] and by Feng and Stewart [43], called the parallel cross-linked pore model. Here, Eqs. 3.5.b-4 to 6 or Eq. 3.5.b-7 are considered to apply to a single pore of radius r in the solid, and the diffusivities interpreted as fte actual values rather than effective diffusivities corrected for porosity and tortuosity. A pore size and orientation distribution function /(r, Q), similar to Eq. 3.4-2, is defined. Then /(r, Q)dri is the fraction open area of pores with radius r and a direction that forms an angle Q with the pdlet axis. The total porosity is then... 

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

TABLE 21-3 Normalized Orientational Part of the Distribution Function in the Parallel-Pore Model for Several Cases and the Corresponding Tortuosity Factors... 

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