Steady-State Binary Molecular Diffusion in Porous Solids

1 Steady-State Binary Molecular Diffusion in Porous Solids 

When treating diffusion of solutes in porous materials where diffusion is considered to occur only in the fluid inside the pores, it is common to refer to an effective diffusivity, DABeg, which is based on (1) the total cross-sectional area of the porous solid rather than the cross-sectional area of the pore and (2) on a straight path, rather than the actual pore path, which is usually quite tortuous. In a binary system, if pore diffusion occurs only by ordinary molecular diffusion, Fick s law can be used with an effective diffusivity that can be expressed in terms of the ordinary diffusion coefficient, DAB, as 

For binary mixtures diffusing inside porous solids, the applicability of equation (1-100) depends upon the value of a dimensionless ratio called the Knudsen number, Kn, defined as 

For liquids, the mean free path is commonly a few angstroms, so the Knudsen number is almost always very small and diffusion inside the pores is usually only by ordinary molecular diffusion. In gases, the mean free path can be estimated from the following (Cussler, 1997)  

Example 1.20 Steady-State Molecular Diffusion in Porous Solid 

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