Ordinary Diffusion in Multicomponent Gases

When considering ordinary diffusion only, the momentum conservation equation for the species i in a multicomponent system can be written as [17] 

Equations 3.13 are known as the Stefan-Maxwell equations and are valid when the total pressure and temperature gradients as well as external forces can be neglected. They have the physical meaning that the rate of momentum transfer between two species is proportional to their concentrations and to the difference in their velocities. The molar average velocities of the species v, and v are defined in a such way that the molar fluxes of the various species are 

In the case of a two-component mixture of A and B Equation 3.14 for component A gives 

This arrangement shows the diffusion flux JA is the resultant of two terms the first is the molar flux of A resulting from the bulk motion of the fluid, and the second is the molar flux of A resulting from the diffusion superimposed on the bulk [17]. 

The ordinary diffusion equations have been presented for the case of a gas in absence of porous medium. However, in a porous medium, whose pores are all wide compared to the mean free path and provided the total pressure gradient is negligible, it is assumed that the fluxes will still satisfy the relationships of Stefan-Maxwell, since intermolecular collisions still dominate over molecule-wall collisions [19]. In the case of diffusion in porous media, the binary diffusivities are usually replaced by effective diffusion coefficients, to yield 

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