Dusty Gas Model for Multicomponent Diffusion

Modeling multicomponent gaseous diffusion in porous media depends upon the value of the Knudsen number. For very large pores, corresponding to very small values of Kn, the Maxwell-Stefan equations (1-34) can be used with effective binary dif-fusivities given by 

For very small pores, corresponding to very large values of Kn, Knudsen diffusion prevails and the flux of each individual component is calculated using equations (1-103) to (1-108). In either case, if there is a significant difference in total pressure across the solid, the hydrodynamic flow contribution must be added. 

The price paid for this simplification is that certain physical features of the porous medium are lost. One of the more important issues is that the model is no longer dealing with channels of finite size corresponding to the pores in the real medium. Thus, there is no introduction of the hydrodynamic fluxes in formal development of the equations. These have to be added empirically. The working form of the dusty ideal gas model equations is (Higler et al., 2000) 

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