Diffusion densities induced

A final point has to do with the relative Insensitivity of the pore averaged dlffuslvlty on the density structure. Both the LADM and the generalized tracer diffusion theory provide a rational explanation for this fact. The reasons for the Insensitivity may be Identified In the double (triple for the tracer diffusion theory) smoothing Induced by the volume averaging and by the very nature of the molecular Interactions In liquids which makes some type of averaging over the densities In the neighborhood of a certain point necessary. 

The velocity, viscosity, density, and channel-height values are all similar to UF, but the diffusivity of large particles (MF) is orders-of-magnitude lower than the diffusivity of macromolecules (UF). It is thus quite surprising to find the fluxes of cross-flow MF processes to be similar to, and often higher than, UF fluxes. Two primary theories for the enhanced diffusion of particles in a shear field, the inertial-lift theory and the shear-induced theory, are explained by Davis [in Ho and Sirkar (eds.), op. cit., pp. 480-505], and Belfort, Davis, and Zydney [/. Membrane. Sci., 96, 1-58 (1994)]. While not clear-cut, shear-induced diffusion is quite large compared to Brownian diffusion except for those cases with very small particles or very low cross-flow velocity. The enhancement of mass transfer in turbulent-flow microfiltration, a major effect, remains completely empirical. 

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