Particle Density and Voidage Porosity

Because of the voidage, the particle density is less than the intrinsic density of the solid catalyst material, ps = mplvs, where vs is the volume of solid in the particle, but is related to it by 

Diffusion is the spontaneous migration of a species in space, relative to other species, as a result of a variation in its chemical potential, in the direction of decreasing potential. 

The variation of chemical potential may arise as a result of variation of concentration or temperature or by other means, but we consider only the effect of concentration here. 

From a molecular point of view inside a catalyst particle, diffusion may be considered to occur by three different modes molecular, Knudsen, and surface. Molecular diffusion is the result of molecular encounters (collisions) in the void space (pores) of the particle. Knudsen diffusion is the result of molecular collisions with the walls of the pores. Molecular diffusion tends to dominate in relatively large pores at high P, and Knudsen diffusion tends to dominate in small pores at low P. Surface diffusion results from the migration of adsorbed species along the surface of the pore because of a gradient in surface concentration. 

Since we don t usually know enough about pore structure and other matters to assess the relative importance of these modes, we fall back on the phenomenological description of the rate of diffusion in terms of Fick s (first) law. According to this, for steady-state diffusion in one dimension (coordinate x) of species A, the molar flux, NA, in, say, mol m-2 (cross-sectional area of diffusion medium) s-1, through a particle is 

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