Grain diffusion through

A parabolic rate law will also be obtained if part or even all, of the diffusion through the product layer is by grain boundary diffusion rather than diffusion through the volume of each grain. The volume diffusion coefficient is quite simply defined as the phenomenological coefficient in Fick s laws. The grain boundary diffusion must be described by a product, DbS, where S is the grain... 

Fig. 1.16 Particle size and grain size in a nanostructured powder. Black points depict hydrogen molecules ( ) in pores between particles, and hydrogen atoms ( ) diffusing through a grain boundary network and gradually entering the grain interior black triangles point to triple points that are preferential sites for hydrogen atom accumulation...

Figure 9.12 Transport of diffusant through a thin polycrystalline film by grain-boundary diffusion.

Atoms diffuse through the crystal from the grain boundary to low-curvature surface regions. 

In the grain model, it is assumed that the CaO consists of spherical grains of uniform size distributed in a porous matrix. The rate of reaction is controlled by the diffusion of SO2 through the porous matrix and the product CaSO layer formed on each grain (11). Allowance can be made for a finite rate of the CaO/SC reaction (12). The models have been found to describe experimental data for many limestones (13) by adjusting the constants in the model, most notably the diffusivity through the product layer. 

Two effects cause the low production capacity of large-grained catalyst. First, large grain size retards transport of the ammonia formed inside the catalyst into the bulk gas stream. This is because the ammonia transport proceeds by slow diffusion through the pore system. The second effect is a consequence of the fact that a single catalyst grain in the oxide state reduces from the outside to the interior of the particle. The water vapor produced inside the catalyst by reduction comes into contact with already reduced catalyst on its way to the outer surface of the catalyst. This induces a severe recrystallization. As an example, if the particle size increases from about 1 to 8 mm, the inner surface decreases from 11 to 16 m2/g to 3 to 8 m2/g74. Therefore the choice of catalyst requires the optimization of 1) catalyst size versus catalyst activity, 2) catalyst size versus pressure drop across the converter and 3) the impact of 1 and 2 on... 

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