Steady-state diffusion moving interface problems

Pore Mouth (or Shell Progressive) Poisoning This mechanism occurs when the poisoning of a pore surface begins at the mouth of the pore and moves gradmuly inward. This is a moving boundary problem, and the pseudo-steady-state assumption is made that the boundary moves slowly compared with diffusion of poison and reactants and reaction on the active surface. P is the fraction of the pore that is deactivated. The poison diffuses through the dead zone and deposits at the interface between the dead and active zones. The reactants diffuse across the dead zone without reaction, followed by diffusion-reaction in the active zone. 

Transport of solute from a fluid phase to a spherical or nearly spherical shape is important in a vari of separation operations such as liquid-liquid extraction, crystallization from solution, and ion exchange. The situation depicted in Fig. 2.3-12 assumes that there is no forced or natural convection in the fluid about the particle so that transport is governed entirely by molecular diffusion. A steady-state solution can be obtained for the case of a sphere of fixed radius with a constant concentration at the interface as well as in the bulk fluid. Such a model will be useful for crystallization from vaqxtrs and dilute solutions (slow-moving boundary) or for ion exchange with rapid irreversible reaction. Bankoff has reviewed moving-boundary problems and Chapters 11 and 12 deal with adsorption and ion exchange. 

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