Limitation in the Dialytic Regime

The dialytic regime is characterized by high surface reaction rate coefficients and by rate-limiting diffusion. The Sherwood number (Sh) characterizes the regimes. Sh is defined as the ratio of the driving force for diffusion in the boundary layer to the driving force for surface reaction alternatively, it is the ratio of the resistivity for diffusion to the resistivity for chemical reaction (reciprocal reaction rate coefficient). Diffusion limitation is the regime at Sh 1 and reaction limitation means Sh 1. The Sherwood number is closely related to the Biot, Nusselt, and Damkohler II numbers and the Thiele modulus. Some call it the CVD number. In the boundary-layer model it is a simple function of the thickness of the boundary layer, the diffusion coefficient, and the reaction rate coefficient. For simplicity a first-order reaction will be considered in the derivation below. 

The diffusion current of a reactant from the bulk gas flow through the boundary layer to the surface is (according to an Ohm-like law)  

The reaction mass current at the surface from precursor to product is (first-order reaction)  

this is an Ohm-like law the reactant conversion mass current J equals the driving force (Cf, — cj divided by the sum of two resistors in series. The resistance for diffusion is d/D and the resistance for chemical reaction is 1/k. 

The Sherwood number equals the ratio of the two driving forces or the two resistances  

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