Reaction in a Slab Reprise

While we have contact with this problem, however, we will look at the asymptotics of reactions in a slab of catalyst. In Chapter 3 we used the special form of the equations for diffusion and reaction to get rather general expressions for the Thiele modulus and effectiveness in terms of the center concentration v 

If we have an external mass transfer resistance at the surface, we need two parameters, v = n(0) and w = (1), 0 v w 1, and then there are various limiting cases according the path that (w, v) takes to the boundary of its triangular domain. The relevant equations are 

In the section entitled Special Forms we introduced Michaelis-Menten kinetics rather abruptly as an example of integration by quadrature. The substrate, as it is often called in biochemical circles, in the reaction A — B disappears at a rate 

This rate law is approximately zero order when a K and first order when a K so that, in some sense, it gets saturated and shows an inhibition of reaction at high concentrations of substrate. It is assumed that the enzyme that catalyses the reaction has a number of sites to which A can attach itself, be transformed to B, and then detach itself. If E denotes the enzyme and eo (and e) the concentration of binding sites it initially (and currently) provides, C the complex of the enzyme and substrate and c its concentration, then because sites that are not occupied are available 

In practice, e0 is very much smaller than a0- The mechanism is A + E - C — B + E, and we assume that these are elementary steps with mass action 

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