Reaction-diffusion systems with decaying catalyst

Reaction-diffusion systems with decaying catalyst 

When the autocatalyst is not indefinitely stable, but instead undergoes further reaction such as the first-order decay process 

The stationary states of eqns (9.18) and (9.19) are concentration profiles of the form ass(p), / ss(p) satisfying the ordinary differential equations 

A typical stationary-state solution for the dimensionless concentration profiles a (p) and P (p) for cubic autocatalysis with decay. The reactant concentration shows simply a central minimum, but the autocatalyst profile has three extrema, including two non-central maxima. 

A typical stationary-state solution is shown in Fig. 9.5 for the specific choice of the three parameters D = 5.2 x 10-3, / = 0.08, and k2 = 0.05. There is considerable consumption of the reactant near to the centre of the reaction zone, but the ass has a similar form to that found in the absence of catalyst decay—a hanging chain with a central minimum and no inflection point. The concentration profile for the autocatalyst has / ss increasing beyond its reservoir concentration near to the edge, but falling again as it approaches the centre. Thus the autocatalyst profile can have non-central extrema, but is always symmetric about p = 0. 

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Reaction-diffusion systems with decaying catalyst... 

The rapid decay of activity is another drawback of the present systems. This may be due to deactivation processes as described above. It may also be due to diffusion control (vide supra). Of the three models, Rp decreases most markedly with reaction for the fixed site or polymer core model. Figure 2 suggests that this applies to the catalyst under discussion. The flow model would have the smallest change of Rp with polymerization. Therefore, a catalyst which is more readily fractured or fragmented may well have nearly constant activity. 

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