Stability of Moving Interfaces with Chemical Reaction

STABILITY OF MOVING INTERFACES WITH CHEMICAL REACTION 

Moving interfaces whrae one or more chemical reactions occur are subject to transport-related instabilities similar to those discussed in Section 8 which lead 

But suppose now that the reaction is exothermic, so that heat must be transported from the interface into the bulk liquid. Now the perturbation also produces a local increase in heat flux at P, which favors a reduction in local temperature and hence reaction rate, a destabilizing effect. If it exceeds the stabilizing effect of reactant diffusion, instability can result (Cannon and Denbigh, 1957a,b Knapp and Aris, 1972 Miller, 1978). 

The stability analysis is very similar to that of Section 8 except that there are equations analogous to Equations 6.61 and 6.62 for both heat and mass transport in the liquid. Moreover, interfacial conservation equations both for energy and for the reactant A must be invoked. 

The key equation in the analysis, however, is the boimdary condition giving the local reaction rate r. For simplicity we assume that the reaction proceeds by formation of an activated complex C in equihbrium with the reactants A and S. The equilibrium constant for this reaction is taken as K. The complex then decays irreversibly with a rate constant fc, to form the product B in the fluid phase thus we have 

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