By James Wei (Ed.)
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Additional info for Advances in Chemical Engineering, Vol. 24
1994) also show that such stationary points are not approached in a spiraling way-in some vague sense, a principle of microscopic reversibility holds. Once a nontrivial stable stationary point has been reached, R stays at some constant value and the overall order of reaction becomes 2 again. [The degeneracy of the xy form for b(x,y) can be seen also from a different viewpoint: can be zero if and only if b(x,x) is zero for some x (the proof is easy). When b ( x , y ) = xy, the condition is satisfied: b(0,O) = 0.
6. Conclusion The discussion in this section illustrates the wealth of results available for the analysis of the overall kinetic behavior of complex mixtures. The variety of available analytical results should not, however, mask the fact that there is a large area where very little has been done, that is, the area of nonlinear kinetics which are not of the cooperative uniform type. Powerful as the assumption of uniformity has turned out to be, remember that it is a strong assumption; in A r i s ’ s (1988) words, “your assumption of uniformity .
Indeed, Luss and Hutchinson (197 1) state explicitly that serious problems arise if one tries a continuous description-one where N approaches 00. The mathematical difficulties connected with the assumption of independent kinetics in the continuous description have been discussed by Ho and Aris (1987). Ho et al. (1990) have presented an approach to the description of independent kinetics that makes use of the “method of coordinate transformation” (Chou and Ho 1988), and which appears to overcome the paradox discussed in the previous paragraph.