A failure of the pool chemical approximation chemical reaction dynamics
Title:
A failure of the pool chemical approximation chemical reaction dynamics
Author:
Merkin, J. H. Scott, S. K.
Appeared in:
Dynamical systems
Paging:
Volume 2 (1988) nr. 3-4 pages 223-233
Year:
1988
Contents:
The 'pooled chemical approximation' in chemical kinetics, a procedure based originally only on intuition, has already proved an extremely valuable route to predicting the possibility of nonlinear dynamical responses such as oscillations or propagating chemical waves for a variety of simple chemical reaction schemes. The use of this technique requires that the concentrations of some initial reactant species be identified (a) as large compared with those of key reactive intermediates and (b) as changing on a relatively slow timescale, and thus can be regarded as constants or, to a higher approximation, as evolving quasisteadily. Though this approach has been found to be successful for a number of classic models this is not universally the case. Here we report on almost disastrous failure for an otherwise acceptable scheme with mass-action kinetics. We show that the oscillatory behaviour predicted by the pooled chemical approximation does not survive into the full scheme, and perhaps more significantly, when we come to consider the behaviour for large values of the initial concentration of the pooled chemical, we find that the time in which this pooled chemical is used up decreases as its initial concentration is increased.
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