Stoichiometric Network Analysis and Associated Dimensionless Kinetic Equations. Application to a Model of the Bray-Liebhafsky Reaction

Faculté des Sciences Appliquées, Universté Libre de Bruxelles, CP165/63, Av. F. Roosevelt 50, 1050 Bruxelles, Belgium.
The Journal of Physical Chemistry A (Impact Factor: 2.69). 01/2009; 112(51):13452-7. DOI: 10.1021/jp8056674
Source: PubMed


The stoichiometric network analysis (SNA) introduced by B. L. Clarke is applied to a simplified model of the complex oscillating Bray-Liebhafsky reaction under batch conditions, which was not examined by this method earlier. This powerful method for the analysis of steady-states stability is also used to transform the classical differential equations into dimensionless equations. This transformation is easy and leads to a form of the equations combining the advantages of classical dimensionless equations with the advantages of the SNA. The used dimensionless parameters have orders of magnitude given by the experimental information about concentrations and currents. This simplifies greatly the study of the slow manifold and shows which parameters are essential for controlling its shape and consequently have an important influence on the trajectories. The effectiveness of these equations is illustrated on two examples: the study of the bifurcations points and a simple sensitivity analysis, different from the classical one, more based on the chemistry of the studied system.

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    • "The destabilizing term is j 2 j 4 2 . It corresponds to that obtained for the related model in batch reactor [56], although the analogous expression in batch reactor has had only 11 terms. The polynomial in inequality (6.4) is very large (it has 69 terms of third order as a consequence of the many currents due to flow), but its symbolic form could be evaluated if we have explicit values for the currents. "
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