Symbolic algebra in the analysis of dynamic chemical-kinetic systems

In order to make predictive statements about the role and reactions of different species in a physically dynamic chemically reactive system, it is necessary to construct a set of partial differential equations which describes the chosen set of chemical reactions within a predetermined flow field. These partial differential equations may be transformed into a set of ordinary differential equations which are soluble under certain conditions. Thus, a continuous problem with infinitely many degrees of freedom becomes a discrete problem with only finitely many unknowns which can be handled by a computer. In this paper, the mathematics of mass transfer with chemical reaction is first reviewed The usefulness of the symbolic algebra package Mathematica in solving such discretized problems is then discussed. Some analytic expressions are derived for simple two-phase problems, in chromatography and bacterial population dynamics and the physical interpretation of the model parameters outlined. Numerical applications of this method in large-scale chemical process kinetics and plasma chemistry modelling are reported.