Consequences of the Partial-Equilibrium Approximation for Chemical Reaction and Transport

This paper is concerned with the relation between various mathematical methods for formulating the equations of convective diffusion in the presence of infinitely-rapid reaction pathways. The notions of general composition variables, reaction invariance and differential geometry provide useful conceptual tools for comparing various methods. In particular, the method of `composite fluxes' is shown to represent a mixed-coordinate description, with separate composition coordinates for spatial fluxes and concentration fields. While this method avoids a coordinate degeneracy sometimes associated with fast-reaction invariants, it is shown that such degeneracy should never occur in chemical systems having stable equilibria for the fast reactions. An elementary reaction scheme, involving mobile intermediates or adsorbed surface species, is treated to illustrate the coupled and facilitated diffusion effects resulting from the partial-equilibrium approximation. Also, the relation of the latter to the well-known quasi steady-state approximation (QSSA) of chemical kinetics is established. It is shown that, apart from certain exceptional circumstances, the usual ab initio invocation of the QSSA has no unforeseen consequences for diffusive transport. On the other hand, strong spatial fluxes can cause breakdown of such equilibrium approximations, in much the same way as strong unsteadiness is known to do.