2ND-ORDER REVERSIBLE-REACTIONS AND DIFFUSION IN A SLAB-LIKE MEDIUM - AN APPLICATION OF THE WEIERSTRASS ELLIPTIC PE-FUNCTION

Analytic solutions to a wide variety of steady-state, simultaneous diffusion plus second-order reaction schemes, both irreversible and reversible, are possible for slab-like media, even though the governing equations are nonlinear. Solutions for concentration profiles are derived in terms of the Weierstrass elliptic Pe-function. The application of this function to practical problems is explored. Standard formulae for internal effectiveness factors are expressed in terms of a new nomenclature standard. These algebraic expressions are all functions of ab initio known parameters and the centerline concentration, given by the analytic solution. New methods to estimate the centerline concentration are developed during the analysis. Three classes of second-order reversible kinetic schemes are observed to possess a true first-order behavior in any coordinate system for practical parameter values. This limiting behavior is examined. The analytic solution method can be extended to other kinetic systems, including third-order ones.