Solute dispersion and weak second-order recombination at large times in parallel flow

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Abstract
This work is concerned with the parallel-flow shear dispersion of a solute which undergoes a second-order recombination reaction. The primary goal of the work is to provide background theory for the determination of the coefficient of diffusion of reactive-gas-phase species. Approximations are sought for large time and weak combination. At first, dispersion dominates recombination, and a modification of the Chatwin (1970) asymptotic expansion gives the concentration distribution as a regular perturbation expansion in e and t−½, where e is a dimensionless parameter characterizing recombination and t is dimensionless time. The regular expansion breaks down for dimensionless times t of O(ε−2) when dispersion and recombination are of the same importance. At these times, the governing equation is nonlinear and this regime is analysed by a numerical method. Finally, a similarity solution is derived for the concentration of solute when ε2t is large. Overall, the major effect of second-order recombination on dispersion is to flatten the peak of the dominant Gaussian concentration distribution. The speed of the centre of mass of the solute cloud is not affected at leading order by recombination.
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