The Rapid Reaction of Two Chemical Species in the Presence of Weak Random Advection and Molecular Diffusion

Abstract

The very rapid reaction of two chemical species in the presence of weak random advection and molecular diffusion is studied. This type of reaction evolves in two stages—an initial layer stage dominated by chemical kinetics and a reaction tail controlled by the interplay of random and molecular diffusive effects. The case of random advection alone is considered in reasonable generality; the use of characteristics ultimately permits the application of known results in the asymptotic theory of stochastic ordinary differential equations (Papanicolaou and Kohler, Asymptotic theory o f mixing stochastic ordinary differential equations, Comm. Pure Appl. Math., 27 (1974)). Simultaneous random advection and molecular diffusion, however, is only considered in the special case of one spatial dimension. Expressions are derived for the concentration moments and examples are considered to illustrate the content of the results.