Study of Mixing and Reaction in the Field of A Vortex

Abstract

Molecular mixing and finite rate chemical reactions in a two dimensional viscous vortex are examined analytically. Two species initially separated across a plane are allowed to diffuse and react in the presence of a line vortex situated at this separation plane. Solution of the species diffusion and reaction equations are obtained locally. From these solutions, the concentration field of the species is composed. The probability density distributions are calculated using Taylor's frozen flow approximation. They are determined for a range of vortex strengths and for several values of Schmidt number at different times during the growth of the vortex. An asymptotic analysis is presented with a favorable comparison of results in the high vortex strength limit. The reacting vortex is computed by use of Green's function solution of the species equation. The results for the reacting vortex are compared with those for the non-reacting vortex and some insight is gained concerning the form of the probability density function in such configurations. The mixedness parameter is found to be approximately linear with Reynolds number (based upon vortex strength), linear with time, and weakly dependent upon Schmidt number.