Advective Coalescence in Chaotic Flows

We investigate the reaction kinetics of small spherical particles with inertia, obeying coalescence type of reaction, B+B→B, and being advected by hydrodynamical flows with time-periodic forcing. In contrast to passive tracers, the particle dynamics is governed by the strongly nonlinear Maxey-Riley equations, which typically create chaos in the spatial component of the particle dynamics, appearing as filamental structures in the distribution of the reactants. Defining a stochastic description supported on the natural measure of the attractor, we show that, in the limit of slow reaction, the reaction kinetics assumes a universal behavior exhibiting a t^-1 decay in the amount of reagents, which become distributed on a subset of dimension D₂, where D₂ is the correlation dimension of the chaotic flow.