INTERACTION OF CHAOTIC ADVECTION AND DIFFUSION

The interaction of molecular diffusion and chaotic advection is examined in both unbounded and bounded flow domains. In unbounded flow domains molecular diffusion enables tracer particles to explore regions of regular particle motion and chaotic particle motion. Consequently the rate of particle dispersion in these mixed regimes by diffusive particles differs from that realized by perfect tracer particles. In bounded flow domains the effect of chaotic advection on the homogenization and dispersion of diffusive tracers is compared with some classical results on the integrable advection of diffusive tracers. Because the process of molecular diffusion is independent of the type of advection the t --> infinity asymptotic behavior is the same in both chaotic advection and integrable advection. However, the rate at which these asymptotic states are approached is more rapid when the advecting flow generates chaotic particle trajectories. Simple scaling arguments are presented to determine the relevant timescale to achieve uniform mixing within a bounded domain. This timescale is also important in the process of shear dispersion.