On the interplay between advection and diffusion in closed laminar chaoticflows

This article illustrates a new and simple approach to the analysis of the e ffects of diffusion in laminar chaotic flows. The approach is based upon th e definition of two quantities, namely diffusional thickness and area of di ffusional influence, which provide a compact and quantitative description o f the spatiotemporal evolution of partially mixed structures. Several impli cations follow from this approach: (A) Dispersion in closed chaotic flows d isplays nonmonotonic behavior induced by the shrinking of diffusional thick ness along the stable directions. A theoretical explanation of this phenome non is provided. (B) It is possible to define a characteristic time corresp onding to the blow-up of the geometric interface induced by the diffusional merging of lamellae. The implications of these results as regards the dyna mics of other physicochemical processes such as chemical reactions are brie fly addressed.