On the interplay between advection and diffusion in closed laminar chaotic flows

This article illustrates a new and simple approach to the analysis of the effects of diffusion in laminar chaotic flows. The approach is based upon the definition of two quantities, namely diffusional thickness and area of diffusional influence, which provide a compact and quantitative description of the spatiotemporal evolution of partially mixed structures. Several implications follow from this approach: (A) Dispersion in closed chaotic flows displays nonmonotonic behavior induced by the shrinking of diffusional thickness along the stable directions. A theoretical explanation of this phenomenon is provided. (B) It is possible to define a characteristic time corresponding to the blow-up of the geometric interface induced by the diffusional merging of lamellae. The implications of these results as regards the dynamics of other physicochemical processes such as chemical reactions are briefly addressed.