Inert and reacting transport

Some aspects of passive transport in fluid flows are reviewed. Two classes of problems are considered: inert substances advected by fluid flows, and substances that chemically (or biologically) react while are advected. Concerning the former issue, we discuss it in the Lagrangian framework. In particular, we address the problem of anomalous diffusion in the asymptotic single particle motion, and we introduce a scale dependent description of the particles pair separation evolution. The Lagrangian description is very useful to characterize the non asymptotic properties of transport that often are interesting ones. For the problem of reacting transport we study the dependence of the front speed on the flow characteristics, considering the case of reaction that are slow or fast with respect to the typical time scales of the advection. Moreover, we comment about the role of Lagrangian chaos on the propagation properties.