Dispersion in confined and fluctuating systems

I will discuss some recent work on the effective transport properties, the effective diffusion constant and late time drifts, in confined systems. In particular I will address diffusion in channel like systems which are relevant for micro-fluidic and biological systems. Geometrical features for time independent geometries can lead to a slowing down of dispersion due to entropic trapping effects and I will present some improvements on the classic Fick-Jacobs approximation for these systems. I will also talk about how Taylor dispersion is modified by potential interactions with the boundaries and variable diffusivity, notably due to the vanishing of the diffusion constants at the boundaries. Finally I will examine dispersion in systems which have geometrical fluctuations, either generated thermally or by driving the surfaces, in these systems geometric fluctuations can either enhance or diminish dispersion with respect to their static counterparts.