Non-Gaussian statistics and anomalous diffusion in porous media

Two time displacement correlation functions < x(t)x(0) > grow linearly with time for ordinary diffusion, but for the case of anomalous diffusion it shows more complex time dependence. Anomalous diffusion is abundant in fluid dynamics with complex flow, generally chaotic and turbulent flow. In porous media this behavior is seen even in absence of flow, i.e. pure diffusion - as well as for hydrodynamic dispersion - molecular transport at low Reynold's number. These involve motion of molecules restricted by structures. We describe how transport of complex fluids contained within complex matrices can be used to explore the physics of complex porous media with their multiple characteristic time and length scales, varying over many orders of magnitude.