Statistical mechanics with three-dimensional particle tracking velocimetry experiments in the study of anomalous dispersion. II. Experiments

In paper I [Phys. Fluids 13, 75 (2001)] we provided a theory for simulating anomalous dispersion which relied on the self-part of the intermediate scattering function. Here we obtain Lagrangian trajectories for a conservative tracer in a porous medium and then use these trajectories to obtain the self-part of the intermediate scattering function. We then use the scattering function as data for the inverse problem and obtain the generalized wave-vector and frequency dependent dispersion tensor developed in paper I. The transverse components of this tensor are then examined as a function of wave vector to see if or when the dispersive process goes asymptotic (Fickian). The matched index (of refraction) technique has been used to obtain a transparent porous medium and three dimensional particle tracking has been used to obtain the trajectories. Over the life of the experiment the transverse dispersive process remained anomalous, though it was gradually approaching the Fickian limit