Analysis of dispersion in porous media via matched-index particle tracking velocimetry experiments

Abstract

Anomalous dispersion, also known as pre-asymptotic dispersion, is the norm in naturally occurring porous systems. This phenomenon is studied in laboratory matched-index homogeneous and heterogeneous media via two- and three-dimensional particle tracking velocimetry. The self part of the intermediate scattering function, relative scattering function, finite size Lyapunov exponent and more classical measures (reactor ratio and variance of the displacement) are discussed and used to examine the dispersive process. The self part of the intermediate scattering function is presented to show the evolution of the passive tracer concentration in time and demonstrates the delayed arrival of particles in the direction of the flow for certain media. The relative scattering function provides evidence of enhanced mixing for the most heterogeneous media. The dilution index confirms the transition to Fickian dispersion for some media and demonstrates that others do not exhibit this behavior over the life of the experiment. This article provides a variety of descriptors for anomalous diffusion and makes connections to previous analyses.