Longitudinal and transverse dispersion in flow through random packings of spheres: a quantitative comparison of...

Pulsed field gradient nuclear magnetic resonance was used to determine the intrinsic longitudinal and transverse dispersivity of random packings of nearly monodisperse spheres in experiments covering 3.5 orders of magnitude in reduced velocity Pe, from the diffusion dominated regime Pe < 1 to the high velocity regime Pe > 1000. Additionally, using lattice-Boltzmann simulations with tracer tracking, the dispersivities of random packings were determined numerically. Experimental and simulation results are shown to agree to within a few percent over the full velocity range. The velocity dependence of transverse and longitudinal dispersion in packed spheres is described by heuristic models with three parameters each. The simulations were extended to regimes not accessible to experiments, dispersing tracers in flows through random "packings" of floating spheres, for comparison with results obtained using jammed packings in which spheres touch. In the regime of fast flows, the jammed packings' longitudinal dispersivities scale with hydrodynamic length. This no longer holds true in the packings with floating spheres, highlighting the role of zones of slow flow or no flow surrounding sphere-sphere contacts.