Abstract
We study the time and length scales of hydrodynamic dispersion in confined monodisperse sphere packings as a function of the conduit geometry. By a modified Jodrey-Tory algorithm, we generated packings at a bed porosity (interstitial void fraction) of epsilon = 0.40 in conduits with circular, rectangular, or semicircular cross section of area 100 pi d(p)(2) (where d(p) is the sphere diameter) and dimensions of about 20d(p) (cylinder diameter) by 6553.6d(p) (length), 25d(p) by 12.5d(p) (rectangle sides) by 8192d(p) or 14.1d(p) (radius of semicircle) by 8192d(p), respectively. The fluid-flow velocity field in the generated packings was calculated by the lattice Boltzmann method for Peclet numbers of up to 500, and convective-diffusive mass transport of 4 x 10(6) inert tracers was modelled with a random-walk particle-tracking technique. We present lateral porosity and velocity distributions for all packings and monitor the time evolution of longitudinal dispersion up to the asymptotic (long-time) limit. The characteristic length scales for asymptotic behaviour are explained from the symmetry of each conduit's velocity field. Finally, we quantify the influence of the confinement and of a specific conduit geometry on the velocity dependence of the asymptotic dispersion coefficients.