Diameter-dependent dispersion in cylindrical bead packs

It has recently been argued that longitudinal dispersion in cylindrical packed beds is enhanced due to radial heterogeneities in the porosity and resulting velocity field. In particular, it is predicted that the time scale to attain asymptotic dispersion in a packed bed of radius R is proportional to R²/D_T, where D_T is the transverse dispersion constant in a homogeneous beadpack, and that the asymptotic longitudinal dispersion constant increases with R/d, where d is the bead diameter. We have measured the asymptotic dispersion rates for packed beds with R/d = 9.5, 12.7, and 25.4 and find good qualitative agreement with the predicted dependence on R/d.