Hydrodynamic and boundary-layer dispersion in bidisperse porous media

Abstract

The small grains in a bidisperse porous medium have the greater influence on the permeability, while the large grains are more effective in dispersing chemical tracers. We compute the dispersion induced by a dilute array of large spheres in a Brinkman medium whose permeability is determined by the radii and volume fraction of the small spheres. The effective diffusivity contains a purely hydrodynamic contribution proportional to Ua1ϕ1 and an O(Ua1ϕ1 ln (Ua1/D)) contribution from the mass transfer boundary layers near the spheres. Here, U is the mean velocity in the medium, a1 and ϕ1 are the radii and volume fraction of the large spheres and D is the molecular diffusivity. The boundary-layer dispersion is small when the Brinkman screening length κ (or square root of permeability) is much smaller than a1, but is important for κ[ges ]O(a1). Experimental results for the dispersion due to flow through a bidisperse packed bed are reported and compared with the theoretical predictions. In addition to its application to bidisperse porous media, the present calculation allows an extension of Koch & Brady's (1985) analysis of monodisperse fixed beds to include higher-order terms in the expansion for small particle volume fraction.