Hydrodynamic and boundary-layer dispersion in bidisperse porous media

The small grains in a bidisperse porous medium have the greater influence o n the permeability, while the large grains are more effective in dispersing chemical tracers. We compute the dispersion induced by a dilute array of l arge spheres in a Brinkman medium whose permeability is determined by the r adii and volume fraction of the small spheres. The effective diffusivity co ntains a purely hydrodynamic contribution proportional to Ua(1)phi(1) and a n O(Ua(1)phi(1) ln(Ua(1)/D)) contribution from the mass transfer boundary l ayers near the spheres. Here, U is the mean velocity in the medium, a(1) an d phi(1) are the radii and volume fraction of the large spheres and D is th e molecular diffusivity. The boundary-layer dispersion is small when the Br inkman screening length kappa (or square root of permeability) is much smal ler than a(1), but is important for kappa greater than or equal to O(a(1)). Experimental results for the dispersion due to flow through a bidisperse p acked bed are reported and compared with the theoretical predictions. In ad dition to its application to bidisperse porous media, the present calculati on allows an extension of Koch & Brady's (1985) analysis of monodisperse fi xed beds to include higher-order terms in the expansion for small particle volume fraction.