Calculation of the geometrical three-point parameter constant appearing in the second order accurate effective medium theory expression for the B-term diffusion coefficient in fully porous and porous-shell random sphere packings

Using computational fluid dynamics (CFD), the effective B-term diffusion constant gamma(eff) has been calculated for four different random sphere packings with different particle size distributions and packing geometries. Both fully porous and porous-shell sphere packings are considered. The obtained gamma(eff)-values have subsequently been used to determine the value of the three-point geometrical constant (zeta(2)) appearing in the 2nd-order accurate effective medium theory expression for gamma(eff). It was found that, whereas the 1st-order accurate effective medium theory expression is accurate to within 5% over most part of the retention factor range, the 2nd-order accurate expression is accurate to within 1% when calculated with the best-fit zeta(2)-value. Depending on the exact microscopic geometry, the best-fit zeta(2)-values typically lie in the range of 0.20-0.30, holding over the entire range of intra-particle diffusion coefficients typically encountered for small molecules (0.1 <= D-pz/D-m <= 0.5). These values are in agreement with the zeta(2)-value proposed by Thovert et al. for the random packing they considered [1]. (C) 2011 Elsevier B.V. All rights reserved.