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 γeff 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 γeff-values have subsequently been used to determine the value of the three-point geometrical constant (ζ2) appearing in the 2nd-order accurate effective medium theory expression for γeff. 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 ζ2-value. Depending on the exact microscopic geometry, the best-fit ζ2-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 ≤ Dpz/Dm ≤ 0.5). These values are in agreement with the ζ2-value proposed by Thovert et al. for the random packing they considered [1].

► Numerical simulated values of the B-term constant in random sphere packings.
► Both fully porous and porous-shell sphere packings are considered.
► The 2nd-order accurate effective medium theory can describe the simulation data.
► ζ2-values are in agreement with the ζ2-values proposed by Thovert et al. [1].