title: 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.
abstract: Using computational fluid dynamics (CFD), the effective B-term diffusion constant γ(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 γ(eff)-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 γ(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 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 ≤ D(pz)/D(m) ≤ 0.5). These values are in agreement with the ζ₂-value proposed by Thovert et al. for the random packing they considered.
authors.affiliation: Vrije Universiteit Brussel, Department of Chemical Engineering, Pleinlaan 2, 1050 Brussels, Belgium.
authors.forename: Sander
authors.initials: S
authors.lastname: Deridder
authors.forename: Gert
authors.initials: G
authors.lastname: Desmet
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D057446:Hydrodynamics; D008956:Models, Chemical; D010316:Particle Size; D016062:Porosity