The mathematical up-scaling of flow past an assembly of spherical particles was analyzed. From an averaged model, a closure problem for the interfacial force obtained via the volume averaging method with closure was solved in cylindrical unit cells with concentric particles. In concordance with reported works in the framework of solid-fluid flows, the interfacial force was expressed in terms of a drag coefficient. Comparisons with available data from direct numerical simulations were in good agreement, and a correlation that fits the calculated data for drag coefficient was proposed. Finally, some remarks on advantages and limitations of the applied approach are made. (C) 2014 Elsevier B.V. All rights reserved.