Cell model calculations of dynamic drag parameters in packings of spheres

Abstract

An external flow approach is used to predict the viscous drag due to oscillating flow in an air-filled stack of fixed identical rigid spheres. Analytical expressions for dynamic and direct current (dc) permeability, high-frequency limit of tortuosity, and the characteristic viscous dimension are derived using a cell model with an adjustable cell radius which allows for hydrodynamic interactions between the spherical particles. The resulting theory requires knowledge of two fixed parameters: the volume porosity and the particle radius. The theory also requires a value for the cell radius. Use of the cell radius corresponding to that of the sphere circumscribing a unit cell of a cubic lattice arrangement is proposed. This is found to enable good agreement between predictions of the new theory and both published data and numerical results for simple cubic and random spherical packings.