Cell model calculations of dynamic drag: parameters in packings of spheres

An external flow approach is used to predict the viscous drag due to oscill ating flow in an air-filled stack of fixed identical rigid spheres. Analyti cal expressions for dynamic and direct current (dc) permeability, high-freq uency limit of tortuosity, and the characteristic viscous dimension are der ived using a cell model with an adjustable cell radius which allows for hyd rodynamic interactions between the spherical particles. The resulting theor y requires knowledge of two fixed parameters: the volume porosity and the p article radius. The theory also requires a value for the cell radius. Use o f 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 g ood agreement between predictions of the new theory and both published data and numerical results for simple cubic and random spherical packings. (C) 2000 Acoustical Society of America. [S0001-4966(00)04405-2].