On the acoustic slow wave in air-filled granular media

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Abstract
The relationship between the slow wave predicted by the rigid-frame limit of the Biot theory propagation in a fluid-saturated poroelastic solid and the modified-fluid wave predicted by classical theory for propagation in a rigid porous solid is examined. An anomalous difference between the two formulations of the viscodynamic operator for noncylindrical pores is exposed and explored. The pore shape factor ratio previously introduced in an extension of the classical approach is redefined. The classical rigid-frame formulation is shown to give good agreement with measured data on air-filled spherical lead shot and sands in the audio-frequency range. Modifications to the Biot viscodynamic operator, and the associated low-frequency/low-permeability approximations, that ensure consistency with the classical formulation, are proposed.

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