Asymptotic limits of some models for sound propagation in porous media and the assignment of the pore characteristic lengths

Modeling of sound propagation in porous media requires the knowledge of several intrinsic material parameters, some of which are difficult or impossible to measure directly, particularly in the case of a porous medium which is composed of pores with a wide range of scales and random interconnections. Four particular parameters which are rarely measured non-acoustically, but used extensively in a number of acoustical models, are the viscous and thermal characteristic lengths, thermal permeability, and Pride parameter. The main purpose of this work is to show how these parameters relate to the pore size distribution which is a routine characteristic measured non-acoustically. This is achieved through the analysis of the asymptotic behavior of four analytical models which have been developed previously to predict the dynamic density and/or compressibility of the equivalent fluid in a porous medium. In this work the models proposed by Johnson, Koplik, and Dashn [J. Fluid Mech. 176, 379–402 (1987)], Champoux and Allard [J. Appl. Phys. 70(4), 1975–1979 (1991)], Pride, Morgan, and Gangi [Phys. Rev. B 47, 4964–4978 (1993)], and Horoshenkov, Attenborough, and Chandler-Wilde [J. Acoust. Soc. Am. 104, 1198–1209 (1998)] are compared. The findings are then used to compare the behavior of the complex dynamic density and compressibility of the fluid in a material pore with uniform and variable cross-sections