The acoustic properties of granular materials with pore size distribution close to log-normal

The majority of realistic porous materials are composed of pores of which the shape is variable and the size of the pores normally obeys a distinctive statistical distribution. Although the variation of pore shape is less important, the statistical parameters of pore size distribution can have a considerable effect on the acoustic properties of porous media. This paper discusses the application of a simple model for the prediction of the acoustic properties of porous granular media with some assumed pore geometry and pore size distribution close to log-normal. The model is based on the rational (Padé) approximation approach [K. V. Horoshenkov, K. Attenborough, and S. N. Chandler-Wilde, J. Acoust. Soc. Am. 104, 1198-1209 (1998)] which has been developed for some simple pore geometries. It is shown that the experimentally determined pore size distribution for a representative range of granular materials is often close to log-normal. This assumption enables accurate predictions of the acoustic performance of these materials using the presented model. The water suction method is proposed to determine the parameters of the log-normal distribution, which are the mean pore size, (phi) and its standard deviation, sigma. This method is nonacoustic, modelless and well-adapted to acoustic materials and, unlike the BET method [S. Brunauer, P. H. Emmett, and E. Teller, J. Am. Chem. Soc. 60, 309-319 (1938)], is easy to reproduce in any basic acoustic laboratory requiring no expensive parts or chemicals. The proposed Padé approximation is based entirely on four measurable nonacoustic parameters, the porosity, omega, flow resistivity, Rb, tortuosity, q2 and the standard deviation of the pore size, sigma. The method is successfully tested on a representative selection of consolidated and nonconsolidated porous granular materials.