Analytical solutions for characterizing tortuosity and characteristic lengths of porous materials using acoustical measurements: Indirect model

Abstract

Under the homogenization hypothesis, wave propagation in porous materials can be described using, for example, macroscopic dynamic density and bulk modulus. These functions depend on statistical geometrical parameters. Classically, five parameters are used: porosity, static air flow resistance, tortuosity, and viscous and thermal characteristic lengths. The three last parameters are generally difficult to measure with existing direct methods, for a wide range of materials. The proposed method is based on the measurement of dynamic density and compressibility, in order to separate viscous and thermal effects. With prior knowledge of airflow resistance and porosity, it is then possible to find analytical solutions for the missing parameters, fitting Johnson–Allard–Champoux model. In the same way, we also tackle the problem of the determination of static ‘‘thermal permeability’’ introduced to improve the description of thermal dissipation effect. Experimental results, obtained with various materials, using a Kundt’s tube, are presented to show the efficiency, and relative simplicity of the method. Moreover, the relevance of using a three parameters model for describing the bulk modulus is discussed.