Time Domain Modelling of Sound Propagation in Porous Media and the Role of Shape Factors

An extended formulation of the relaxational model proposed by Wilson et al. in 1993 is presented in this paper. The proposed semi-empirical models for complex tortuosity and compressibility functions satisfy physically correct low and high frequency limits and allow analytical transformation into the time domain. These models are based on the assumption, that two configurations of pore networks with two characteristic size distributions can approximate an internal structure of a porous material. The models require the knowledge of two relaxation times. Numerical time domain calculations confirm that the contribution of both viscous and thermal effects on the evolution of acoustic pulses as they propagate through a porous material can be accounted for simultaneously within the framework of the model. A good agreement between the model predictions with data of different porous materials has been found.