Diffusion of ultrasonic waves in porous glass bead sinters

Abstract

Sintered networks of glass beads form an interesting example of a porous medium, analogous to a very porous rock, in which very strong multiple scattering of elastic waves is observed when the ultrasonic wavelength is comparable with the size of the pores. To investigate the diffusive transport of energy by multiply scattered waves, the transmission of the diffuse energy flux through finite slabs of this material has been measured. From these data, the diffusion coefficient D, as well as the absorption time, was determined by fitting the predictions of the diffusion approximation to the experimental time-of-flight profiles. To accurately measure D, the internal reflection of diffuse waves at the sample boundaries was taken into account by extending the method used previously for acoustic waves [J. H. Page et al., Phys. Rev. E 52, 3106 (1995)]. The frequency dependence of the diffusion coefficient was measured over an extended range of frequencies, and compared with estimates of D from ballistic measurements of the scattering mean free path and group velocity. Because of its relatively simple structure, this material may be an ideal system for probing the diffusion of elastic waves, where diffuse waves have mixed character consisting of both longitudinal and transverse polarizations.