Wave Propagation in Dispersed Random Media
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WAVE PROPAGATION IN DISPERSED RANDOM MEDIA PING SHENG, XIAODUN JING*, AND MINYAO ZHOU Exxon Research & Engineering Co., Annandale, NJ 08801 *Present address: Department of Materials Science and Chemical Engineering, University of Minnesota, Minneapolis, Minnesota 55455
ABSTRACT We present a generalized coherent potential approximation for the identification of quasi propagating modes in dispersed random media and the calculation of their dispersion relations. The validity of this approach is supported by multiple-scattering calculations, numerical simulation, and comparison with experimental data on acoustic excitations in colloidal suspensions. Our theory yields excellent quantitative agreement with the measured dispersion relations and provides an explanation for the observed frequency gaps in the excitations spectra.
INTRODUCTION Classical wave propagation and scattering is a topic extensively studied by both the physics and the engineering communities. It is the conventional wisdom that an isotropic, homogeneous elastic solid has one longitudinal and two transverse modes, and a fluid has only one longitudinal acoustic mode due to its lack of shear restoring force. For the fluidsolid composites, there are generally two types of behavior depending on the composite microstructure. For fluid-saturated porous media, where both the solid and the fluid phases form connected networks, Biot [1] has predicted the existence of two longitudinal modes, in addition to the two shear modes, where the fast longitudinal mode travels predominantly in the solid frame and the slow longitudinal model mainly in the fluid. This prediction was indeed confirmed experimentally [2]. On the other hand, for dispersed random media where the solid particles form a discrete dispersion embedded in a fluid matrix, i.e. a colloidal suspension, it has been shown both theoretically and experimentally that at low frequencies there is only one acoustic mode [3,4]. As the frequency increases so that the wavelength becomes comparable to the scale of the random inhomogeneities, the character of wave propagation is generally expected to change drastically due to the possibility of strong multiple scattering. For the solid-fluid system, James [5] first derived a formula for the scattering of acoustic wave by a solid sphere immersed in fluid, which served as a basis for the multiple scattering calculations to follow. Many different theoretical schemes, such as the T-matrix method [6-7] of Waterman, coherent potential approximation (CPA), and the quasicrystalline approximation [3,4,8,9,10], have been developed for the calculation of multiple scattering effects. Wave localization phenomena have also been predicted [11] to result from multiple and resonant scatterings. However, despite extensive studies there has still been a lack of systematic understanding of wave transport behavior in the intermediate frequency regime. This situation is evidenced by the following development. Figure 1 shows the results of recent Brillouin scattering experiment [12] on co
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