Phonon Dispersion in Suspensions of Hard Sphere Colloids
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PHONON DISPERSION IN SUSPENSIONS OF HARD SPHERE COLLOIDS* D.A. WEITZ, J. LIU, L. YE AND PING SHENG Exxon Research and Engineering Co., Rt 22E, Annandale, NJ 08801. ABSTRACT We use Brillouin scattering to measure the dispersion of the propagating acoustic modes in a suspension of hard sphere colloids. We find two distinct longitudinal modes when the sound wavelength becomes comparable to the sphere diameter. The higher frequency mode has a velocity intermediate between those of the pure solid and the pure liquid phases, and its velocity increases with increasing volume fraction, 0. The lower frequency mode has a velocity less than the velocities in either the pure fluid or pure solid phases, and its velocity decreases with increasing 0. We interpret the higher frequency mode as a compressional wave which propagates through both the solid and the fluid, as expected for a composite medium. The lower frequency mode has not been observed before, and is interpreted as a surface acoustic mode, which propagates between adjacent spheres through a decaying portion of the excitation in the fluid. INTRODUCTION The propagation of acoustic waves through a random, disordered material is one of the most fundamental properties that characterize the medium. This is particularly true of granular materials, where the structure and correlations between the grains can have a profound effect on the propagation of acoustic waves. One class of granular material whose acoustic properties have been widely studied is porous media, comprised of solid and fluid phases. Their acoustic properties are of immense practical importance because of their utility for seismic investigations and other non-intrusive probes; they are also of great fundamental interest because of the rich variety of fascinating phenomena that have been observed. The complex interplay between the acoustic frequency, sound wavelength and characteristic size of the microstructure, as well as the presence of large interfacial areas and the frequency dependence of the viscous coupling between the solid and the liquid, lead to new mechanisms for the propagation of acoustic waves in these materials. The structure and connectivity of the solid grains play a critical role in determining the propagation of acoustic waves through these media. One of the simplest and most fundamental structures consists of uniform solid spheres immersed in a fluid.' The characteristics of this system are highly controllable, as the grain size, solid volume fraction, acoustic wavelength and acoustic frequency can all be independently varied. An example of such a structure is a hard sphere colloid.2 This consists of a dispersion of monodisperse, solid spheres immersed in a fluid, interacting solely by the hard sphere repulsion due to the fact that two solid spheres can not occupy the same volume. In this paper, we present the results of a study of the acoustic propagation through a hard sphere colloid. 3 We report Brillouin scattering measurements of the thermally excited, propagating acoustic modes, and
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