A MULTIPHASE CONTINUUM THEORY FOR SOUND-WAVE PROPAGATION THROUGH DILUTE SUSPENSIONS OF PARTICLES

The hydrodynamic or continuum approach is utilized to examine sound wa ve propagation through a dilute suspension of spherical particles in a viscous, heat-conducting fluid. The acoustical theory accounts for me chanical particle-fluid interactions such as Stokes drag, as well as c oupled phase phenomena, collectively called phoresis effects due to gr adients of temperature, density, or concentration (e.g., processes of thermophoresis, pcynophoresis, and diffusion phoresis). Linearized vol ume-averaged balance equations for mass, linear momentum, and energy a re solved for a plane wave of arbitrary frequency. Approximations are provided to enable better physical interpretation of the results and t o compare to the earlier treatment by Temkin and Dobbins [J. Acoust. S oc. Am. 40, 317-324 (1966)] for an inviscid fluid phase, but with a St okes drag force on each particle. The investigation also considers sev eral generalizations for the case when the phoresis terms can be negle cted. For example, a distribution of particle sizes is accounted for b y developing a frequency-dependent function that weights the drag forc es by a particle-size distribution function. Furthermore, by invoking the correspondence principle, the drag force function for a Newtonian fluid is extended to a viscoelastic particle-laden material by using c omplex viscosities for shear and compressional relaxation functions. I n the limit that the concentration of particles goes to zero, and the viscosity is Newtonian, the classical Kirchhoff-Langevin equation is o btained. Several calculated results are provided for comparison to ava ilable experimental measurements and a viscoelastic fluid suspension s imulation illustrates attenuation and dispersion relationships versus particle size and concentration.