Analytical studies of suspension acoustics

The one-dimensional unsteady flow of the suspension is considered taking into account the standard assumptions for this problems: the mixture is monodisperse, there is no crushing and sticking of particles, viscosity and thermal conductivity are essential only in the process of interfacial interaction. The mixture supposed perfect. The particles are taken absolutely solid and spherical, and the liquid is linearly compressible. The frictional force acting on a single spherical particle is taken into account. The solution to the original system is sought in the form of a traveling wave. On the basis of one-dimensional unsteady equations of fluid flow with solid particles dispersion relations are written out and formulas for phase velocities are derived. Formulas for the attenuation coefficient of the perturbation frequency are got. It has been established that at low frequencies, depending on the magnitude of $\tilde {\rho}_{p0}^{0}={ \rho_{p0}^{0}}/{\rho_{\ell 0}^{0}}$ the equilibrium speed can be higher or lower than the speed of sound in the carrier phase. If the dispersed phase is heavier than the carrier phase $ (\tilde {\rho}_{p0}^{0}> 1)$, then the equilibrium velocity exceeds the speed of sound. This is due to the fact that at low frequencies, when velocity equilibrium is realized, the compressibility of the mixture occurs only owing to the carrier phase, and the mixture becomes heavier (inertial) because of the content of the dispersed phase at $ (\tilde {\rho}_{p0}^{0}> 1)$ . When $(\tilde{\rho}_{p0}^{0}<1)$, the mixture in contrast is lighter than the carrier phase, and the equilibrium velocity becomes higher than the speed of sound. At high frequencies the sound velocity does not depend on $\tilde{\rho}_{p0}^{0}$ and is equal to the sound velocity for the carrier phase.