Influence of unsteady forces acting on a particle in a suspension application to the sound propagation

Abstract

First, the influence of the unsteady forces (the pressure gradient, the virtual mass effect and the Basset history term) on the complex velocities ratio of the fluid and of the dispersed phases has been studied. To this end, the particle momentum equation is linearized for small oscillating motion of the two phases which are at rest in the reference state. It is shown that the unsteady terms are of great importance when the coefficient χ, mass density of the particle divided by the mass density of the fluid, becomes small. A particular study of the Basset history term is also investigated. Then, a two fluids theory, including viscous and thermal losses effects, is developed for calculating the velocity and the damping of the sound propagating in a two-phase flow. As the former treatment, the classical equations of the multiphase flows are linearized and the dispersion equation of the acoustical wave is obtained. Several tendencies and the special part played by the Basset history term in acoustics are pointed out.