A model for sound propagation in a suspension of solid particles (Q1893921)

This paper considers a very dilute monodispersed suspension of solid particles (\(< 70\) parts per \(10^6\), e.g., as in urban atmosphere) in a low frequency regime. The particles are treated as dispersed phase, therefore only the viscous part of the drag force, the Stokes drag force on the particles, is considered. The low frequency approximation of the Stokes drag force is used. Fluid is assumed to be with viscosity and thermal conductivity. The formulation is done in the framework of irreversible thermodynamics for a dilute biphasic system. The two phases are assumed in mutual thermal equilibrium, so that the system interacts with its surroundings as a whole through Fourier's law with a single heat conductivity \(\lambda\) approximated by that of the fluid's. Plane waves in acoustic approximation are sought, the linearized dispersion relation is a modified Kirchhoff-Stokes relation. The total damping is modified by the addition of a frequency dependent term and by a correction of the thermodynamic coefficient of the thermal diffusivity term. Both modifications depend on the concentration of the particles and the equation of state of the fluid. The velocity of the sound wave is also modified, so that it depends on the equation of the state of the fluid, on the concentration, and on the density of the particle material. Examples that show the relative importance of the viscous contribution and the contribution of the Stokes term are given. The frequency dependent contribution can be overwhelming in comparison to the viscous attenuation in the lowest frequency region depending on the concentration of the particles and their radii. The Stokes contribution can be between 1.2 times and 140 times the viscous absorption at \(\omega= 10 s^{-1}\).