Galimzyanov M.N., Shagapov V.Sh. Analytical studies of suspension acoustics. Multiphase Systems. 14 (2019) 1. 27–35 (in Russian).
Analytical studies of suspension acoustics
Mavlyutov Institute of Mechanics, UFRC RAS, Ufa
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
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 (ρ̃0p0>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 (ρ̃0p0>1). When (ρ̃0p0<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 ρ̃0p0 and is equal
to the sound velocity for the carrier phase.
Problem: Derivation of dispersion equations describing the motion of an acoustic wave through a suspension, based on which formulas for phase velocities are derived.
Methods: 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, from which formulas for phase velocities are obtained.
In a study
The one-dimensional unsteady suspension flow was investigated. On the basis of one-dimensional unsteady equations of fluid flow with solid particles, taking into account standard assumptions for the problems under consideration,
dispersion relations are written out and formulas for the phase velocities are obtained. Formulas for the dependence of the attenuation coefficient on the disturbance frequency are written. It has been established that at low
frequencies, depending on the magnitude of ρ̃0p0=ρ0p0/ρ0ℓ0 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 (ρ̃0p0>1), then the equilibrium velocity exceeds the speed of sound. When
ρ̃0p0<1, the mixture, on the contrary, 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 ρ̃0p0 and is equal to the sound velocity for the carrier phase.
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