Acoustic probing of the particle concentration in turbulent granular suspensions in air

Dilute gas–particle suspensions in which the particles are carried by the fluid are found in various industrial and geophysical contexts. One fundamental issue that limits our understanding of such systems is the difficulty to obtain information on the particle concentration inside these often optically opaque suspensions. To overcome this difficulty, we develop ultrasonic spectroscopy to monitor the local particle concentration [Formula: see text] of glass particles (with diameters [Formula: see text] 77 [Formula: see text] m or 155 [Formula: see text] m) suspended in air. First, we determine the minimal air velocity, [Formula: see text] , necessary to suspend the particles from the maximum decrease in the transmitted wave amplitude and velocity of ultrasound propagating through the suspension. Next, setting the air velocity at [Formula: see text] , we increase the mass of particles and monitor acoustically the local solid volume fraction, [Formula: see text] , by measuring the ultrasound wave attenuation coefficient and phase velocity as a function of frequency on the basis of classical scattering and hydrodynamic models. For the frequency ranges and suspensions considered here, the viscous dissipation dominates over scattering and thermal conduction losses. We show that, for a characteristic air velocity [Formula: see text] , the locally measured [Formula: see text] reaches a critical value, in agreement with a recent study on turbulent gas–particle mixtures. Moreover, we find that this critical [Formula: see text] increases with the size of the particles. Finally, analysis of the temporal fluctuations of the locally measured solid volume fraction, suggests that high density regions (clusters) are present even in suspensions with concentrations below the critical concentration. This differs from the current hypothesis according to which the critical concentration coincides with the onset of cluster formation.