What is the maximum solid phase concentration in volcanic turbulent gas-particle mixtures? Experimental observations and implications for natural flows

Turbulent mixtures of gas and solid particles are commonly generated by explosive volcanic eruptions in the form of plumes or pyroclastic density currents. The concentration of particles is fundamental because it controls the dynamics of these mixtures by essentially modifying their density. Although previous studies suggest that the turbulent gas can carry quantities of particles up to a few volume percent, the maximum particle concentration of dilute mixtures is poorly known. We addressed this issue through laboratory experiments in a vertical pipe, where quasi-static dilute gas-particle mixtures were created by injecting a turbulent air flow from below at mean velocities corresponding to the terminal settling velocities for the grain sizes studied. Particle concentrations were measured using pressure sensors. We investigated turbulent mixtures of air and nearly monodisperse beads of glass (grain sizes of 77 μm to 1550 μm) or ceramic (grain sizes size of 115 μm to 730 μm), with macroscopic Reynolds numbers ~10⁴-10⁶. The experiments revealed that the mixtures had maximum particle concentration C_max=1.0-2.8 vol. %, which was set by onset of clustering and increased with the degree of turbulence. Tests conducted at higher initial bulk concentrations showed that the mixtures consisted of an upper dilute turbulent part at C_max and a lower dense fluidized bed fed by clusters settling from the dilute part. Particles were ejected from the dense bed, and a balance of particles cycling between the two regions set the maximum concentration of particles in the dilute part. We found that C_max increased with the particle Reynolds number according to C_max=0.78×Re_p^0.17, suggesting that particle-scale processes control the maximum solid phase concentration of turbulent mixtures. This is also consistent with the fact that C_max is set by particle clustering, which is caused by particle-scale processes such as hydrodynamic instabilities. Application of our empirical law to natural volcanic mixtures with Re_p~10²-10⁵ gives maximum particle concentrations of ~2-5 vol. %. This result can help constrain models input/output data as well as field observations.