Exploring the Behavior of Solid/Gas Mixtures via Shock-Tube Experiments With Relevance to Vulcanian Eruptions

Scaled 1-D shock-tube experiments were conducted to understand the behavior of rapidly-decompressed solid-gas mixtures, with relevance to the initial phase of Vulcanian explosions. Using experimental apparatus and methods similar to Cagnoli et al. (2002; J. Volcanol.Geotherm. Res., 101-113), a bed of very-well-sorted glass spheres and interstitial air was suddenly decompressed from atmospheric to vacuum pressures in a vertical glass shock tube. Decompression was achieved by nearly instantaneous rupture of a diaphragm separating the high-pressure mixture from the low-pressure region. Pressure ratios across the diaphragm and particle size were varied systematically. Velocities were determined by photogrammetric analysis of high-speed video footage. Pressure evolution was recorded at 0.30, 0.90 and 1.20 m above the diaphragm by high frequency (100,000 Hz sampling rate) PCB pressure sensors, revealing pressure wave velocity and relative strength. Pressure waveforms recorded in the experiments resemble those recorded by microbarographs of Vulcanian explosions. Mixture and pressure wave velocities are lower than typically observed in eruptions, likely due to lower pressure ratios across the diaphragm. Results show particle size plays an important role in overall behavior. As expected, mixture velocity increases with increasing pressure ratio across the diaphragm and decreases with increasing particle size. Several existing formulations intended to predict behavior of solid-gas mixtures were tested against the data. Pseudo-gas approximations of fluid properties are sufficient to allow 1-D shock-tube theory to mimic behavior of the finest (4-45 microns) mixtures, whereas inertial effects become important for larger-particle experiments causing deviation from theory. Pressure wave velocity and strength are reduced from those predicted for an ideal gas, suggesting momentum loss from the gas phase due to frictional interaction with the particle beds. The well-accepted theory of Ergun (1952) and other standard drag relationships used to parameterize interactions between gas phases and high concentrations of solids in numerical models of explosive eruptions are also tested.