The terminal velocity of volcanic particles with shape obtained from 3D X-ray microtomography

Abstract

New experiments of falling volcanic particles were performed in order to define terminal velocity models applicable in a wide range of Reynolds number Re. Experiments were carried out with fluids of various viscosities and with particles that cover a wide range of size, density and shape. Particle shape, which strongly influences fluid drag, was measured in 3D by High-resolution X-ray microtomography, by which sphericity Φ3D and fractal dimension D3D were obtained. They are easier to measure and less operator dependent than the 2D shape parameters used in previous papers. Drag laws that make use of the new 3D parameters were obtained by fitting particle data to the experiments, and single-equation terminal velocity models were derived. They work well both at high and low Re (3×10−2<Re<104), while earlier formulations made use of different equations at different ranges of Re. The new drag laws are well suited for the modelling of particle transportation both in the eruptive column, where coarse and fine particles are present, and also in the distal part of the umbrella region, where fine ash is involved in the large-scale domains of atmospheric circulation. A table of the typical values of Φ3D and D3D of particles from known plinian, subplinian and ash plume eruptions is presented. Graphs of terminal velocity as a function of grain size are finally proposed as tools to help volcanologists and atmosphere scientists to model particle transportation of explosive eruptions.