The size distribution of pyroclasts and the fragmentation sequence in explosive volcanic eruptions

In an explosive eruption, the atmospheric column dynamics depend strongly on the mass fraction of gas in the erupting mixture, which is fixed by fragmentation in the volcanic conduit. At fragmentation, gas present in vesicular magmatic liquid gets partitioned between a continuous phase separating magma clasts and a dispersed phase in individual bubbles within the clasts, As regards flow behavior, it is the former, continuous, gas phase which matters, and we show that its amount is determined by the fragment size. Analysis of 25 fall deposits and 37 flow deposits demonstrates that ash and pumice populations follow a power law size distribution such that N, the number of fragments with radii larger than r, is given by N;proportional to r(-D). D values range from 2.9 to 3.9 and are always larger than 3.0 in fall deposits. D values for pyroclastic flow deposits are systematically smaller than those of fall deposits. We show that at fragmentation the amount of continuous gas phase is an increasing function of the D value. Large D values cannot be attributed to a single fragmentation event and are due to secondary fragmentation processes. Laboratory experiments on bubbly magma and on solid pumice samples demonstrate that primary breakup leads to D values of 2.5+/-0.1 and that repeated fragment collisions act to increase the D value,. A model for size-dependent refragmentation accounts for the observations. We propose that in a volcanic conduit, fragmentation proceeds as a sequence of events. Primary breakup releases a small amount of gas and is followed by fragment collisions. Due to refragmentation and decompression, both the mass and volume fractions of continuous gas increase. The final D value, and hence the mass fraction of continuous gas at the vent: depends on the time spent between primary fragmentation and eruption out of the vent.