Scaling vesicle distributions and volcanic eruptions

Models of coalescence-decompressive expansion of the later stages of bubble growth predict that for diverse types of volcanic products the vesicle number densities (n(V)) are of the scaling form n(V) proportional to V(-B)3(-1) where V is the volume of the vesicles and B-3 the 3-dimensional scaling ( power law) exponent. We analyze cross sections of 9 pumice samples showing that over the range of bubble sizes from approximate to 10 mu m to 3 cm, they are well fit with B-3 approximate to 0.85. We show that to within experimental error, this exponent is the same as that reported in the literature for basaltic lavas, and other volcanic products. The importance of the scaling of vesicle distributions is highlighted by the observation that they are particularly effective at "packing" bubbles allowing very high vesicularities to be reached before the critical percolation threshold, a process which - for highly stressed magmas - would trigger explosion. In this way the scaling of the bubble distributions allows them to be key actors in determining the rheological properties and in eruption dynamics.