BND (bubble number density) decompression rate meter for explosive volcanic eruptions

This decade has been witness to substantial progress in the understanding of bubble dynamics and its role in volcanic eruptions. A comparison between the results of experiments and a model for bubble nucleation shows that bubble number density (BND) can be calculated as a function of decompression rate for given physical properties, such as the diffusivity of water in a silicate melt and interfacial tension, within an acceptable margin of error. Conversely, in this paper, we propose a method (hereafter referred to as BND decompression rate meter) to estimate the decompression rate by using BND data of natural pumice samples from volcanic eruptions. As a result of the application of the BND decompression rate meter to pumice and scoria from explosive eruptions, it is found that the decompression rates increase in the range from 106 to 108 (Pa/s) with the eruption column heights; these rates are proportional to the 4th power of the eruption column heights and are linear to the discharge rates. The absolute values of the estimated decompression rates are very high and cannot be explained by the existing models of conduit flows. In order to explain such high rates of decompression and the correlation with discharge rate, we propose a possible model according to which the bubble nucleation propagates downward as a rarefaction shock wave in the conduit.