Establishment of scaling law concerning the intra-conduit mechanics using pumice

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Developing bubble number density (BND) decompression rate meter and microlite number density (MND) water exsolution rate meter, we have established the method to quantitatively estimate the decompression rate or water exsolution rate from measured values of BND or MND for given the magma temperature, compositions, and initial water content.Applications of this method to nature have revealed the following things. For explosive eruptions, 1) the decompression rates at bubble nucleation for plinian eruptions are up to 10^6 to 10^8 Pa/s, which must be accompanied by the rapid decompression like due to a rarefaction shock wave. 2) In subplinian eruptions of basaltic andesitic magmas, the water exsolution at the microlite nucleation proceeds the diffusion limited bubble growth during the disequilibrium vesiculation. BND or crystallinity has correlations with the temporal variation of eruptions such as changes of exit velocities. 3)The fact that pyroclasts erupted at the same time have the variation in estimated rates of water exsolution suggests that the flow in the conduit is turbulent For non-explosive eruptions, 4) estimated water exsolution rate is approximately 10^<-5> wt%/s, and 0.01 to 0.1 m/s of ascent velocity and 10^2-10^3 Pa/s of decompression rate. 5)The water exsolution rates are uniform across the conduit 6) The water exsolution might proceeds at deeper level of the conduit though it is still unclear whether the vesiculation is equilibrium or disequilibrium. These facts suggests that the flow in the conduit for non-explosive eruptions is like a plug flow.Carrying out a combined simulation of vesiculation and crystallization, and making a comparison with the laboratory experiments by Couch, et. al. (2003), we have found that MND is controlled by the amount of decompression through the driving force of diffusive bubble growths under disequilibrium vesiculation.