Driving force of lateral permeable gas flow in magma and the criterion of explosive and effusive eruptions

The release of gas from ascending magma is one of the most important factors that controls the style of volcanic eruptions. It is proposed in this paper that the viscous resistance of decompressed magma to gas expansion coupled with the lateral gradient of the ascent velocity can work as a driving force of the permeable gas flow that may transport gas in magma toward the country rock. Based on this idea, the rate of gas loss from magma is calculated in terms of the mean ascent velocity, the gas volume fraction and the ‘degassing factor’ that is proportional to the magma viscosity and the permeability in the limit of the large gas volume fraction. This formulation of gas loss is applied to a simulation of the magma ascent process to examine the eruption style. For the simulation we employ a model of one-dimensional, non-stationary conduit flow in which volatiles are assumed to move upward with the same speed as the liquid magma and to deposit on bubbles in an amount exceeding the solubility. The simulation reveals that the gas volume fraction in the erupting magma sharply drops from nearly unity to significantly lower values as the dimensionless degassing factor increases and crosses a critical value that is only slightly dependent on various conditions. This consequence yields a simple criterion of the eruption style that displays the ranges of explosive and effusive eruptions on the viscosity–permeability plane separated by a boundary line that shifts following the size and geometry type of the conduit.