The effects of outgassing on the transition between effusive and explosive silicic eruptions

The eruption style of silicic magmas is affected by the loss of gas (outgassing) during ascent. We investigate outgassing using a numerical model for one-dimensional, two-phase, steady flow in a volcanic conduit. By implementing Forchheimer's equation rather than Darcy's equation for outgassing we are able to investigate the relative influence of Darcian and inertial permeability on the transition between effusive and explosive eruptions. These permeabilities are defined by constitutive equations obtained from textural analysis of pyroclasts and determined by bubble number density, throat–bubble size ratio, tortuosity, and roughness. The efficiency of outgassing as a function of these parameters can be quantified by two dimensionless quantities: the Stokes number, the ratio of the response time of the magma and the characteristic time of gas flow, and the Forchheimer number, the ratio of the viscous and inertial forces inside the bubble network. A small Stokes number indicates strong coupling between gas and magma and thus promotes explosive eruption. A large Forchheimer number signifies that gas escape from the bubble network is dominated by inertial effects, which leads to explosive behaviour. To provide context we compare model predictions to the May 18, 1980 Mount St. Helens and the August–September 1997 Soufrière Hills eruptions. We show that inertial effects dominate outgassing during both effusive and explosive eruptions, and that in this case the eruptive regime is determined by a new dimensionless quantity defined by the ratio of Stokes and Forchheimer number. Of the considered textural parameters, the bubble number density has the strongest influence on this quantity. This result has implications for permeability studies and conduit modelling