Counter-current convection in a volcanic conduit

Volcanoes of Strombolian type are able to maintain their semi-permanent eruptive states through the constant convective recycling of magma within the conduit leading from the magma chamber. In this paper we study the form of this convection using an analytic model of degassing two-phase flow in a vertical channel. We provide solutions for the flow at small Grashof and large Prandtl numbers, and we suggest that permanent steady-state counter-current convection is only possible if an initial bubbly counter-current flow undergoes a régime transition to a churn-turbulent flow. We also suggest that the magma in the chamber must be under-pressured in order for the flow to be maintained, and that this compromises the assumed form of the flow.