One-dimensional adiabatic flow of equilibrium gas-particles mixtures in long vertical ducts with friction

The equations of the steady, adiabatic, one-dimensional flow of an equilibrium mixture of a perfect gas and incompressible particles, in constant-area ducts with friction, are derived taking into account the effects of gravity and of the finite volume of the particles. As is the case for a pure gas, the mixture is shown to be subject to the phenomenon of choking, and the possibility of an adiabatic heating of the mixture in a subsonic expansion is also theoretically predicted for certain flow inlet conditions. The model may be used to approximately describe the conditions existing in portions of volcanic conduits during the Plinian phases of explosives eruptions. illustrate the possibility of the adiabatic heating of the mixture.