Adiabatic temperature changes of magma-gas mixtures during ascent and eruption

Most quantitative studies of flow dynamics in eruptive conduits during volcanic eruptions use a simplified energy equation that ignores either temperature changes, or the thermal effects of gas exsolution. In this paper we assess the effects of those simplifications by analyzing the influence of equilibrium gas exsolution and expansion on final temperatures, velocities, and liquid viscosities of magma–gas mixtures during adiabatic decompression. For a given initial pressure (p ₁ ), temperature (T ₁ ) and melt composition, the final temperature (T _f ) and velocity (u _max ) will vary depending on the degree to which friction and other irreversible processes reduce mechanical energy within the conduit. The final conditions range between two thermodynamic end members: (1) constant enthalpy (dh=0), in which T _f is maximal and no energy goes into lifting or acceleration; and (2) constant entropy (ds=0), in which T _f is minimal and maximum energy goes into lifting and acceleration. For ds=0, T ₁ =900 °C and p ₁ =200 MPa, a water-saturated albitic melt cools by ~200 °C during decompression, but only about 250 °C of this temperature decrease can be attributed to the energy of gas exsolution per se: the remainder results from expansion of gas that has already exsolved. For the same T ₁ and p ₁ , and dh=0, T _f is 10–15 °C hotter than T ₁ but is about 10–25 °C cooler than T _f in similar calculations that ignore the energy of gas exsolution. For ds=0, p ₁ =200 MPa and T ₁ =9,000 °C, assuming that all the enthalpy change of decompression goes into kinetic energy, a water-saturated albitic mixture can theoretically accelerate to ~800 m/s. Similar calculations that ignore gas exsolution (but take into account gas expansion) give velocities about 10–15% higher. For the same T ₁ , p _I =200 MPa, and ds=0, the cooling associated with gas expansion and exsolution increases final melt viscosity more than 2.5 orders of magnitude. For dh=0, isenthalpic heating decreases final melt viscosity by about 0.7 orders of magnitude. Thermal effects of gas exsolution are responsible for less than 10% of these viscosity changes. Isenthalpic heating could significantly reduce flow resistance in eruptive conduits if heat generation were concentrated along conduit walls, where shearing is greatest. Isentropic cooling could enhance clast fragmentation in near-surface vents in cases where extremely rapid pressure drops reduce gas temperatures and chill the margins of expanding pyroclasts.