Fluid dynamical models of volcanic eruptions are usually made in the homogeneous approximation where gas and liquid are constrained to move at the same velocity. Basaltic eruptions exhibit the characteristics of separated flows, including transitions in their flow regime, from bubbly to slug flow in Strombolian eruptions and from bubbly to annular flow in Hawaiian ones. These regimes can be characterized by a parameter called the melt superficial velocity, or volume flux per unit cross section, which takes values between 10-3 and 10-2 m/s for bubbly and slug flow, and about 1 m/s for annular flow. We use two-phase flow equations to determine under which conditions the homogeneous approximation is not valid. In the bubbly regime, in which many bubbles rise through the moving liquid, there are large differences between the two-phase and homogeneous models, especially in the predictions of gas content and pressure. The homogeneous model is valid for viscous lavas such as dacites because viscosity impedes bubble motion. It is not valid for basaltic lavas if bubble sizes are greater than 1 cm, which is the case. Accordingly, basaltic eruptions should be characterized by lower gas contents and lower values of the exit pressure, and they rarely erupt in the mist and froth regimes, which are a feature of more viscous lavas

The two-phase flow framework allows for the treatment of different bubble populations, including vesicles due to exsolution by pressure release in the volcanic conduit and bubbles from the magma chamber. This yields information on poorly constrained parameters including the effective friction coefficient for the conduit, gas content, and bubble size in the chamber. We suggest that the observed flow transitions record changes in the amount and size of gas bubbles in the magma chamber at the conduit entry.