A novel diffusive model for volcanic eruptions

Volcanic eruptions are complex phenomena not yet fully understood. Here we propose a novel analytical diffusive model to describe explosive Strombolian eruptions. These are caused by the accumulation of gas bubbles beneath the cooler upper surface of the magma chamber which deforms until breaking it, thus resulting in an explosive ejection of material. The diffusive model we propose is based on a few key ingredients: denser magma bodies, or blobs, diffuse within the magma chamber; blobs coalesce upon collision; gas bubbles vesiculate beneath the blobs resulting in an effective upward buoyancy force; a blob is erupted when the buoyancy force balances the gravity force acting on it. The resulting distributions of the blobs erupted volumes follows a power law decay with an exponential cut-off at large volumes, qualitatively closely matching experimental data. More quantitively, a fit of our analytical model to these data shows very good agreement. Further validation of our model comes from Brownian dynamics simulations with coalescing Brownian particles. In addition to confirming the above results, simulations additionally reveal that, even though developed for Strombolian eruptions, our model can be applied also to other eruption styles with proper parameter adjustments.