The Physics of Eruptions

The magma of a volcano is the significant factor in regards to an eruption. Magma viscosity can be, very roughly, broken down into basaltic (low viscosity), intermediate (high viscosity), and rhyolitic (very high viscosity). Magmas contain volatiles, gasses such as water vapor, carbon dioxide, sulfur, and methane. Magma tends to be less dense than the surrounding rock, rising to the surface. As it rises, the pressure exerted on the volatiles inside the magma lessen, allowing them to coalesce into bubbles. The more gas in the magma, the more bubbles can form. Henry's Law is a relatively simple gas law that gives us a good idea of how much gas a magma with known composition may contain.

Once the ration of bubbles to magma reaches a critical point, the fragmentation point, the bubbles pop, letting the gas escape energetically out of the magma, generally taking a large volume of the now fractured magma with it. This is the classic, Plinean style eruption characterized by large billowing clouds of ash and chunks of rock.

The speed at which bubbles move in the magma can have an impact on the type of eruption as well. Bubbles that move up slower than the magma that they are in tend to form explosive eruptions, if the magma is rhyolitic or intermediate, or effusive, lava-splashing eruptions if the magma is basaltic.

This function defines the drag force of the magma on the bubbles within, with n being the viscosity, r is the bubble radius and u is the bubble rise speed. Since we assume there is an equilibrium between the drag force and the buoyancy force, we can find u by inserting a derivative of Boyle's Law:

Assuming we know(or can just assume) the density of the magma and gas. Hawaiian volcanos are well known effusive type eruptions with basalt lavas. Volcanoes along Alaska's Aleutian chain are known for their more explosive eruptions and intermediate lavas.