Percolating magmas and explosive volcanism

Abstract

Magma under pressure rises in conduits, depressurizes, forms bubbles by the exsolution of gas and – at void fractions (P) typically of the order of 0.7 – can fragment and explode. The study of overlapping geometrical units – percolation theory – predicts that at a critical volume fraction Pc the size of the largest simply connected region becomes infinite. We apply percolation theory to overlapping bubbles arguing that this geometric singularity at Pc implies a physical singularity in the magma rheology. This would imply that if the magma is under stress, ‐ whether it is ductile or brittle ‐ this rapid development of a network of infinitely long “bubbles” triggers fragmentation and explosion. Classical monodisperse (equal size) continuum percolation theory predicts Pc = 0.2985 ± 0.005 which is far from the observed values. However, it has recently been shown that the bubble distribution is a power law associated with a huge range of bubble sizes. Using Monte Carlo percolation simulations, we show that distributions exhibiting the empirical exponents are very efficient at “packing” the bubbles, drastically raising Pc to the value = 0.70 ± 0.05. Explosive volcanism is thus explained by singular rheology at Pc.