A scaling growth model for bubbles in basaltic lava flows

Pahoehoe, aa and massive lavas from Mount Etna show common statistical properties from one sample to another which are independent of scale/size over certain ranges. The gas vesicle distribution shows two scale-invariant regimes with number density n(V) proportional to V--B-1, where V is the volume and empirically B approximate to 0 for small bubbles and B approximate to 1 for medium to large bubbles. We introduce a bubble growth model which explains the B > 1 range by a strongly non-linear cascading growth regime dominated by a quasi-steady-state coalescence process. The small bubble region is dominated by diffusion; its role is to supply small bubbles to the coalescence regime. The presence of measured dissolved gas in the matrix glass is consistent with the notion that bubbles generally grow in quasi-steady-state conditions. The basic model assumptions are quite robust with respect to the action of a wide variety of processes, since we only require that the dynamics are scaled over the relevant range of scales, and that during the coalescence process, bubble volumes are (approximately) conserved. The model also predicts a decaying coalescence regime (with B > 1) associated with a depletion of the gas source or, alternatively, a loss of large vesicles through the surface of the flow. Our model thus explains the empirical evidence pointing to the coexistence of two different growth mechanisms in subsurface lava flows, but acting over distinct ranges of scale, with non-linear coalescence as the primary growth process. The total vesicularity of each sample can then be well estimated from the partial vesicularity of each growth regime without any outlier problems.