Flow Evolution in Magmatic Conduits: A Constructal Law Analysis of Stochastic Basaltic and Felsic Lava Dynamics

Abstract

This study probabilistically assesses magma ascent by modeling dike propagation as a fully coupled fluid-flow, thermo-mechanical problem, explicitly accounting for the stochastic heterogeneity of the crustal host rock. We study felsic (rhyolite) lava flow and two distinct basaltic feeding regimes that correspond to the conditions necessary to produce the contrasting pahoehoe and ʻaʻā surface morphologies. Basaltic dikes demonstrate high propagation efficiency to the surface (pahoehoe-feeding regime 99.5%; ʻaʻā-feeding regime 97.5%), whereas rhyolite dikes have an 89% failure rate, attributed to significant friction. Both regimes represent distinct constructal approaches aimed at maximizing flow persistence. The pahoehoe-feeding regime is a thermally regulated, stable design characterized by low-velocity, cooling-dominated dynamics. Its slow, persistent flow allows for significant conductive heating of the surrounding rock wall, creating an efficient, pre-heated thermal conduit. In contrast, the ʻaʻā-feeding regime is a mechanically dominated design governed by high-velocity, stochastic dynamics. This morphology is driven by forceful flow, and its thermal budget is supplemented by intense viscous dissipation (internal friction). Rhyolite magma flow fails upon losing constructal viability, driven by a coupled mechanical–thermal cascade. The sequence begins when a mechanical barrier halts the magma velocity, which triggers a freezing event and leads to permanent arrest.