A quasi-2D model of dike propagation with non-equilibrium magma crystallization

Magma transport in dikes is usually modelled by means of lubrication theory, assuming that magma properties are uniform across the dike. We explore the influence of cross-dike temperature heterogeneity on the dynamics of dike propagation using a quasi-2D model, derived from a full 2D model with an assumption of small width to length ratio. The model couples elastic fracture mechanics with multiphase magma flow, solving the governing equations using a hybrid numerical approach that combines the Displacement Discontinuity Method for elasticity with finite volume discretization for fluid flow and heat transfer. The model includes heat exchange with wall rocks, shear heating and latent heat release. It accounts for non-equilibrium magma crystallization, implementing temperature-dependent crystallization kinetics using an Arrhenius formulation for the relaxation timescale. As a case study, we simulate the ascent of a volatile-rich dacite from a source at 30 km depth. The distribution of temperature, crystallinity, and, thus, viscosity across the dike leads to a plug-like velocity profile with magma stagnation near the walls, substantially different from the parabolic Poiseuille flow assumed in classical lubrication theory. With temperature-dependent crystallization rate, rapid cooling of magma near the dike walls can generate a glassy chilled margin. The adjacent magma has higher crystallinity due to intermediate cooling rates, while the hotter core remains depleted in crystals throughout dike propagation. The dike propagates further and is thinner than predicted by (1D) lubrication theory because the low-viscosity core continues to facilitate vertical transport while the wall zones become progressively more viscous due to cooling and crystallization. The latent heat of crystallization can have a substantial impact in slowing down cooling and prolonging propagation. Other important factors include the characteristic crystal growth time, initial magma temperature and water content. Our quasi-2D approach bridges the gap between oversimplified 1D models and computationally expensive 3D simulations, providing a practical framework for investigating magma transport in silicic dikes.