Parameterized model of a cooling magma chamber

Igneous rocks are significant sources of rare Earth elements. Their composition is affected by processes in magma chambers, liquid reservoirs residing beneath the surface of Earth. Crystallization of these reservoirs is typically assumed to be fractional, but it is unclear what is the primary mechanism behind separating the solid phase from the liquid: i) in-situ crystallization along the walls of the intrusion, or ii) sedimentation of crystals from suspension within the liquid magma. The latter scenario should be imprinted in the crystal size distribution of the deposit, as differently sized crystals have different residence times in the liquid. Solidification of magmatic systems is a complex problem and its individual aspects are often investigated separately. Physics-based models that couple the dynamics of solidification, settling laws derived from particle-laden flow experiments, and kinetic laws of crystal growth and nucleation remain scarce. 

Here, we build upon [1] and present a parameterized model of convection inside a magma chamber that explicitly treats crystal nucleation, growth, and gravitational settling in a vigorously and turbulently convecting fluid. The call for a new self-consistent model of a cooling magma chamber is driven, among others, by the recently formulated unified settling law that captures also the transition from particles that are well mixed by the convective currents to those sinking nearly vertically with their Stokes velocity, [2]. By invoking the energy balance and compositional evolution of the system (in this initial phase treated as a binary alloy), we show how the shape of the crystal size distribution and crystal grading in the sedimented lower part of the solidified body evolve as the fluid cools and the sediment layer increases in size. The model predicts dimensional results and aspires to model the microstructure of intrusions formed from authentic magmatic systems. To this end, we incorporate realistic laws of crystal growth and nucleation derived explicitly from thermodynamics principles. The model provides an initial framework for studying the link between flow dynamics inside the chamber, thermal/compositional evolution, and sediment signature, and can be easily built upon. 

 

[1] Jarvis, R.A., Woods, A.W., 1994. The nucleation, growth and settling of crystals from a turbulently convecting fluid. J. Fluid Mech. 273, 83–107

[2] Patočka, V., Tosi, N. & Calzavarini, E. (2022). Residence time of inertial particles in 3D thermal convection: implications for magma reservoirs. Earth and Planetary Science Letters 591, 117622.