On the kinematics and dynamics of crystal-rich systems

Partially molten rocks, often called a mush, are examples of a hydrogranular mixture where the dynamics are controlled by both fluid and crystal-crystal interactions. An obstacle to progress in understanding high-temperature hydrogranular systems has been the lack of adequate levels of description of microphysical processes. Here we rationalize the hydrogranular kinematic and dynamic states by applying the concept of particle (crystal) force chains. We exemplify this with discrete-element computational fluid dynamic simulations of the intrusion of a basaltic melt into an olivine-basalt mush, where crystal-scale force chains, crystal transport, and melt mixing are resolved. To describe the microscale kinematics of the system, we introduce the coordination number and the fabric tensors of particle contacts and forces. We quantify the changing contact and force fabric anisotropy, coaxiality, and the connectedness of the mush, under dynamic conditions. To describe the dynamics, particle and fluid characteristic response times are derived. These are used to define local and bulk Stokes numbers, and viscous and inertia numbers, which quantify the multiphase coupling under crystal-rich conditions. We employ the Sommerfeld number, which describes the importance of crystal-melt lubrication, with a viscous number to illustrate the dynamic regimes of crystal-rich magmas. We show that the notion of mechanical lock up is not uniquely identified with a particular crystal volume fraction and that distinct mechanical behaviors can emerge simultaneously within a crystal-rich system. We also posit that this framework describes magmatic fabrics and processes which unlock a crystal mush prior to eruption or mixing.