Silicic magma bodies are formed by repeated injections of mobile magma and reside as a crystal-rich mush. Numerical studies of open-system events have revealed the complexity of mixing and rheological behavior. This is associated with the dilation of the crystal network and the possible occurrence of a lubricated regime. Lubrication forces are hydrodynamic interactions occurring when neighboring crystals have relative motion. The effect of such dissipative forces has not yet been explored in the case of magmatic mush. Here, we investigate the effects of lubrication on mush dynamics and on magma transport. First, we propose scaling relationships to assess the relative importance of the forces controlling the motion of one crystal within a mush by adding lubrication terms into the Basset-Boussinesq-Oseen equation that describes crystal motion in a viscous melt. We then investigate lubrication effects at the macroscopic scale with computational fluid dynamics with discrete element modeling (CFD-DEM) simulations that include these forces. We explore two cases: crystal mush sedimentation and the injection of a crystal-free magma inside a mush. We perform all simulations twice, with and without lubrication forces, and compare the results. At the grain scale, we show that three dimensionless numbers and the crystal content can describe the competition between viscous drag, buoyancy, and lubrication (Fig 1). Two of these numbers (Stokes and Froude numbers) have been previously employed in the context of dilute suspensions. The third is a new form of the Sommerfeld number that measures the importance of lubrication. At the macroscopic scale, simulation pairs (with and without lubrication forces) exhibit very similar behavior when in steady state. The duration of the transient regime preceding steady state, however, is increased when lubrication forces are included (Fig. 2). Lubrication causes an apparent bulk strain hardening followed by softening at the initiation of the mush motion. Our results show that lubrication opposes dilation and the initiation of motion within the magmatic mush during this transient phase (Fig. 3). Our results highlight the control that the crystal network exerts on magma transport and provide a novel way to evaluate when lubrication matters.
Figure 1: Force diagram summarizing scaling results. Axes have logarithmic scales with the ratios Avp/UT as abscissa and vf/2αUT as ordinate. vf is the relative velocity between the particle and the surounding liquid, A is a geometrical parameter depending on the organisation of the particle network and porosity, α is a parameter depending on the porosity, and UT is the terminal velocity of the particle. The red, blue and green areas correspond to the domains where buoyancy, drag and lubrication dominate, respectively. Boundaries between the domains are reported with black lines. Boundaries meet at a point where all forces have the same importance on particle motion.
Figure 2: Snapshots from simulations acounting for and neglecting lubrication after 0 s [A], 6 s [B], 12 s [C], 15 s [D], 18.8 s [E] and 25 s [F]. Snapshots [A]–[C] are truncated and snapshots [D]–[F] represent the entire simulation domain. Filled and open circles represent the particles. Black disks represent the simulation involving lubrication forces. Open red circles correspond to the simulation without lubrication. The green open circles represent the run mimicking lubrication using an alternative approach.
Figure 3: Analysis of the results of the simulation involving lubrication with the scaling summarized in Fig. 1. Plots [A], [B], [C], [D], and [E] represent snapshots after 6 s, 12 s, 15 s, 18.8 s, and 25 s, respectively. Particles are represented by disks, the color of which depends on the value of the average relative velocity between a particle and its neighbors. The group of tracked particles is indicated by purple circles. Graph [F] displays the position of the group of tracked particles on the force scaling graph. The red, blue, and green areas represent the domain where buoyancy, drag, or lubrication dominates, respectively. The positions of the tracked particles at time steps [A]–[E] are indicated by red squares. The blue curve represents the dynamic history of the tracked particles.
Related publication: Carrara, A., Burgisser, A., Bergantz, G.W., 2019. Lubrication effects on magmatic mush dynamics. Journal of Volcanology and Geothermal Research, 380, 19–30. http://doi.org/10.1016/j.jvolgeores.2019.05.008