On the kinematics and dynamics of crystal‐rich systems

Abstract

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.

Flow‐to‐Sliding Transition in Crystal‐Bearing Magma

“…Our simulations are consistent with the discrepancies in experimental measurements constraining the onset of shear thinning behavior with different apparatuses (Bergantz et al, ; Mader et al, ). For example, our comparison of the Couette device and the rotational viscometer is consistent with the measurements from Ishibashi () and Mueller et al ().…”

“…Summarizing, our analyses show that the observed diversity of rheological behavior in different laboratory geometries is related to varying microphysical properties of the crystalline phase, as hypothesized by Bergantz et al (). In contrast to Bergantz et al (), however, the different microphysical properties in our simulations are not related to a varying nature of the contact between crystals, which Bergantz et al () categorized as either frictional or lubricated. In fact, the crystals in our simulations never touch, because the pressure in the thin melt film separating the crystal interfaces impedes direct contact, at least for the smooth crystal interface considered in our simulations.…”

“…It is only logical to expect that the force chains forming at this interface depend not only on the overall crystal fraction and shape but also on the geometry of the experimental apparatus used. While discrepancies between different devices have been noted in the literature (e.g., Mader et al, ; Picard et al, ; Bergantz et al, ), few explanations exist for why they arise.…”

“…For example, building on the seminal early works by Einstein (), Roscoe (), and Brinkman (), an entire research field is dedicated to constraining the rheology of solid‐bearing suspensions. Numerous rheological models for magmatic systems have emerged out of these efforts, as recently reviewed by Mader et al () and Bergantz et al (). However, existing models vary notably in their parameterization of the effective mixture viscosity and the critical crystal fraction at which they predict the onset of nonlinear behavior (Costa, ; Ishibashi, ; Lejeune & Richet, ; Petford, ; Philpotts et al, ; Ryerson et al, ).…”

A review of laboratory and numerical modelling in volcanology

“…This could explain rhythmic layering but also larger-scale zonation observed in large igneous bodies. Bergantz et al (2017) used a discrete-element computational fluid dynamics simulation to study the intrusion of basalt into an olivine-basalt mush by considering crystalscale force chains, crystal transport, and mixing processes. They found that the conditions for mechanical "lock up" were not uniquely identified by a specific crystal volume fraction.…”