Figure - available from: Journal of Geophysical Research: Solid Earth
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Illustration of the transition from distributed shear flow to plug flow facilitated by localized slip in a volcanic conduit.
Source publication
The presence of crystals in magmatic flows introduces spatial heterogeneity, which can build up to the degree that the flow behavior of the crystal‐bearing magma becomes substantially different from that of a pure melt. One example is the transition from flow to sliding, in which the deformation in the crystalline magma is concentrated almost entir...
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Citations
... While magma mushes are often simplified as porous media for continuum calculations, in reality they are complex multiphase mixtures where forces can be transmitted at the particle-particle scale . Such hydrogranular behavior leads to local energy dissipation and phase segregation such that the final state of the mixture cannot be predicted even if the initial conditions are constrained Philpotts et al., 1998;Qin & Suckale, 2020;. Numerical approaches to modeling magma mushes as granular media have been pursued by studies including Bergantz et al. (2017), who developed granular models capable of capturing such complex particle-particle behavior in magma mushes. ...
... These discontinuities were termed "load drops" by Hoyos et al. (2022) and were attributed to the disruption or failure of force chains. Force chains-collections of jammed particles prevented from freely rotating and translating Philpotts et al., 1998;Qin & Suckale, 2020;-build up over the duration of the experiment. The formation of force chains acts to jam the granular medium and is a highly stochastic process, as illustrated from the variable evolution of Σ for repeated experiments using the same particle shape, size, and distribution. ...
Before large volumes of crystal poor rhyolites are mobilized as melt, they are extracted through the reduction of pore space within their corresponding crystal matrix (compaction). Petrological and mechanical models suggest that a significant fraction of this process occurs at intermediate melt fractions (ca. 0.3–0.6). The timescales associated with such extraction processes have important ramifications for volcanic hazards. However, it remains unclear how melt is redistributed at the grain‐scale and whether using continuum scale models for compaction is suitable to estimate extraction timescales at these melt fractions. To explore these issues, we develop and apply a two‐phase continuum model of compaction to two suites of analog phase separation experiments—one conducted at low and the other at high temperatures, T, and pressures, P. We characterize the ability of the crystal matrix to resist porosity change using parameterizations of granular phenomena and find that repacking explains both data sets well. A transition between compaction by repacking to melt‐enhanced grain boundary diffusion‐controlled creep near the maximum packing fraction of the mush may explain the difference in compaction rates inferred from high T + P experiments and measured in previous deformation experiments. When upscaling results to magmatic systems at intermediate melt fractions, repacking may provide an efficient mechanism to redistribute melt. Finally, outside nearly instantaneous force chain disruption events occasionally recorded in the low T + P experiments, melt loss is continuous, and two‐phase dynamics can be solved at the continuum scale with an effective matrix viscosity.
... While magma mushes are often simplified as porous media for continuum calculations, in reality they are complex multiphase mixtures where forces can be transmitted at the particle-particle scale (Bergantzet al. , 2017). Such hydrogranular behavior leads to local energy dissipation and phase segregation such that the final state of the mixture cannot be predicted even if the initial conditions are constrained , Philpotts et al. , 1998, Qin & Suckale, 2020. Numerical approaches to modeling magma mushes as granular media have been pursued by studies including Bergantz et al. (2017), who developed granular models capable of capturing such complex particle-particle behavior in magma mushes. ...
... These discontinuities were termed "load drops" by Hoyos et al. (2022) and were attributed to the disruption or failure of force chains. Force chains -collections of jammed particles prevented from freely rotating and translating , Philpotts et al. , 1998, Qin & Suckale, 2020 -build up over the duration of the experiment. The formation of force chains acts to jam the granular medium and is a highly stochastic process, as illustrated from the variable evolution of Σ for repeated experiments using the same particle shape, size, and distribution. ...
... These simulations demonstrate that the flow field affects both the spatial distribution of crystals and the alignment of individual crystals. The tendency of crystals to distribute heterogeneously is a consequence of the long-range, hydrodynamic interactions between individual crystals that, in the absence of inertial forces limiting their spatial range, break the symmetry of the flow in a similar way as turbulence in the inertial limit (36), as demonstrated in previous studies (12,37,38). Figure 5 also shows that crystals in all three flow fields display a range of individual alignment angles with respect to the flow. ...
... We emphasize that our finding of short-lived crystal contact in pure shear applies only at the relatively low crystal fractions considered here, when there is still enough space for crystals to rotate. As the crystal fraction increases, rotations are increasingly suppressed and longlived crystal contact emerges in shear-dominated flow as well (12,38). However, the crystal aggregates formed under these conditions tend to be larger in size, resembling force chains or fragments from networks (12,38). ...
... As the crystal fraction increases, rotations are increasingly suppressed and longlived crystal contact emerges in shear-dominated flow as well (12,38). However, the crystal aggregates formed under these conditions tend to be larger in size, resembling force chains or fragments from networks (12,38). Crystal aggregates formed in shear at intermediate crystal fraction are hence observationally distinct from the Kīlauea Iki aggregates, most of which contain two to four individual crystals. ...
Developing reliable, quantitative conduit models that capture the physical processes governing eruptions is hindered by our inability to observe conduit flow directly. The closest we get to direct evidence is testimony imprinted on individual crystals or bubbles in the conduit and preserved by quenching during the eruption. For example, small crystal aggregates in products of the 1959 eruption of Kīlauea Iki, Hawaii contain overgrown olivines separated by large, hydrodynamically unfavorable angles. The common occurrence of these aggregates calls for a flow mechanism that creates this crystal misorientation. Here, we show that the observed aggregates are the result of exposure to a steady wave field in the conduit through a customized, process-based model at the scale of individual crystals. We use this model to infer quantitative attributes of the flow at the time of aggregate formation; notably, the formation of misoriented aggregates is only reproduced in bidirectional, not unidirectional, conduit flow.
... The main objective of the present work is to apply the above mentioned Couette analogy to the case of two mixer type geometries presently available for a commercial rotational rheometer [13], namely, a double helical ribbon tool and a square-shaped stirrer, indicated by the manufacturer as tools to measure the rheology of large-size concentrated suspensions [14]. The calibration constants for the two geometries are obtained by applying the Couette analogy to a Newtonian fluid and to a non-Newtonian, shear thinning polymer solution, whose rheological responses are quantitatively known. ...
The rheology of macroscopic particle suspensions is relevant in many industrial applications, such as cement-based suspensions, synthetic and natural drilling fluids. Rheological measurements for these complex, heterogeneous systems are complicated by a double effect of particle size. On the one hand, the smallest characteristic length of the measuring geometry must be larger than the particle size. On the other hand, large particles are prone to sediment, thus calling for the use of rotational tools that are able to keep the suspension as homogeneous as possible. As a consequence, standard viscometric rotational rheometry cannot be used and complex flow geometries are to be implemented. In this way, however, the flow becomes non-viscometric, thus requiring the development of approximate methods to translate the torque vs. rotation speed raw data, which constitute the rheometer output, into viscosity vs. shear rate curves. In this work the Couette analogy methodology is used to establish the above equivalence in the case of two complex, commercial geometries, namely, a double helical ribbon tool and a square-shaped stirrer, which are recommended for the study of relatively large size suspensions. The methodology is based on the concept of the reduction of the complex geometry to an equivalent coaxial cylinder geometry, thus determining a quantitative correspondence between the non-standard situation and the well-known Couette-like conditions. The Couette analogy has been used first to determine the calibration constants of the non-standard geometry by using a Newtonian oil of known viscosity. The constants have been subsequently used to determine the viscosity curves of two non-Newtonian, shear thinning fluids, namely a homogeneous polymer solution and two heterogeneous concentrated suspensions. The results show that the procedure yields a good agreement between the viscosity curves obtained by the reduction method and those measured by a standard viscometric Couette geometry. The calibration constants obtained in this work from the coaxial cylinder analogy are also compared with those provided by the manufacturer, indicating that the calibration can improve the accuracy of the rheometer output.
Using laboratory experiments on a network scale together with numerical simulations on a granular scale, we investigate the displacement process as air invades a highly compacted granular material. Experiments in a vertically placed Hell-Shaw cell reveal a non-monotonic behavior of branching formation as air injection rate Q increases from 0.1 to 50 ml min–1 when the liquid viscosity is less than 22.5 mPa s. In the low-injection-rate region where Q < 1 ml min–1, fractures grow in random directions, and the number of branches increases as the air injection rate decreases. However, after the transition to the high-injection-rate region where Q≥ 1 ml min–1, the number of branches increases with increasing air injection rate. At a given air injection rate, increasing the liquid viscosity from 1.01 to 219 mPa s leads to an increasingly concentrated air flow. The numerical simulations exhibit good agreement with the experimental results. More importantly, they shed light on the physics underlying the growth of the fractures by capturing the distribution of the magnitude of velocity, as well as computing the inter-grain force chains in the granular material. The simulations suggest that a high liquid viscosity concentrates the velocity field and force chains and reduces the speeds and inter-grain forces of the grains adjacent to fractures, while a higher air injection rate increases the grain speeds and inter-grain forces. In addition, the distribution of the forces chains behaviors non-monotonically as the air injection rate decreases, which explains the non-monotonic behavior of branching formation observed in the experiments.
Crystal‐hosted melt embayments and melt inclusions partially record magmatic processes at depth, but it is not always obvious how to interpret this record. One impediment is our incomplete understanding of how embayments and melt inclusions form. In this study, we investigate the formation mechanism of embayments and melt inclusions during quartz growth to quantify the relationship between the compositions of the entrapped and average melt. We study the growth of embayments and inclusions through direct numerical simulations that couple the growth of a crystal surface with the evolution of the concentrations of incompatible components in the surrounding melt. We find that H2O is more enriched in the interior of defects on crystal surface compared to the exterior. The resultant lower disequilibrium in the defect interior causes lower growth rate than in the exterior, elongating the defect into an embayment. If crystal growth stops, the composition in the embayment equilibrates with the average melt within days to months. If crystal growth continues until the embayment neck closes, a melt inclusion forms. The melt entrapped by both embayments and melt inclusions is enriched in incompatible components, such as H2O and CO2. In addition to inclusion size, the enrichment of incompatible components in melt inclusions also depends on component diffusivity and the crystal growth regime. High‐diffusivity components like H2O have similar enrichment levels in all scenarios, while lower‐diffusivity components like CO2 are more enriched in melt inclusions with smaller sizes or formed in continuous crystal growth.
We investigate the morphology and dynamics of the pattern of immiscible invasion by injecting a high-viscosity liquid into a granular suspension consisting of movable solid grains in a low-viscosity liquid. Laboratory experiments conducted in a Hele–Shaw cell shed light on how the frictional forces of the grains and the viscous forces of the liquids affect the instability of the liquid–liquid interface and the formation of viscous fingers. The frictional force increases with an increase in either the volume fraction or the size of the grains, leading to higher resistance to the invading pattern. Upon changing the grain shape from spherical to irregular, both the frictional force and the rotational energy of the grains increase, resulting in more numerous but narrower fingers. Increasing either the injection rate or the viscosity of the injected liquid increases the viscous pressure within the fingers, promoting the splitting of the pattern. Although the defending liquid always has a lower viscosity than the invading liquid in this study, the former's viscous force becomes non-negligible as the viscosity ratio of the invading liquid to the defending liquid decreases to near unity, which destabilizes the fluid–fluid interface and causes a transition to an asymmetric pattern.
Numerical simulations of volcanic processes play a fundamental role in understanding the dynamics of magma storage,
ascent, and eruption. The recent extraordinary progress in computer performance and improvements in numerical modeling techniques
allow simulating multiphase systems in mechanical and thermodynamical disequilibrium. Nonetheless, the growing complexity of these simulations requires the development of flexible computational tools that can easily switch between sub-models and solution techniques.
In this work we present MagmaFOAM, a library based on the open-source computational fluid dynamics software OpenFOAM that incorporates models for solving the dynamics of multiphase, multicomponent magmatic systems. Retaining the modular structure of OpenFOAM, MagmaFOAM allows runtime selection of the solution technique depending on the physics of the specific process and sets a solid framework for in-house and community model development, testing, and comparison. MagmaFOAM models thermomechanical nonequilibrium phase coupling and phase change, and it implements state-of-the-art multiple volatile saturation models and constitutive equations with composition-dependent and space–time local computation of thermodynamic and transport properties. Code testing is performed using different multiphase modeling approaches for processes relevant to magmatic systems: Rayleigh–Taylor instability for buoyancy-driven magmatic processes, multiphase shock tube simulations propaedeutical to conduit dynamics studies, and bubble growth and breakage in basaltic melts. Benchmark simulations illustrate the capabilities and potential of MagmaFOAM
to account for the variety of nonlinear physical and thermodynamical processes characterizing the dynamics of volcanic systems.
The transcrustal, mush‐dominated magma storage paradigm, which posits liquid melt is heterogeneously distributed within a vertically extensive magma mush, differs significantly from classical geodetic models, where melt is stored within liquid‐dominant chambers within an elastic crust. Here, we present mechanical models consistent with transcrustal melt storage by separating the magmatic system into three domains: liquid melt lenses, surrounding crystal‐dominated poroelastic magma mush, and elastic crust. Our results indicate that pressure changes within the melt lens may induce surface displacements that approximate the displacements predicted by spheroidal pressure sources that mimic the geometry of the mush zone. Adopting constitutive parameters of the mush dependent on mush melt fraction, we show that a magma storage system will have an effective geometry inferred from surface displacements that smoothly transitions from the geometry of the melt lens to the geometry of the mush as mush melt fraction increases. This holds true across multiple storage zone geometries, including a “transcrustal” storage zone with a magma mush that extends deep in the crust. Accounting for the presence of a magma mush can lead to an increase in the estimated volume of injected or withdrawn magma (by several multiples) compared to values obtained using fully elastic models. Comparing erupted magma volumes to source volume changes allows for an estimation of magma compressibility; we show the presence of a mush can increase this estimated magma compressibility by up to approximately 50%, suggesting magmas may have higher bubble fraction than previous geodetically derived estimates.
Crystals retain an imprint of the dynamic changes within a magma reservoir and hence contain invaluable information about the evolving conditions inside volcanic plumbing systems. However, instead of telling a single, simple story, they comprise overprinted evidence of numerous processes relating to temperature, pressure and composition that drive crystal precipitation and dissolution in magmatic systems. To decipher these different elements in the story that crystals tell, we attempt to identify the observational signatures of a simple, yet ubiquitous process: crystal precipitation and dissolution during magma cooling. To isolate this process in a complex magmatic system with intricate dynamic feedbacks, we assume that synthetic crystals precipitate and dissolve rapidly in response to deviations from thermodynamic equilibrium. In our crystalline‐scale simulations, synthetic crystals drag along the cooler‐than‐ambient melt in which they precipitated and can drive a temperature‐dependent, crystal‐driven convection. We analyze the non‐dimensional conditions for this coupled convection and record the heterogeneous thermal histories that synthetic crystals in this flow regime experience. We show that many synthetic crystals dissolve, loosing their thermal record of the convection. Based on our findings, we suggest that heterogeneity in the thermal history of crystals is more indicative of local, crystal‐scale processes than the overall, system‐wide cooling trend.
