Bubble rise in molten glasses and silicate melts during heating and cooling cycles.

The Hadamard-Rybczynski equation describes the steady-state buoyant rise velocity of an unconfined spherical bubble in a viscous liquid. This solution has been experimentally validated for the case where the liquid viscosity is held constant. Here, we extend this result for non-isothermal conditions, by developing a solution for bubble position in which we account for the time-dependent liquid viscosity, liquid and gas densities, and bubble radius. We validate this solution using experiments in which spherical bubbles are created in a molten silicate liquid by cutting gas cavities into glass sheets, which are stacked, then heated through the glass transition interval. The bubble-bearing liquid, which has a strongly temperature-dependent viscosity, is subjected to various heating and cooling programs such that the bubble rise velocity varies through the experiment. We find that our predictions match the final observed position of the bubble measured in blocks of cooled glass to within the experimental uncertainty, even after the application of a complex temperature-time pathway. We explore applications of this solution for industrial, artistic, and natural volcanological applied problems.

Dendritic crystallization in hydrous basaltic magmas controls magma mobility within the Earth's crust.

The majority of basaltic magmas stall in the Earth's crust as a result of the rheological evolution caused by crystallization during transport. However, the relationships between crystallinity, rheology and eruptibility remain uncertain because it is difficult to observe dynamic magma crystallization in real time. Here, we present in-situ 4D data for crystal growth kinetics and the textural evolution of pyroxene during crystallization of trachybasaltic magmas in high-temperature experiments under water-saturated conditions at crustal pressures. We observe dendritic growth of pyroxene on initially euhedral cores, and a surprisingly rapid increase in crystal fraction and aspect ratio at undercooling ≥30 °C. Rapid dendritic crystallization favours a rheological transition from Newtonian to non-Newtonian behaviour within minutes. We use a numerical model to quantify the impact of rapid dendritic crystallization on basaltic dike propagation, and demonstrate its dramatic effect on magma mobility and eruptibility. Our results provide insights into the processes that control whether intrusions lead to eruption or not.

Rheology of three-phase suspensions determined via dam-break experiments.

Three-phase suspensions, of liquid that suspends dispersed solid particles and gas bubbles, are common in both natural and industrial settings. Their rheology is poorly constrained, particularly for high total suspended fractions (≳0.5). We use a dam-break consistometer to characterize the rheology of suspensions of (Newtonian) corn syrup, plastic particles and CO2 bubbles. The study is motivated by a desire to understand the rheology of magma and lava. Our experiments are scaled to the volcanic system: they are conducted in the non-Brownian, non-inertial regime; bubble capillary number is varied across unity; and bubble and particle fractions are 0 ≤ ϕ gas ≤ 0.82 and 0 ≤ ϕ solid ≤ 0.37, respectively. We measure flow-front velocity and invert for a Herschel-Bulkley rheology model as a function of ϕ gas , ϕ solid , and the capillary number. We find a stronger increase in relative viscosity with increasing ϕ gas in the low to intermediate capillary number regime than predicted by existing theory, and find both shear-thinning and shear-thickening effects, depending on the capillary number. We apply our model to the existing community code for lava flow emplacement, PyFLOWGO, and predict increased viscosity and decreased velocity compared with current rheological models, suggesting existing models may not adequately account for the role of bubbles in stiffening lavas.

A novel experimental apparatus for investigating bubbly flows in a slot geometry.

Bubbly flows occur in a wide variety of industrial and environmental settings. While there is a broad literature that describes bubbly flow behavior in pipes and channels, flow in a high aspect ratio slot has received little attention. We describe the design and construction of a new experimental apparatus to investigate the processes associated with bubbly flows in a slot geometry. The apparatus is designed to perform scaled analog experiments to investigate the flow of bubbly magma through the sub-volcanic plumbing system, but it is sufficiently flexible to address many other flow scenarios. The main bubble column, which can be inclined up to 30° from the vertical, comprises a glass-walled slot 3 m wide and 2 m tall, with 3 cm gap width. A modular and flexible gas injection system allows the number, spacing, and diameter of the gas emission points to be varied, as well as gas injection flux, and a pumped recirculation system allows the concurrent liquid flow rate to be controlled and varied. A dedicated data acquisition system synchronizes high-speed videography with temperature and pressure data from different points in the apparatus. Preliminary data are presented to demonstrate the operation of the apparatus and to illustrate the types of fluid dynamic information that can be captured.

Explosive-effusive volcanic eruption transitions caused by sintering.

Silicic volcanic activity has long been framed as either violently explosive or gently effusive. However, recent observations demonstrate that explosive and effusive behavior can occur simultaneously. Here, we propose that rhyolitic magma feeding subaerial eruptions generally fragments during ascent through the upper crust and that effusive eruptions result from conduit blockage and sintering of the pyroclastic products of deeper cryptic fragmentation. Our proposal is supported by (i) rhyolitic lavas are volatile depleted; (ii) textural evidence supports a pyroclastic origin for effusive products; (iii) numerical models show that small ash particles ≲10-5 m can diffusively degas, stick, and sinter to low porosity, in the time available between fragmentation and the surface; and (iv) inferred ascent rates from both explosive and apparently effusive eruptions can overlap. Our model reconciles previously paradoxical observations and offers a new framework in which to evaluate physical, numerical, and geochemical models of Earth's most violent volcanic eruptions.

Sintering of polydisperse viscous droplets.

Sintering-or coalescence-of compacts of viscous droplets is driven by the interfacial tension between the droplets and the interstitial gas phase. The process, which occurs in a range of industrial and natural settings, such as the manufacture of ceramics and the welding of volcanic ash, causes the compact to densify, to become stronger, and to become less permeable. We investigate the role of droplet polydispersivity in sintering dynamics by conducting experiments in which populations of glass spheres with different size distributions are heated to temperatures above the glass transition interval. We quantify the progress of sintering by tracking changes in porosity with time. The sintering dynamics is modeled by treating the system as a random distribution of interstitial gas bubbles shrinking under the action of interfacial tension only. We identify the scaling between the polydispersivity of the initial droplets and the dynamics of bulk densification. The framework that we develop allows the sintering dynamics of arbitrary polydisperse populations of droplets to be predicted if the initial droplet (or particle) size distribution is known.

Size limits for rounding of volcanic ash particles heated by lightning.

Volcanic ash particles can be remelted by the high temperatures induced in volcanic lightning discharges. The molten particles can round under surface tension then quench to produce glass spheres. Melting and rounding timescales for volcanic materials are strongly dependent on heating duration and peak temperature and are shorter for small particles than for large particles. Therefore, the size distribution of glass spheres recovered from ash deposits potentially record the short duration, high-temperature conditions of volcanic lightning discharges, which are hard to measure directly. We use a 1-D numerical solution to the heat equation to determine the timescales of heating and cooling of volcanic particles during and after rapid heating and compare these with the capillary timescale for rounding an angular particle. We define dimensionless parameters-capillary, Fourier, Stark, Biot, and Peclet numbers-to characterize the competition between heat transfer within the particle, heat transfer at the particle rim, and capillary motion, for particles of different sizes. We apply this framework to the lightning case and constrain a maximum size for ash particles susceptible to surface tension-driven rounding, as a function of lightning temperature and duration, and ash properties. The size limit agrees well with maximum sizes of glass spheres found in volcanic ash that has been subjected to lightning or experimental discharges, demonstrating that the approach that we develop can be used to obtain a first-order estimate of lightning conditions in volcanic plumes.

Topological inversions in coalescing granular media control fluid-flow regimes.

Sintering-or coalescence-of viscous droplets is an essential process in many natural and industrial scenarios. Current physical models of the dynamics of sintering are limited by the lack of an explicit account of the evolution of microstructural geometry. Here, we use high-speed time-resolved x-ray tomography to image the evolving geometry of a sintering system of viscous droplets, and use lattice Boltzmann simulations of creeping fluid flow through the reconstructed pore space to determine its permeability. We identify and characterize a topological inversion, from spherical droplets in a continuous interstitial gas, to isolated bubbles in a continuous liquid. We find that the topological inversion is associated with a transition in permeability-porosity behavior, from Stokes permeability at high porosity, to percolation theory at low porosity. We use these findings to construct a unified physical description that reconciles previously incompatible models for the evolution of porosity and permeability during sintering.

Sintering of viscous droplets under surface tension.

We conduct experiments to investigate the sintering of high-viscosity liquid droplets. Free-standing cylinders of spherical glass beads are heated above their glass transition temperature, causing them to densify under surface tension. We determine the evolving volume of the bead pack at high spatial and temporal resolution. We use these data to test a range of existing models. We extend the models to account for the time-dependent droplet viscosity that results from non-isothermal conditions, and to account for non-zero final porosity. We also present a method to account for the initial distribution of radii of the pores interstitial to the liquid spheres, which allows the models to be used with no fitting parameters. We find a good agreement between the models and the data for times less than the capillary relaxation timescale. For longer times, we find an increasing discrepancy between the data and the model as the Darcy outgassing time-scale approaches the sintering timescale. We conclude that the decreasing permeability of the sintering system inhibits late-stage densification. Finally, we determine the residual, trapped gas volume fraction at equilibrium using X-ray computed tomography and compare this with theoretical values for the critical gas volume fraction in systems of overlapping spheres.

The α-ß phase transition in volcanic cristobalite.

Cristobalite is a common mineral in volcanic ash produced from dome-forming eruptions. Assessment of the respiratory hazard posed by volcanic ash requires understanding the nature of the cristobalite it contains. Volcanic cristobalite contains coupled substitutions of Al3+ and Na+ for Si4+; similar co-substitutions in synthetic cristobalite are known to modify the crystal structure, affecting the stability of the α and ß forms and the observed transition between them. Here, for the first time, the dynamics and energy changes associated with the α-ß phase transition in volcanic cristobalite are investigated using X-ray powder diffraction with simultaneous in situ heating and differential scanning calorimetry. At ambient temperature, volcanic cristobalite exists in the α form and has a larger cell volume than synthetic α-cristobalite; as a result, its diffraction pattern sits between ICDD α- and ß-cristobalite library patterns, which could cause ambiguity in phase identification. On heating from ambient temperature, volcanic cristobalite exhibits a lower degree of thermal expansion than synthetic cristobalite, and it also has a lower α-ß transition temperature (∼473 K) compared with synthetic cristobalite (upwards of 543 K); these observations are discussed in relation to the presence of Al3+ and Na+ defects. The transition shows a stable and reproducible hysteresis loop with α and ß phases coexisting through the transition, suggesting that discrete crystals in the sample have different transition temperatures.