)) yielding three rheometric parameters: consistency K (cognate with viscosity); flow index n (a measure of shear-thinning); yield stress τ 0 . The consistency K of suspensions of particles of arbitrary aspect ratio can be accurately predicted by the model of Maron & Pierce (Maron & Pierce 1956 J. Colloid Sci. 11, 80-95 (doi:10.101690023-X)) with the maximum packing fraction φ m as the only fitted parameter. We derive empirical relationships for φ m and n as a function of average particle aspect ratio r p and for τ 0 as a function of φ m and a fitting parameter τ * . These relationships can be used to predict the rheology of suspensions of prolate particles from measured φ and r p . By recasting our data in terms of the Einstein coefficient, we relate our rheological observations to the underlying particle motions via Jeffery's (Jeffery 1922 Proc. R. Soc. Lond. A 102, 161-179 (doi:10.1098/rspa.1922.0078)) theory. We extend Jeffery's work to calculate, numerically, the Einstein coefficient for a suspension of many, initially randomly oriented particles. This provides a physical, microstructural explanation of our observations, including transient oscillations seen during run start-up and changes of rheological regime as φ increases.

The gas permeability of volcanic rocks may influence various eruptive processes. The transition from a quiescent degassing dome to rock failure (fragmentation) may, for example, be controlled by the rock's permeability, in as much as it affects the speed by which a gas overpressure in vesicles is reduced in response to decompression. Using a modified shock-tube-based fragmentation bomb (Alidibirov and Dingwell 1996a,b;Spieler et al. 2003a), we have measured unsteady-state permeability at a high initial pressure differential. Following sudden decompression above the rock cylinder, pressurized gas flows through the sample. Two pressure transducers record the pressure signals above and below the sample. A transient 1D filtration code has been developed to calculate permeability using the experimental decay curve of the lower pressure transducer. Additionally an analytical steady-state method to achieve permeability is presented as an alternative to swiftly predict the sample permeability in a sufficiently precise manner. Over 100 permeability measurements have been performed on samples covering a wide range of porosity. The results show a general positive relationship between porosity and permeability with a high data scatter. Our preferred interpretation of the results is a combination of two different, but overlapping effects. We propose that at low porosities, gas escape occurs predominantly through microcracks or elongated micropores and therefore could be described by simplified forms of Kozeny-Carman relations (Carman 1956) and fracture flow models. At higher porosities, the influence of vesicles becomes progressively stronger as they form an increasingly connected network. Therefore, a model based on the percolation theory of fully penetrable spheres is used, as a first approximation, to describe the permeability-porosity trend. In the data acquired to date it is evident, that in addition to the porosity control, the sample's bubble size, shape and distribution strongly influence the permeability. This leads to a range of permeability values up to 2.5 orders of magnitude at a given porosity.

Fragmentation of porous magma that is subject to gas overpressure is considered to be a crucial process in the generation of explosive volcanic eruptions. A decompressive event (e.g., rapid magma ascent, landslide, dome collapse) disrupts the stress equilibrium between the gas phase and the surrounding melt. When the gas in the pores is exposed to a pressure gradient, it may either fragment the surrounding magma or escape from the magma along an existing pathway of cracks and interconnected bubbles. Therefore, magma permeability can be a decisive parameter in determining if an eruption experiences fragmentation (i.e., whether it is explosive or effusive, or exhibits a temporal transition between the two eruptive styles). Despite the central role that gas permeability may play in the fragmentation of volcanic rocks, previous studies have not experimentally verifi ed or quantifi ed this infl uence. Based on a comprehensive database of combined permeability and fragmentation experiments, we show that high permeability substantially increases the overpressure required to fragment porous volcanic rocks. Our results allow us to deduce a fragmentation criterion that incorporates gas permeability as well as porosity and internal overpressure. This criterion implies that the energy required for fragmentation is less dependent on the actual pore geometry than on the way the void space is interconnected and, thus, on the contribution of permeable gas fl ow to decompression.

1] The rheology of crystal-bearing magma and lava depends on both the shape and volume fraction of the suspended crystals. We present the results of analogue rheometric experiments on monodisperse suspensions of solid particles in a Newtonian liquid, in which particle volume fraction and aspect ratio r p are varied systematically. We find that the effect of on viscosity is well captured by the Maron-Pierce model, and that this model is valid across the range of particle aspect ratios investigated (0.04 ≤ r p ≤ 22, i.e., strongly-oblate to strongly-prolate) when the maximum packing fraction m is treated as a fitting parameter. The value of m derived from fitting to our experimental data depends strongly and systematically on particle aspect ratio; hence, m represents an effective proxy for the influence of particle shape on suspension rheology. We present a simple relationship for m (r p ) which allows the viscosity of a suspension to be calculated as a function of and r p only. We investigate the impact of accounting for crystal shape when modelling volcanic flows by simulating the eruption of magma carrying crystals of different aspect ratio, and conclude that the effect of crystal shape should not be neglected. Citation: Mueller, S., E. W. Llewellin, and H. M. Mader (2011), The effect of particle shape on suspension viscosity and implications for magmatic flows, Geophys. Res. Lett., 38, L13316,

Changes in the physical, chemical and rheological properties of ascending magma regulate the style of volcanic eruptions. Volcán de Colima's eruptive cycles of lava dome growth and explosions have been thoroughly monitored during the period 1998-2010 and provide a remarkable opportunity for deepening our understanding of the underlying processes responsible for the evolution of magma properties. Here, we integrate direct observation with analytical and experimental data to: (1) constrain the configuration of the shallow plumbing system and its influence on eruptive activity, (2) describe the rheological behaviour of the magma and (3) assess the conditions that lead to fragmentation and, ultimately, to explosive eruptions. The configuration of the shallow plumbing system was inferred from direct observation of extrusion sites and porosity of the erupted products. During the ongoing eruptive phase, magma was never extruded from a central vent: Both explosive and effusive activities were restricted to discrete vents inside the crater. Extensive field-based density measurements on 500 blocks in pyroclastic flow deposits reveal a bimodality of porosity at values of 12 and 26 vol.%. The least porous rocks tend to be altered, whereas the more porous rocks are pristine. This bimodal distribution, combined with the lack of a central vent, suggests the presence of a central, dense, altered plug, the fragments of which are entrained during explosive eruptions. During effusive periods, the plug appears to deflect the ascent of magma at a shallow depth and, consequently, the site of lava extrusion. The rheological properties and deformation-induced seismogenic behaviour of the magmas were investigated using a uniaxial deformation apparatus instrumented with acoustic sensors. The homogeneity in the physicochemical properties of the erupted magma permits the description of a flow law at eruptive temperature and strain rate conditions. The crystal-rich magma of Volcán de Colima exhibits a shear thinning rheology and becomes increasingly brittle at higher strain rates. Complete failure of magma can be predicted using the material failure forecast method, which integrates the acceleration of released acoustic energy throughout the deformation. Rapid decompression experiments of samples pressurised with argon were performed to assess the fragmentation conditions under which explosive eruptions progress. In the absence of gas loss due to permeable flow, the pore pressure required to fragment volcanic products is inversely proportional to the porosity. At Volcán de Colima, a rapid decompression of >6 MPa is required to fragment magma averaging 26 vol.% pores and to thereby instigate an explosive eruption. Analysis of ballistic impacts (4-6 km Editorial responsibility: M.A. Clynne

We develop a model for the rheology of a three-phase suspension of bubbles and particles in a Newtonian liquid undergoing steady flow. We adopt an ‘effective-medium’ approach in which the bubbly liquid is treated as a continuous medium which suspends the particles. The resulting three-phase model combines separate two-phase models for bubble suspension rheology and particle suspension rheology, which are taken from the literature. The model is validated against new experimental data for three-phase suspensions of bubbles and spherical particles, collected in the low bubble capillary number regime. Good agreement is found across the experimental range of particle volume fraction (0≤ϕp≲0.5) and bubble volume fraction (0≤ϕb≲0.3). Consistent with model predictions, experimental results demonstrate that adding bubbles to a dilute particle suspension at low capillarity increases its viscosity, while adding bubbles to a concentrated particle suspension decreases its viscosity. The model accounts for particle anisometry and is easily extended to account for variable capillarity, but has not been experimentally validated for these cases.

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