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A semiempirical constitutive model for the visco-elastic rheology of bubble suspensions with gas volume fractions φ < 0.5 and small deformations (Ca 1) is developed. The model has its theoretical foundation in a physical analysis of dilute emulsions. The constitutive equation takes the form of a linear Jeffreys model involving observable material parameters: the viscosity of the continuous phase, gas volume fraction, the relaxation time, bubble size distribution and an empirically determined dimensionless constant. The model is validated against observations of the deformation of suspensions of nitrogen bubbles in a Newtonian liquid (golden syrup) subjected to forced oscillations. The effect of φ and frequency of oscillation f on the elastic and viscous components of the deformation are investigated. At low f , increasing φ leads to an increase in viscosity, whereas, at high f , viscosity decreases as φ increases. This behaviour can be understood in terms of bubble deformation rates and we propose a dimensionless quantity, the dynamic capillary number Cd, as the parameter which controls the behaviour of the system. Previously published constitutive equations and observations of the rheology of bubble suspensions are reviewed. Hitherto apparently contradictory findings can be explained as a result of Cd regime. A method for dealing with polydisperse bubble size distributions is also presented.

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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,

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The geometry of the vein system in ice has been investigated using photographs of enlarged veins in ice samples that were grown in the laboratory. The veins, which are non-uniform, act as tiny triangular-shaped, water-filled prisms that refract the light passing through them.The three vein widths in the cross-section of a vein can be deduced from two photographs taken from different directions. The dihedral angle along a given vein edge can be observed directly by viewing it at a node, where four veins meet, from a particular direction. The dihedral angles range from 25° ± 1° to 105° ± 1°. It is shown that the vein cross-section can be constructed, given the three widths of a vein and one of the dihedral angles, providing that the radius of curvature around the vein wallsrv is a constant. This assumption can be checked if the values of at least two of the dihedral angles associated with the vein cross-section are known. Ifrv is a constant, then the solid-liquid interfacial energy ϒsl must be isotropic for the veins in question and any deviations from uniform equilibrium geometry must derive primarily from anisotropy in the grain-boundary energy ϒss. The cross-sections of three veins that meet in a particular node are constructed. The assumption of isotropic ϒsl is found to hold for this node.

[1] Magmas in volcanic conduits commonly contain microlites in association with preexisting phenocrysts, as often indicated by volcanic rock textures. In this study, we present two different experiments that investigate the flow behavior of these bidisperse systems. In the first experiments, rotational rheometric methods are used to determine the rheology of monodisperse and polydisperse suspensions consisting of smaller, prolate particles (microlites) and larger, equant particles (phenocrysts) in a bubble-free Newtonian liquid (silicate melt). Our data show that increasing the relative proportion of prolate microlites to equant phenocrysts in a magma at constant total particle content can increase the relative viscosity by up to three orders of magnitude. Consequently, the rheological effect of particles in magmas cannot be modeled by assuming a monodisperse population of particles. We propose a new model that uses interpolated parameters based on the relative proportions of small and large particles and produces a considerably improved fit to the data than earlier models. In a second series of experiments we investigate the textures produced by shearing bimodal suspensions in gradually solidifying epoxy resin in a concentric cylinder setup. The resulting textures show the prolate particles are aligned with the flow lines and spherical particles are found in well-organized strings, with sphere-depleted shear bands in high-shear regions. These observations may explain the measured variation in the shear thinning and yield stress behavior with increasing solid fraction and particle aspect ratio. The implications for magma flow are discussed, and rheological results and textural observations are compared with observations on natural samples.