The effect of particle shape on suspension viscosity and implications for magmatic flows

Abstract

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,

Propagation of viscous gravity currents inside confining boundaries: the effects of fluid rheology and channel geometry

“…Consideration of non-Newtonian effects is essential for studying several environmental, industrial and biological phenomena, such as the spreading of muds in submarine settings [9]; the motion of natural suspensions containing sand, silt, clay and organic fractions [10,11]; debris flows in mountainous areas [12]; the propagation of pyroclastic flows produced by volcanic eruptions [13,14]; magma flow at sub-liquidus temperatures, owing to gas bubbles and to the presence of crystals [15]; the disposal of mine tailings in the minerals industry [16]; the flow of biomass slurries [17]; blood motion in arterioles [18]. In a number of instances, the fluid rheological behaviour is appropriately described by a Cross or Carreau-Yasuda model, but can be approximated over a certain range of shear rates by the simpler Ostwald-de Waele powerlaw model [19] if the yield stress is limited.…”

Rheological controls on the eruption potential and style of an andesite volcano: A case study from Mt. Ruapehu, New Zealand

“…Other experiments were conducted on synthetic magmas at high temperature and pressure (Caricchi et al, 2007), which were then built into a 355 model that considered the influence of crystals on a suspension viscosity (Costa et al, 2009). For consistency, we have accounted for the effect of crystals (and bubbles) on the relative viscosity (η r cr ) using the equations of Mader et al (2013), which are mainly based on Mueller et al (2010aMueller et al ( , 2011. A series of steps are required to determine the relative effect of crystals, which take into account the shape, size and maximum packing fraction of crystals within the suspension.…”

“…A number of papers investigated the effect of crystals on the apparent viscosity of the suspension 2 (e.g., Jeffery, 1922;Jeffrey and Acrivos, 1976;Mueller et al, 2010aMueller et al, , 2011. In particular, the experiments of Mueller et al (2010aMueller et al ( , 2011) examined a range of crystal sizes, aspect ratios and volume fraction to derive an empirical model for the apparent viscosity of a crystal-melt suspen-35 sion.…”

“…In particular, the experiments of Mueller et al (2010aMueller et al ( , 2011) examined a range of crystal sizes, aspect ratios and volume fraction to derive an empirical model for the apparent viscosity of a crystal-melt suspen-35 sion. Based on the average aspect ratio and size, the formulation of Mader et al (2013) (using the data from Mueller et al (2010aMueller et al ( , 2011) can be used to determine the maximum packing fraction; an important parameter for developing yield strength (e.g., Hoover et al, 2001;Saar et al, 2001). …”

Viscosity of andesitic lava and its implications for possible drain-back processes in the 2011 eruption of the Shinmoedake volcano, Japan

“…Marsh (1981) suggested that ϕ m should be 0.60 from petrographic evidence that there is an upper limit to the phenocryst content of lavas. Mueller et al (2011) experimented on the effect of crystal shape on relative viscosity and suggested that ϕ m may be less than 0.65, and ϕ m ε should be 2. Mueller did not take the size dispersion of the crystals into account, and it may increase ϕ m (Ishibashi and Sato, 2007).…”