Effects of crystal shape‐ and size‐modality on magma rheology

Abstract

Erupting magma often contains crystals over a wide range of sizes and shapes, potentially affecting magma viscosity over many orders of magnitude. A robust relation between viscosity and the modality of crystal sizes and shapes remains lacking, principally because of the dimensional complexity and size of the governing parameter space. We have performed a suite of shear viscosity measurements on liquid-particle suspensions of dynamical similarity to crystal-bearing magma. Our experiments encompass five suspension types, each consisting of unique mixtures of two different particle sizes and shapes. The experiments span two orthogonal subspaces of particle concentration, as well as particle size and shape for each suspension type, thereby providing insight into the topology of parameter space. For each suspension type, we determined the dry maximum packing fraction and measured shear rates across a range of applied shear stresses. The results were fitted using a Herschel-Bulkley model and augment existing predictive capabilities. We demonstrate that our results are consistent with previous work, including friction-based constitutive laws for granular materials. We conclude that predictions for ascent rates of crystal-rich magmas must take the shear-rate dependence of viscosity into account. Shear-rate dependence depends first and foremost on the volume fraction of crystals, relative to the maximum packing fraction, which in turn depends on crystal size and shape distribution.

Volcanic tremor and frequency gliding during dike intrusions at Kı̄lauea—A tale of three eruptions

“…The switch from inflation to deflation at the summit in both 2007 and 2011 and the onset of dike intrusion implies a rapid increase in the speed V m of magma flowing from the summit conduit and reservoir into the ERZ, that is followed, in turn, by a slow decrease in V m related to a relatively slow relief of magmatic overpressure. This speed is reduced further because an increase in from 0.1 to 0.2, say, will cause magma viscosity to rise by a factor of ∼2 [ Gonnermann and Manga , ; Moitra and Gonnermann , ]. Consequently, we expect the downglide of f c in 2007 to be by a factor of >4 or more through effects on V m , assuming a factor of 2 decrease in flow speed.…”

“…Guided by Matoza et al [], for H 2 O in the conduit we use ρ m =2700kg/m 3 and h e =100m. We take as a lower bound required to define continuous cloud mixture physical properties such as density, viscosity, and compressibility [ Crowe et al , ], noting that magma viscosities become very large for [ Gonnermann and Manga , ; Moitra and Gonnermann , ]. We thus require L c ≈ 30–10 m to give f c ∼ 1–3 Hz.…”

“…The resistance of a bubble cloud to disruption is challenging to characterize. We assume that bubble cloud break up is akin to the disruption of solid particle‐fluid mixtures [ Hodge et al , ; Moitra and Gonnermann , ] where the resistance can be described by a mixture “yield force” ∼ σ y D 2 , where the effective yield stress for disaggregation of the mixture σ y depends on the cloud microstructure [ Wildemuth and Williams , ; Hoover et al , ; Moitra and Gonnermann , ], and the effective stiffness of the cloud depends on the cloud cross‐sectional area D 2 . Balancing this yield force with the pressure force gives a condition for disrupting vertically extensive bubble clouds to produce smaller clouds with a characteristic length: …”

Blowing Off Steam: Tuffisite Formation As a Regulator for Lava Dome Eruptions

“…Therefore, for this analysis, using the Maron-Pierce equation with φ m = 0.635 we can predict how the melt viscosity is increased as particle fractions are added. While alternative formulations exist for the effect of suspended crystals on magmatic melt viscosities, the simplicity of the MaronPierce equation has been thoroughly experimentally validated (e.g., Mueller et al, 2010Mueller et al, , 2011Moitra and Gonnermann, 2015) and is considered valid for the slow viscous sintering process which is limited by the rate of surface-stress driven fluid flow.…”

Field and model constraints on silicic melt segregation by compaction/hindered settling: The role of water and its effect on latent heat release

“…And with further decrease in porosity, the framework becomes largely locked, though the framework as a whole can still deform under its own weight or by external stresses. In all these cases, we assume that the crystal-rich magma does not convect because effective viscosities increase by orders of magnitude with increasing crystal volume fraction (decreasing porosity) (Dufek and Bachmann 2010;Lejeune and Richet 1995;Mader et al 2013;Marsh 1981;Moitra and Gonnermann 2015). We thus treat melt-crystal segregation by hindered settling and compaction, following the spirit of Bachmann and Bergantz (2004).…”