The rheology of suspensions of solid particles

Abstract

)) 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.

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

“…Importantly, because plagioclase is the dominant mineral phase (i.e., 15 vol %), the relatively high aspect ratio has a significant effect on the magma rheology. Therefore, with a phenocryst content of ∼ 30 %, and from Mueller et al (2010a), yield stress develops when the crystal 510 volume fraction is more than 80 % of the maximum packing fraction (i.e., φ cr /φ m > 0.8), our calculations show that there is no yield stress developed until microlite growth because (φ cr /φ m = 0.70, when r p = 5). Because φ m is strongly dependant on the aspect ratio (r p ), it is possible that the mixed pyroxene and plagioclase crystal population results in a lowered average aspect ratio, and therefore a reduced φ m .…”

“…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). …”

“…To account for the effect of shear thinning due to crystal alignment, Mueller et al (2010a) developed an empirical model (Eq. 13) for the flow index (n) as…”