The rheology of two-phase magmas: A review and analysis

• Published in: Journal of volcanology and geothermal research Vol. 257; pp. 135 - 158
• Main Authors: Mader, H.M., Llewellin, E.W., Mueller, S.P.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier B.V 01-05-2013; Elsevier
• Subjects: Bubbles; Constitutive equations; Constitutive relationships; Crystalline rocks; Crystals; Earth sciences; Earth, ocean, space; Exact sciences and technology; Igneous and metamorphic rocks petrology, volcanic processes, magmas; Magma; Mathematical models; Melts; Multiphase; Rheology; Texture; Vesicles; Viscosity; Viscosity; Bubbles; Vesicles; Multiphase; Rheology; Crystals; Magma; strain rates; constitutive equation; textures; accuracy; packing; silicate melts; particles; oscillations; suspension; strain; stress; models; crystals; rheology; unsteady flow; magmas; capillarity; fracturing; viscosity; new data; bubbles; melts
• ISSN: 0377-0273; 1872-6097
• DOI: 10.1016/j.jvolgeores.2013.02.014

We consider the current state of our understanding of the rheology of two-phase magmas, that is suspensions of either bubbles or crystals in a viscous silicate melt. The discussion is restricted to strain-rates at which the suspending melt can be considered Newtonian. We start by considering the range of textures found in magmas and the bubble deformation and particle motions caused by shearing. We then review proposed models for suspensions, focussing on those functions of the form ηr=f(ϕ) or τ=fγ˙ that have been most widely used to describe magmatic systems (ηr is the relative apparent viscosity of the suspension, ϕ is the volume fraction of the suspended phase, τ is the driving stress, and γ˙ is the strain-rate). Both theoretical and empirical methods are presented and then compared against the available analogue (i.e. non-magmatic) and magmatic data. The paper contains new data and significant re-analysis of previously published data. We present a new semi-empirical constitutive model for bubble-bearing magmas that is valid for steady and unsteady flow and large strains and strain-rates. This equation utilises a new parameter, the capillarity Cx, that encapsulates the combined effect of shearing and unsteadiness on bubble suspensions. We also present a new scheme for dealing with polydispersivity of bubble suspensions. New data on the rheology of particle suspensions undergoing forced-oscillations are presented. These data show that the Cox–Merz rule only holds for dilute particle suspensions ϕ≲0.25. A re-analysis of all available experimental data that relate rheology to particle aspect ratio provides distinct curves of maximum packing as a function of aspect ratio for smooth and rough particles with magmatic data lying on the curve appropriate for rough particles. We analyse several rheological datasets of crystal-bearing basaltic magmas and find that they are in good agreement with the constitutive equations derived from analogue data. By contrast, the same equations do not agree well with data for high-viscosity, haplogranitic melts. This may be an effect of fracturing or viscous dissipation within these samples. The paper concludes with a practical ‘rheological recipes’ section giving a step-by-step method for calculating a constitutive equation for a two-phase magmatic suspension and assessing its likely accuracy.
•Review of recent advances in the rheology of two-phase magmas•New data and significant re‐analysis of previously published data•‘Rheological recipes’ to establish constitutive equations for magmas