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

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 ran...

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Published inJournal of volcanology and geothermal research Vol. 257; pp. 135 - 158
Main Authors Mader, H.M., Llewellin, E.W., Mueller, S.P.
Format Journal Article
LanguageEnglish
Published Oxford Elsevier B.V 01.05.2013
Elsevier
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Abstract 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
AbstractList 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
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 IDTr = f(I) or I = f [gamma] E that have been most widely used to describe magmatic systems (IDTr is the relative apparent viscosity of the suspension, I is the volume fraction of the suspended phase, I is the driving stress, and [gamma] E 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 CoxaMerz rule only holds for dilute particle suspensions I a2 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 arheological recipesa section giving a step-by-step method for calculating a constitutive equation for a two-phase magmatic suspension and assessing its likely accuracy.
Author Llewellin, E.W.
Mueller, S.P.
Mader, H.M.
Author_xml – sequence: 1
  givenname: H.M.
  surname: Mader
  fullname: Mader, H.M.
  email: h.m.mader@bristol.ac.uk
  organization: School of Earth Sciences, University of Bristol, Wills Memorial Building, Queens Road, Bristol, BS8 1RJ, UK
– sequence: 2
  givenname: E.W.
  surname: Llewellin
  fullname: Llewellin, E.W.
  email: ed.llewellin@durham.ac.uk
  organization: Department of Earth Sciences, Durham University, Science Labs, Durham DH1 3LE, UK
– sequence: 3
  givenname: S.P.
  surname: Mueller
  fullname: Mueller, S.P.
  email: sebastian.mueller@uni-mainz.de
  organization: School of Earth Sciences, University of Bristol, Wills Memorial Building, Queens Road, Bristol, BS8 1RJ, UK
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=27357634$$DView record in Pascal Francis
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Keywords 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
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Snippet 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...
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SubjectTerms 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
Title The rheology of two-phase magmas: A review and analysis
URI https://dx.doi.org/10.1016/j.jvolgeores.2013.02.014
https://search.proquest.com/docview/1448219541
Volume 257
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