Viscosity of magmatic liquids: A model
Introduction
Viscosity is the single most important physical property governing the production, transport and eruption of magmas (Papale, 1999, Sparks, 2004, Dingwell, 2006). The viscosity of naturally-occurring silicate magmas can span more than 15 orders of magnitude (10− 1–1014 Pa s) primarily in response to variations in temperature (T), melt composition and the proportions of suspended solids and/or exsolved fluid phases (Dingwell, 1996, Giordano et al., 2004a, Giordano et al., 2004b). Dissolved volatiles, such as H2O (Giordano et al., 2004a) and F (Giordano et al., 2004b), are of particular importance because small variations in their concentrations can generate large (> 105) and strongly nonlinear changes in melt viscosity that drastically affect magma transport, ascent and eruption dynamics. These effects may even dictate whether eruptions are effusive or explosive (Dingwell, 1996, Papale, 1999, Sparks, 2004). Other volatile components (CO2, Cl, Br, I, S) appear to be less important in terms of directly influencing viscosity (e.g., Dingwell and Hess, 1998, Bourgue and Richet, 2001, Zimova and Webb, 2006). Thus, the accurate prediction of silicate melt viscosity as a function of temperature and composition, including H2O and F, is of paramount importance for modelling and understanding magmatic and volcanic processes.
The task of creating such models has been hampered, to date, by the complexity of incorporating these volatile effects, together with multicomponent melt compositional effects, into the framework of a non-Arrhenian model (Baker, 1996, Hess and Dingwell, 1996, Russell et al., 2002, Giordano and Dingwell, 2003, Russell and Giordano, 2005, Giordano et al., 2006, Vetere et al., 2006, Hui and Zhang, 2007). The earliest models for predicting the viscosity of geologically-relevant silicate melts adopted a strictly Arrhenian temperature dependence (Shaw, 1972, Bottinga and Weill, 1972). These models were based on a relatively small number of high-T experiments (~ 130). They were, and remain, quite effective in reproducing silicate melt viscosities over a restricted range of compositions at high, generally near-liquidus, temperatures. Arrhenian models, however, inevitably fail when extrapolated to lower temperatures. This is a simple consequence of the now universal observation that silicate melts show pronounced non-Arrhenian temperature dependence (Dingwell et al., 1993, Richet and Bottinga, 1995).
Accordingly, the next generation of viscosity models for silicate melts adopted a non-Arrhenian T-dependence usually involving 3 (rather than 2) adjustable parameters. These models were, however, designed to span restricted ranges in melt composition and some are extremely effective in doing so. For example, several of these computational schemes were developed to model the effects of H2O on the viscosity of single specific melt composition (Baker, 1996, Hess and Dingwell, 1996, Giordano et al., 2004a, Vetere et al., 2006). There are several models for melt viscosity that incorporate a non-Arrhenian T-dependence and span wide ranges of melt composition (e.g., Giordano and Dingwell, 2003, Russell and Giordano, 2005, Giordano et al., 2006). However, they do not incorporate the effects of dissolved volatiles (especially H2O and F). The sole exception is the model published by Hui and Zhang (2007) which predicts melt viscosity as a function of temperature and composition and is applicable to hydrous silicate melts. Currently, this is the only viscosity model for multicomponent silicate melts that accounts for the effects of H2O.
Here we present a multicomponent chemical model for predicting the viscosity of naturally-occurring silicate melts based on experimental measurements of viscosity at T(K) on melts of known composition (Fig. 1) at atmospheric pressure (105 Pa). The model has the following attributes: i) it spans most of the compositional range found in naturally-occurring volcanic rocks, ii) it captures the effects of 10 major and minor oxide components and the volatile components H2O and F, iii) it is computationally continuous across the entire compositional and temperature spectrum of the database, iv) it is capable of accommodating both strong (near-Arrhenian T-dependence) and fragile (non-Arrhenian T-dependence) behaviour of silicate melts (e.g., Angell, 1985), and v) it reproduces observed relationships between melt composition and transport properties such as glass transition temperature (Tg) and fragility (m) (Angell, 1995, Plazek and Ngai, 1991) (see Section 5.2 for definition).
We anticipate this model finding widespread use in the petrological and volcanological sciences because of these traits. In particular, the low number (i.e. 18) of model parameters should facilitate incorporation into complex applications (e.g., volcanic eruption models) that involve dynamic changes in melt composition and for greater stability when the model is extrapolated outside the compositional range of the experimental database.
Section snippets
Experimental database
The primary dataset, against which the model is calibrated, comprises 1774 experimentally measured pairs of values of T(K) and log η on silicate melts of known composition. Our database includes measurements from many laboratories but most are from work in experimental labs from the past 20 years; sources of data are available as supporting material in the Appendix. Most measurements derive from high-T concentric cylinder experimentation (η ~ 10− 1 to 105 Pa s) and from
Model optimization
The experimental database comprises only viscosity measurements that are coupled to melts for which there are complete and accurate compositions, including direct analysis of volatiles (e.g., spectroscopic or volumentric). We use the oxide mol% as a chemical basis and treat all iron as FeO even though there is evidence that Fe2O3 and FeO play distinct roles in governing melt structure (Mysen, 1988) and that the redox state of very Fe-rich melts does measurably influence viscosity (Dingwell, 1991
Model quality
There is excellent agreement between values of viscosity obtained by experiment and those predicted by the model (Fig. 3). The model has a root-mean-square-error (RMSE) of 0.40 log units and anhydrous and hydrous melts have an average misfit (∣observed − predicted∣) of ± 0.25 and ± 0.35 logunits, respectively. The data plotted in Fig. 3 show that the largest residuals derive from the low-T data where viscosity values exceed 108 Pa s (Table 3; Fig. 3A, B). Over this range of viscosity, the absolute
Model consequences
The quality of our model is demonstrated, in part, by how well it reproduces measured values of melt viscosity (Fig. 3). However, higher-level models have the power to extrapolate and have logical consequences that can serve as testable predictions (Greenwood, 1989). The model we have presented here can be tested against the expected behaviour of other transport properties with respect to composition (Fig. 7, Fig. 8).
Applications
Our multicomponent chemical model provides a means to predict the viscosity of volatile-enriched melts. It does so over the full range of compositions found in naturally-occurring silicate melts. A feature that sets this model apart from all others is that it allows for accurate, continuous prediction of melt properties as a function of temperature and melt composition. The effects of pressure on the silicate melt viscosity are not accounted for in this model. Natural systems feature constantly
Conclusions
We have presented a computational model that predicts, within inter-laboratory experimental error, viscosity and other melt properties (i.e., Tg and m) for most of the T-X space found in naturally-occurring silicate melts. The model accommodates the properties of fragile (non-Arrhenian) to strong (near-Arrhenian) melts equally well. The model also reproduces the T-log η relationships for melts not used for calibration purposes (see Appendix A) suggesting that the model can be extrapolated past
Acknowledgements
A portion of this research was completed when D. Giordano held a post-doctoral fellowship from the Dorothy Killam Trust administered by The University of British Columbia. JKR is supported by the Natural Sciences and Engineering Research Council of Canada. This work was supported by the 2005–2006 INGV-DPC project V3-2/UR17. Experimental viscometry activities of Dingwell´s group contributing to the completeness of the data set that was a prerequisite for this model have been supported by the
References (48)
Relaxation in liquids, polymers and plastic crystal-strong/fragile patterns and related problems
J. Non-Cryst. Solids
(1991)Pressure and temperature dependence of viscosity of glassforming and of geoscientifically relevant system
J. Volcanol. Geotherm. Res.
(2007)- et al.
A rheological investigation of vesicular rhyolite
J. Volcanol Geotherm. Res.
(1992) - et al.
The effect of dissolved CO2 on the density and viscosity of silicate melts: a preliminary study
Earth Planet. Sci. Lett.
(2001) - et al.
Viscosity of peridotite liquid
Earth Planet. Sci. Lett.
(2004) - et al.
Non-Arrhenian multicomponent melt viscosity: A model
Earth Planet. Sci. Lett.
(2003) - et al.
The viscosity of trachytes, and comparison with basalts, phonolites, and rhyolites
Chem. Geol.
(2004) - et al.
The combined effects of water and fluorine on the viscosity of silicic magmas
Geochim. Cosmochim. Acta
(2004) - et al.
An expanded non-Arrhenian model for silicate melt viscosity: A treatment for metaluminous, peraluminous and peralkaline melts
Chem. Geol.
(2006) - et al.
Toward a general viscosity equation for natural anhydrous and hydrous silicate melts
Geochim. Cosmochim. Acta
(2007)
A model for silicate melt viscosity in the System CaMgSi2O6–CaAl2Si2O8–NaAlSi3O8
Geochim. Cosmochim. Acta
Rheology of welding: Inversion of field constraints
J. Volcanol. Geotherm. Res.
Viscosity of andesitic melts — New experimental data and a revised calculation model
Chem. Geol.
The viscosity of hydrous phonolites and trachytes
Chem. Geol.
Granitic melt viscosities: Empirical and configurational entropy models for their calculation
Am. Mineral.
The viscosity of magmatic silicate liquids: a model for calculation
Am. J. Sci.
Redox state, microstructure and viscosity of a partially crystallized basalt melt
Earth Planet. Sci. Lett.
Redox viscometry of some Fe-bearing silicate liquids
Am. Mineral.
Volcanic dilemma: Flow or blow?
Science
Transport properties of magmas: Diffusion and rheology
Elements
Melt viscosities in the system Na–Fe–Si–O–F–Cl: Contrasting effects of F and Cl in alkaline melts
Am. Mineral.
Structural relaxation on silicate melts and non-Newtonian melt rheology in geologic processes
Phys. Chem. Miner.
Magma rheology. Experiments at high pressures and application to the earth's mantle
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