Daniele Giordano

Non-Arrhenian multicomponent melt viscosity: a model

Newtonian viscosities of 19 natural multicomponent melts ranging in composition from basanite through phonolite and trachyte, to dacite have been analysed in the range of 100–1012 Pa s. These data, together with the results of previous investigations obtained using concentric-cylinder, parallel-plate and micropenetration methods, form the basis of an analysis of multicomponent non-Arrhenian Newtonian viscosity. Regressions of the combined (high and low temperature) viscosities (ca 350 data points) were performed using the three-parameter Tammann–Vogel–Fulcher (TVF) equation: log10η=ATVF+BTVFT−T0 The resulting TVF parameters were used to compose the first non-Arrhenian model for multicomponent silicate melt viscosity. The model accommodates the effects of composition via an empirical parameter, here termed the structure modifier content (SM). SM is the mol% summation of molar oxides of Ca, Mg, Mn, Fetot/2, Na and K. The approach is validated by the predictive capability of the viscosity model. The model reproduces the entire original dataset to within <10% on a logarithmic scale, over 10 orders of magnitude of viscosity, 1000°C and the entire range of composition. Comparison with other empirical parameters and the Shaw model [Shaw, Am. J. Sci. 272 (1972) 870–893] is also provided.

High-temperature limits on viscosity of non-Arrhenian silicate melts

Abstract The prediction of viscosity in silicate melts, over the range of conditions found in nature, remains one of the most challenging and elusive goals in Earth Sciences. We present a strategy for fitting non-Arrhenian models [e.g., Vogel-Tammann-Fulcher (VTF) or Adam-Gibbs (AG)] to viscosity data that can be employed toward a full multicomponent model for melt viscosity. Our postulate is that the high-T viscosities of silicate melts converge to a common value. The implications are twofold. First, the number of composition-dependent parameters is reduced by a third. Second, our optimization constrains the experimentally inaccessible, high-T properties of silicate melts. The high-T limits to melt viscosity are constrained by the VTF and AG models to between 10-4.3±0.74 and 10-3.2±0.66 Pa·s, respectively, and overlap in the interval 10-3.86 to 10-3.56 Pa·s.

The dry and hydrous viscosities of alkaline melts from Vesuvius and Phlegrean Fields

Abstract Sophisticated models of volcanic scenarios are increasingly sensitive to the accuracy of their input parameters and constitutive equations for magma properties. Viscosity is certainly one of the most important magma properties, but only recently systematic investigations on silicate liquids with natural compositions have started. We investigated the Newtonian viscosity of dry and hydrous phonolitic and trachytic melts from Vesuvius and Phlegrean Fields volcanic complexes, respectively. The analysed samples come from the deposits of the AD 1631 (Vesuvius) and ca. 4400 BP Agnano Monte Spina (AMS) (Phlegrean Fields) eruptions that are commonly taken as reference events for the most hazardous scenarios in case of reactivation of the two volcanoes. Samples were hydrated via piston cylinder synthesis at P =10 kbar and T =1600 °C. The dry high temperature and dry or hydrous low temperature viscosities were measured by a combination of micropenetration and concentric cylinder techniques, covering a total temperature range from about 400 to 1500 °C, water content range from virtually dry to 3.8 wt.%, and viscosity range from 10 2 to 10 12 Pa s. The viscosity data for each composition were fitted by a modified Tamman–Vogel–Fulcher equation, allowing viscosity calculations at eruption temperatures and for dissolved water contents in the range of those examined. The viscosity data and model calculations were used for a comparison with other natural or synthetic phonolitic and trachytic melts, as well as with rhyolitic melts, for which viscosities had been measured. At water contents less than 1 wt.%, a trend of increasing viscosity from phonolitic to trachytic to rhyolitic melts is found. At water contents larger than 1 wt.%, the viscosity of trachytic melts is close to that of rhyolitic melts, while the viscosity of phonolitic melts is one to two orders of magnitude lower. A compositional parameter given by the (Na+K+H)/(Si+Al) molar ratio is found to be linearly related to the low- T hydrous viscosity of the trachytic and phonolitic melts considered, either analysed in this work or taken from literature. Differently, the rhyolitic melt shows significant variations from the trend found for phonolitic and trachytic melts.

Predicting shear viscosity during volcanic processes at the glass transition: a calorimetric calibration

The viscosity of volcanic melts at the glass transition has been determined for 11 compositions ranging from basanite to rhyolite. Determination of the temperature dependence of viscosity, together with the cooling rate dependence of the glass transition, permits the calibration of the value of the viscosity at the glass transition at a given cooling rate for each melt. Temperature-dependent viscosities have been obtained using micropenetration methods in the range 10 8 ^10 12 Pa s. Glass transition temperatures have been obtained using differential scanning calorimetry. For each investigated melt composition, the activation energies yielded by calorimetry and viscometry are identical. This confirms that a simple shift factor can be used for each in order to determine the viscosity at the glass transition for a given cooling rate in nature. The results of this study indicate that there is a subtle but significant compositional dependence of the shift factor of a factor of 10 (in log terms) from 10.8 to 9.8. The composition dependence of the shift factor is cast here in terms of a compositional parameter, the mol% of excess oxides (defined within). Using such a parameterisation we obtain a non-linear dependence of the shift factor upon composition that matches the 17 observed values within error. The resulting model permits the prediction of viscosity at the glass transition, during the cooling of glassy volcanic rocks to within 0.1 log units. fl 2002 Elsevier Science B.V. All rights reserved.

The kinetic fragility of natural silicate melts

Newtonian viscosities of 19 multicomponent natural and synthetic silicate liquids, with variable contents of SiO2 (41–79 wt%), Al2O3 (10–19 wt%), TiO2 (0–3 wt%), FeOtot (0–11 wt%); alkali oxides (5–17 wt%), alkaline-earth oxides (0–35 wt%), and minor oxides, obtained at ambient pressure using the high-temperature concentric cylinder, the low-temperature micropenetration, and the parallel plates techniques, have been analysed. For each silicate liquid, regression of the experimentally determined viscosities using the well known Vogel–Fulcher–Tammann (VFT) equation allowed the viscosity of all these silicates to be accurately described. The results of these fits, which provide the basis for the subsequent analysis here, permit qualitative and quantitative correlations to be made between the VFT adjustable parameters (AVFT, BVFT, and T0). The values of BVFT and T0, calibrated via the VFT equation, are highly correlated. Kinetic fragility appears to be correlated with the number of non-bridging oxygens per tetrahedrally coordinated cation (NBO/T). This is taken to infer that melt polymerization controls melt fragility in liquid silicates. Thus NBO/T might form an useful ingredient of a structure-based model of non-Arrhenian viscosity in multicomponent silicate melts.

Dynamics of magma ascent and fragmentation in trachytic versus rhyolitic eruptions

Abstract We have performed a parametric study on the dynamics of trachytic (alkaline) versus rhyolitic (calc-alkaline) eruptions by employing a steady, isothermal, multiphase non-equilibrium model of conduit flow and fragmentation. The employed compositions correspond to a typical rhyolite and to trachytic liquids from Phlegrean Fields eruptions, for which detailed viscosity measurements have been performed. The investigated conditions include conduit diameters in the range 30–90 m and total water contents from 2 to 6 wt%, corresponding to mass flow rates in the range 106–108 kg/s. The numerical results show that rhyolites fragment deep in the conduit and at a gas volume fraction ranging from 0.64 to 0.76, while for trachytes fragmentation is found to occur at much shallower levels and higher vesicularities (0.81–0.85). An unexpected result is that low-viscosity trachytes can be associated with lower mass flow rates with respect to more viscous rhyolites. This is due to the non-linear combined effects of viscosity and water solubility affecting the whole eruption dynamics. The lower viscosity of trachytes, together with higher water solubility, results in delayed fragmentation, or in a longer bubbly flow region within the conduit where viscous forces are dominant. Therefore, the total dissipation due to viscous forces can be higher for the less viscous trachytic magma, depending on the specific conditions and trachytic composition employed. The fragmentation conditions determined through the simulations agree with measured vesicularities in natural pumice clasts of both magma compositions. In fact, vesicularities average 0.80 in pumice from alkaline eruptions at Phlegrean Fields, while they tend to be lower in most calc-alkaline pumices. The results of numerical simulations suggest that higher vesicularities in alkaline products are related to delayed fragmentation of magmas with this composition. Despite large differences in the distribution of flow variables which occur in the deep conduit region and at fragmentation, the flow dynamics of rhyolites and trachytes in the upper conduit and at the vent can be very similar, at equal conduit size and total water content. This is consistent with similar phenomenologies of eruptions associated with the two magma types.

High-temperature deformation of volcanic materials in the presence of water

Abstract We describe an experimental apparatus used to perform deformation experiments relevant to the volcanological sciences. The apparatus supports low-load, high-temperature deformation experiments under dry and wet conditions on natural and synthetic samples. The experiments recover the transient rheology of complex (melt ± porosity ± solids) volcanic materials during uniaxial deformation. The key component to this apparatus is a steel cell designed for high-temperature deformation experiments under controlled water pressure. Experiments are run under constant displacement rates or constant loads; the range of accessible experimental conditions include: 25-1100 °C, load stresses 0 to 150 MPa, strain rates 10-6 to 10-2 1/s, and fluid pressures 0-150 MPa. The apparatus is calibrated against standard values of viscosity using constant-load experiments on cores of NIST (NBS) 717a borosilicate glass. We also report results of constant-displacement rate (~10-6 m/s) experiments on porous (~70%) sintered cores of ash from the Rattlesnake Tuff. The cores of volcanic ash were deformed in experiments under ambient (“dry”) and elevated water pressures (“wet”). Dry experiments at ~870 °C show an increase in effective viscosity (109.5 to 1010.4 Pa·s) with increasing strain (~30%) due to porosity reduction during compaction. Experiments under ~1-3 MPa PH₂O recover lower values of apparent viscosity (109.2 to 109.4 Pa·s) despite being run at lower temperatures (640-665 °C). The wet experiments also do not show a rise in viscosity with increased strain (decreasing porosity) as observed in dry experiments. Rather, the presence of an H2O fluid phase expands the window of viscous deformation and delays the onset of strain hardening that normally accompanies porosity reduction.

Modelling the non-Arrhenian rheology of silicate melts Numerical considerations

Future models for predicting the viscosity of geologically relevant silicate melts must find a means of partitioning the effectsof composition acrossa system that showsvarying degrees of non-Arrhenian temperature dependence. Inthe short term, the decisionsgoverninghowtoexpandthenon-Arrhenianparametersintermsofcompositionwillprobablyderivefromempiricalstudy. The non-linear character of thenon-Arrhenian modelsensuresstrong numerical correlationsbetween model parameterswhich may mask the effects of composition. We present a numerical analysis of the nature and magnitudes of correlations inherent in fitting a non-Arrhenian model ( e.g., Tamman-Vogel-Fulcher function) to published measurements of melt viscosity. Furthermore, we demonstrate the extent towhich the quality and distribution of experimental data can affectcovariances betweenmodel parameters. Theextentofnon-Arrhenianbehaviourofthemeltalsoaffectsparameterestimation.Weexplorethiseffectusingalbiteanddiopside meltsas representativeof strong,nearlyArrhenian meltsand fragile,non-Arrhenianmelts, respectively. The magnitudes and nature ofthesenumericalcorrelationstendtoobscuretheeffectsofcompositionand,therefore,areessentialtounderstandpriortoassigning compositional dependencies to fit parameters in non-Arrhenian models.

A rheological model for glassforming silicate melts in the systems CAS, MAS, MCAS

Viscosity is the single most important property governing the efficacy, rates, and nature of melt transport. Viscosity is intimately related to the structure and thermodynamics properties of the melts and is a reflection of the mechanisms of single atoms slipping over potential energy barriers. The ability to predict melt viscosity accurately is, therefore, of critical importance for gaining new insights into the structure of silicate melts. Simple composition melts, having a reduced number of components, offer an advantage for understanding the relationships between the chemical composition, structural organization and the rheological properties of a melt. Here we have compiled a large database of ∼970 experimental measurements of melt viscosity for the simple chemical systems MAS, CAS and MCAS. These data are used to create a single chemical model for predicting the non-Arrhenian viscosity as a function of temperature (T ) and composition (X) across the entire MCAS system. The T -dependence of viscosity is accounted for by the three parameters in each of the model functions: (i) Vogel‐Fulcher‐Tamman (VFT); (ii) Adam‐Gibbs (AG); and (iii) Avramov (AV). The literature shows that, in these systems, viscosity converges to a common value of the pre-exponential factors (A) that can be assumed to be independent of composition. The other two adjustable parameters in each equation are expanded to capture the effects of composition. The resulting models are continuous across T ‐X space. The values and implications of the optimal parameters returned for each model are compared and discussed. A similar approach is likely to be applicable to a variety of non-silicate multicomponent glassforming systems.

Rapid Updating and Improvement of Airborne LIDAR DEMs Through Ground-Based SfM 3-D Modeling of Volcanic Features

We present a workflow to create, scale, georeference, and integrate digital elevation models (DEMs) created using open-source structure-from-motion (SfM) multiview stereo (MVS) software into existing DEMs (as derived from the light detection and ranging data in the presented cases). The workflow also maps the root-mean-square error between the base DEM and the SfM surface model. This allows DEM creation from field-based surveys using consumer-grade digital cameras with open-source and custom-built software. We employ this workflow on three examples of different scales and morphology: 1) a scoria cone on Mt. Etna; 2) a lava channel on Mauna Ulu (Ki̅lauea); and 3) a flank collapse scar on Mt. Etna. This represents a new approach for rapid low-cost construction and updating of existing DEMs at high temporal and spatial resolutions and for areas of up to several thousand square meters. We assess the self-consistency of the method by comparison of DEMs of the same features, created from independent data sets acquired on the same day and from the same vantage points. We further evaluate the effect of grid cell size on the reconstruction error. This method uses existing DEMs as a georeferencing tool and can therefore be used in limited access and potentially hazardous areas as it no longer relies exclusively on control targets on the ground.