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A model for the viscosity of melts within the Phlegraen Fields, Italy Matysek, Nikolas Apr 30, 2016

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 A MODEL FOR THE VISCOSITY OF MELTS WITHIN THE PHLEGRAEN FIELDS, ITALY     by  NIKOLAS MATYSEK       A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF  THE REQUIREMENTS FOR THE DEGREE OF   BACHELOR OF SCIENCE (HONOURS)  in   THE FACULTY OF SCIENCE  (Geological Sciences)          This thesis conforms to the required standard   ……………………………………… Kelly Russell  THE UNIVERSITY OF BRITISH COLUMBIA  (Vancouver)  APRIL 2016      © Nikolas Matysek, 2016    ii Abstract   The viscosity of silicate melts is perhaps the most important factor in volcanic processes. Presented here is a model that predicts the non-Arrhenian Newtonian viscosity of 25 anhydrous and hydrous naturally-occurring silicate melts as a function of temperature. This model was created from 437 measurements of viscosity on 16 real-world samples, of which 9 were enriched with water content ranging from 0.30 to 6.32 Wt%. The VFT equation [log η = A + B/(T(K)-C)] was used to describes the non-Arrhenian temperature dependence of viscosity. A high-temperature viscosity limit (A) was assumed and the optimal value was calculated to be -4.74 (e.g. η = 10-4.7 Pa s). The parameters B and C account for the compositional dependence but a method to calculate them from chemical data was not determined. The model predicts viscosity continuously across 14 orders of magnitude (103 – 1016 Pa s) and can calculate the glass transition temperature (Tg) and melt fragility (m). Model parameters B and C are compared against each other and show a strong negative correlation. Anhydrous parameters show noticeable trends when compared against all measures but is clearest against SiO2. The affect of water is complex and seems to have little systemic influence expect for when B is compared against NBO/T. These cases provide the best avenues of investigation for determining the compositional dependence.           iii Table of Contents  Cover Page.......................................................................................................................................i Abstract..........................................................................................................................................ii Table of Contents..........................................................................................................................iii List of Figures................................................................................................................................iv List of Tables..................................................................................................................................v Summary of Digital Files..............................................................................................................vi Acknowledgements......................................................................................................................vii 1. Introduction................................................................................................................................1 1.1 Phlegraen Fields Volcanic Complex.............................................................................1 2. Experimental database..............................................................................................................2 3. Modeling methodology..............................................................................................................7 3.1 Constant A rationale......................................................................................................7 3.2 Modeling procedure.......................................................................................................8 4. Model assessment......................................................................................................................9 4.1 Comparison against Misiti et al., 2011........................................................................15 5. Discussion.................................................................................................................................18 5.1 B vs. C..........................................................................................................................18 5.2 B and C vs. SiO2, H2O, NBO/T, SM.............................................................................19 5.3 Glass transition temperature and fragility..................................................................21 6. Recommendations....................................................................................................................22 7. References.................................................................................................................................24          iv List of Figures   Fig. 1. Map of Phlegraen Fields and surrounding area....................................................................2 Fig. 2. Melt compositions, SiO2 vs. Na2O + K2O............................................................................5 Fig. 3. Summary of viscosity - temperature data.............................................................................5 Fig. 4. Examples of data quality analysis, V_1631_W....................................................................6 Fig. 5. Example of comparison between preliminary and new model, V_1631_W......................10 Fig. 6. Comparison of initial model parameters............................................................................11 Fig. 7. Measured vs. predicted viscosity, new model....................................................................13 Fig. 8. Examples of compositions with good model fits...............................................................14 Fig. 9. Compositions with error > ± 0.25 log units.......................................................................15 Fig. 10. Comparison of new model vs. Misit et al., 2011..............................................................17 Fig. 11. Comparison of B and C parameters.................................................................................18 Fig. 12. B vs. SiO2, H2O, NBO/T, SM..........................................................................................20 Fig. 13. C vs. SiO2, H2O, NBO/T, SM..........................................................................................20 Fig. 14. Comparison of glass transition temperature and fragility................................................22               v List of Tables   Table 1. Summary of experimental data.........................................................................................3 Table 2. Summary of model fit parameters...................................................................................12                        vi Summary of Digital Files  Included on the CD affixed to the inside of the back cover:  - Complete experimental database. - MATLAB scripts used for modelling and figure creation.                      vii Acknowledgements    I would like to his supervisor, Dr. Kelly Russell for his continuous support during the research and writing of this thesis. Although at times never-wracking, our regular meetings obliged me to justify my positions and communicate them effectively. Thank you to Daniele Giordano and Kai – Uwe Hess for their input on the experimental database and for providing additional information on suspect experiments. Thank you to Alex Wilson and Luke Hilchie for their assistance with MATLAB and for allowing me to work in their witty and irreverent office.    1 1. Introduction  Magma viscosity is the most important physical property controlling magma production, transport and eruption (Giordano et al., 2008). In natural systems, magma viscosity varies over 15 orders of magnitude and is governed by temperature, composition, and the amount of suspended solids and exsolved fluids. Of the compositional components, dissolved water is especially important. Along with other volatiles CO2 and F, H2O can dramatically affect the magma viscosity and therefore the explosivity of eruptions. The addition of dissolved H2O can cause an effusive mafic volcanic complex to exhibit explosive behaviour (Giordano et al., 2002).   However, the affect of water compared against nominally dry compositions is most pronounced at low concentrations (1 – 3 Wt.% H2O) and changes become less prominent with Wt.% H2O > 5 (Hess and Dingwell, 1996).  Due to the importance of viscosity in magmatic processes, the need for a reliable temperature – composition model is especially acute. Numerous attempts have been made in the last fifteen years at models for both specific regions and the general case (Hui and Zhang, 2007, Giordano et al., 2008, Misiti et al., 2011). The work presented here uses the methodology of Giordano et al. (2008).  Despite many years of labour, interactions between factors such as composition, temperature and pressure, are complex and have inhibited progress. This model is only another step towards the ultimate goal of a consistent, compositionally-dependant, model for viscosity based on temperature and pressure.   1.1 Phlegraen Fields Volcanic Complex The Phlegraen Fields (Italian: Campi Flegrei) is a nested caldera structure created by two of the most powerful eruptions of the volcanic system: Campanian Ignimbrite 37 ka and the Neapolitan Yellow Tuff 12 ka (Orsi et al., 1996 and references therein) (Fig. 1). It is situated in southern Italy, on the western edge of the city of Napoli. The city’s dense urban population and proximity to an active and previously explosive complex creates a significant volcanic risk (Costa et al., 2009). Thus there is compelling motivation for a model that may better assess and constrain possible hazards.  To this end, work has been done by Misiti et al. (2006, 2011) and their experimental data has proved invaluable in the creation of this updated model. The efforts presented here are   2 towards creating a multicomponent model for predicting the viscosity of naturally-occurring silicate melts. It is built using experimental measurements of viscosity across a range of temperatures at atmospheric pressure on samples of known composition. This model should be noted for its range of compositions of naturally-occurring volcanic rocks found both within the Phlegraen Fields and without, the range of water contents of each base composition and the close relationship between observed and predicted viscosities. It is hoped that this work will form the foundation on to which later work can better determine the parameterization of the compositional dependence.    2. Experimental database   The database that was used to create the model contains 437 experimental measurements of viscosity (log η) at a temperature, T(K) for 16 well-characterized, anhydrous base compositions. Of these 16 base compositions, 9 of them were enriched with variable amounts of water, ranging from 0.30 to 6.32 Wt% H2O. This brings the total number of unique compositions included in the model to 51 (Table 1).  Fig. 1. Phlegraen Fields and surrounding area.   3 		Table 1. Summary of microprobe data used in the calibration of the model. No.Label 1Label 2No. Exp.Rock TypeSiO2TiO 2Al2O3FeO tMnOMgOCaONa2OK 2OP 2O 5H 2OCO2_SM drySM hydrous (NBO/T) hydrous(NBO/T) dryReferencemol (ppm)1AMS_D1AMS_D1_dry14Trachyte 60.860.3918.273.500.120.902.964.128.5000.0215.7715.850.080.08Romano et al. (2003)2AMS_D1AMS_D1_6435Trachyte 60.860.3918.273.500.120.902.964.128.5001.1515.1319.300.170.08Romano et al. (2003)3AMS_D1AMS_D1_6414Trachyte 60.860.3918.273.500.120.902.964.128.5002.0414.6521.870.250.08Romano et al. (2003)4AMS_D1AMS_D1_6404Trachyte 60.860.3918.273.500.120.902.964.128.5002.3814.4722.830.280.08Romano et al. (2003)5AMS_D1AMS_D1_6393Trachyte 60.860.3918.273.500.120.902.964.128.5003.7513.7826.500.390.08Romano et al. (2003)6AMS_B1AMS_B1_dry11Trachyte 61.260.3818.383.500.140.742.974.588.0400.0215.6415.710.080.08Romano et al. (2003)7AMS_B1AMS_B1_6424Trachyte 61.260.3818.383.500.140.742.974.588.0400.7915.2018.090.140.08Romano et al. (2003)8AMS_B1AMS_B1_6386Trachyte 61.260.3818.383.500.140.742.974.588.0401.1914.9819.280.170.08Romano et al. (2003)9AMS_B1AMS_B1_6367Trachyte 61.260.3818.383.500.140.742.974.588.0401.2614.9419.490.180.08Romano et al. (2003)10AMS_B1AMS_B1_6376Trachyte 61.260.3818.383.500.140.742.974.588.0403.7813.6526.450.390.08Romano et al. (2003)11V_1631_WV_1631_W_dry14Phonolite53.520.6019.844.800.141.766.764.667.9100.0221.8921.970.200.20Romano et al. (2003)12V_1631_WV_1631_W_6406Phonolite53.520.6019.844.800.141.766.764.667.9101.1720.9825.220.310.20Romano et al. (2003)13V_1631_WV_1631_W_6433Phonolite53.520.6019.844.800.141.766.764.667.9102.2120.2028.000.400.20Romano et al. (2003)14V_1631_WV_1631_W_6425Phonolite53.520.6019.844.800.141.766.764.667.9103.3219.4230.800.500.20Romano et al. (2003)15V_1631_GV_1631_G_dry14Phonolite53.140.5919.844.720.131.776.754.778.2800.0222.3022.380.210.21Romano et al. (2003)16V_1631_GV_1631_G_6374Phonolite53.140.5919.844.720.131.776.754.778.2801.2621.3025.860.320.21Romano et al. (2003)17V_1631_GV_1631_G_6384Phonolite53.140.5919.844.720.131.776.754.778.2802.0420.7027.940.390.21Romano et al. (2003)18V_1631_GV_1631_G_6393Phonolite53.140.5919.844.720.131.776.754.778.2803.0719.9530.560.490.21Romano et al. (2003)19MNV18Trachyte 63.880.3117.102.900.130.241.825.676.820.050.0213.8013.870.060.05Giordano et al. (2004)20MNV4Trachyte 63.880.3117.102.900.130.241.825.676.820.051.0013.3116.920.130.05Giordano et al. (2004)21MNV3Trachyte 63.880.3117.102.900.130.241.825.676.820.051.3913.1218.090.170.05Giordano et al. (2004)22MNV2Trachyte 63.880.3117.102.900.130.241.825.676.820.052.4112.6521.050.250.05Giordano et al. (2004)23MNV4Trachyte 63.880.3117.102.900.130.241.825.676.820.053.8612.0124.990.370.05Giordano et al. (2004)24IGC18Trachyte 60.740.2719.223.370.180.282.115.286.320.060.0213.7513.820.020.02Giordano et al. (2004)25IGC6Trachyte 60.740.2719.223.370.180.282.115.286.320.060.8113.3516.320.080.02Giordano et al. (2004)26IGC3Trachyte 60.740.2719.223.370.180.282.115.286.320.061.5412.9918.530.140.02Giordano et al. (2004)27IGC3Trachyte 60.740.2719.223.370.180.282.115.286.320.062.0112.7719.910.180.02Giordano et al. (2004)28IGC2Trachyte 60.740.2719.223.370.180.282.115.286.320.062.9612.3422.610.260.02Giordano et al. (2004)29IGC3Trachyte 60.740.2719.223.370.180.282.115.286.320.063.4112.1523.840.290.02Giordano et al. (2004)30MST21Andesite60.710.5818.296.380.192.587.103.570.850.000.0216.8016.880.120.12Giordano et al. (2006)31STB*21Trachybasalt49.070.9816.918.360.225.7310.882.632.200.000.0226.7026.770.410.41Giordano et al. (2006)32Fra27Latite55.410.7218.387.310.162.395.764.234.580.000.0218.8018.870.160.16Giordano et al. (2006)33CI_OF*20Trachyte 68.800.2312.583.170.141.243.434.016.180.030.0214.5514.620.150.15Giordano et al. (2006)34SLP*17Basanite45.762.2712.5211.300.2511.4211.452.651.070.860.0233.6033.670.880.87Giordano et al. (2006)35MRP22Andesite53.530.8218.959.030.193.429.233.451.640.000.0221.1321.200.220.22Giordano et al. (2006)36MDV17Moldavite79.430.209.941.890.031.642.420.493.420.000.028.148.210.040.04Giordano et al. (2006)37FRd_126Latite56.080.8918.836.570.132.485.874.214.670.640.0118.8918.930.190.19Misiti et al. (2011)38FRd_15Latite56.080.8918.836.570.132.485.874.214.670.640.3018.6919.790.210.19Misiti et al. (2011)39FRd_13Latite56.080.8918.836.570.132.485.874.214.670.640.5018.5620.380.230.19Misiti et al. (2011)40FRd_13Latite56.080.8918.836.570.132.485.874.214.670.640.8018.3621.250.260.19Misiti et al. (2011)41MINad_124Shoshonite52.860.8416.277.000.135.6610.292.283.770.430.0125.9225.950.430.43Misiti et al. (2011)42MINad_13Shoshonite52.860.8416.277.000.135.6610.292.283.770.430.5025.4727.230.470.43Misiti et al. (2011)43MINad_13Shoshonite52.860.8416.277.000.135.6610.292.283.770.432.4323.8131.960.650.43Misiti et al. (2011)44FRFR_dry11Latite56.630.8218.006.700.172.415.604.614.560.460.0218.8418.920.190.19Di Genova et al. (2014)45FRFR_1.64Latite56.630.8218.006.700.172.415.604.614.560.461.5917.8023.400.330.19Di Genova et al. (2014)46FRFR_2.75Latite56.630.8218.006.700.172.415.604.614.560.462.6917.1226.340.430.19Di Genova et al. (2014)47FRFR_3.83Latite56.630.8218.006.700.172.415.604.614.560.463.7616.4929.050.520.19Di Genova et al. (2014)48FRFR_6.33Latite56.630.8218.006.700.172.415.604.614.560.466.3215.1134.980.760.19Di Genova et al. (2014)49FRFR_I_CO 26Latite56.630.8218.006.700.172.415.604.614.560.460.7822918.3321.130.260.19Di Genova et al. (2014)50FRFR_II_CO25Latite56.630.8218.006.700.172.415.604.614.560.460.3855318.6019.980.220.19Di Genova et al. (2014)51FRFR_III_CO25Latite56.630.8218.006.700.172.415.604.614.560.460.5373218.4920.410.240.19Di Genova et al. (2014)Weight Percent (Wt %)  4 The experimental data was collected at a variety of laboratories over 11 years, from 2003 to 2014 (see Digital Files). Viscosity of high temperature melts (log η -0.31 – 4.80) was measured using a concentric cylinder apparatus and lower temperature melts (log η 8.00 – 12.40),  micropenetration. Hydrous samples were synthesized using piston cylinder apparatus at high temperature and pressure (T = 1600 oC, P = 10 kbar) or an internally heated pressure vessel (T = 1523 K, P = 300 MPa (Romano et al., 2003, Misiti et al., 2014). Samples were allowed to sit for up to 24 hours to ensure proper mixing. The gap in viscosity measurements between log η ~ 5 – 8 is due to a conflict between the timescales of processes that modify the melt (crystallization, vesiculation) and the timescale of viscosity measurement.  The range of melt compositions used in this model spans from basalt to trachyte and from andesite to phonolite (Fig. 2). Nine of the unique base compositions are from various locations within the Phlegraen Fields (AMS_D1, AMS_B1, V_1631_W, V_1631_G, FRd_1, MINad_1, FR). This subset has a smaller variation in compositions, from Basaltic trachy-andesite to trachyte. The remaining seven samples are from outside the Phlegraen Fields (MST, STB, Fra, CL_OF, SLP, MRP, MDV). They are included because they are well characterized and increased the robustness of the model. All of these samples are from natural systems and no synthetically produced compositions have been included.  Of the 437 experimental measurements, 295 are done on anhydrous melt compositions spanning all 16 base compositions. Temperatures range from 955 – 1916 T(K) and viscosities from 10-0.31 – 1011.60 Pa s (Fig. 3). Also included are 142 measurement pairs on 9 base compositions that have been enriched with H2O and in one case, CO2. The ranges of both temperature 633 – 959 T(K) and viscosity 108.00 – 1012.40 Pa s are smaller than the those of the anhydrous experiments. This model is calibrated on compositions spanning the following oxide weights (Wt. %): SiO2 (45.76 – 79.43), TiO2 (0.20 – 2.27), Al2O3 (9.94 – 19.84), FeOTot (1.89 – 11.30), MnO (0.03 – 0.25), MgO (.24 – 11.42), CaO (1.82 – 11.45), Na2O (0.49 – 5.67), K2O (0.85 – 8.50), P2O5 (0 – 0.86). Enriched volatiles: H2O (0.30 to 6.32 Wt. %), CO2 (0 – 732 mol(ppm)).   The analysis is two-fold. Firstly, each dataset comprising the anhydrous base composition and its hydrous counterparts are fit with independent model parameters. This was done to assess the quality of the experimental data (Fig. 4.). Using the methodology described in Giordano et al. (2008), each composition at a given water content was fit with a curve that modelled its    5                            SiO2 (Wt. %)40 45 50 55 60 65 70 75Na2O + K2O (Wt. %)02468101214MDV[79.43, 3.91]104/T(K)4 6 8 10 12 14 16Log [η (Pa s)]-202468101214Fig. 2. Melt compositions used in calibration of model for silicate melt viscosity; SiO2 vs. Na2O + K2O. Fig. 3. Summary of all experimental data used to calibrate model. Open symbols denote anhydrous compositions and the filled blue symbols, hydrous.   6  Fig. 4. An example of data quality analysis for composition V_1631_W. The black line denotes anhydrous base composition and blue, hydrous.  Symbol size is proportional to H2O Wt%. predicted viscosity across a continuous range of temperatures. Samples with a predicted viscosity that was significantly different than the experimental measurements were investigated further. Data that had improbable relationships between temperature and viscosity were dropped from further consideration. The spread of experimental data for each H2O content is likely due to the difficulty of obtaining reliable viscosity measurements at temperatures close to the compositions’ glass transition temperature (Tg). Other possible sources of error are undetected devolatilization, loss of H2O or vesiculation (Daniele Giordano, personal communication, December 28th, 2015). An analysis of the entire dataset led to the rejection of a single low temperature experiment (log η = 9.94, T(K) = 811.45, Wt% H2O = 2.01, Giordano et al., 2004)    104/T(K)4 6 8 10 12 14 16 18 20Log [η(Pas)]-202468101214SiO2 wt%: 53.52A: -6.7766Maximum H2O wt%: 3.32Minimum H2O wt%: 0.02PhonoliteRomano et al. (2003)V_1631_WB: 12218C: 264B: 11416C: 150B: 10186C: 150B: 9620C: 154  7 3. Modelling methodology   The experimental data used in these preliminary steps of modeling includes only temperature – viscosity measurements on samples on accurately determined composition. Although the compositional dependence of model parameters are not fully determined herein, it is hoped that this solid foundation of verified data will enable others to complete the task. It also bears noting that all the iron is considered as FeO despite evidence that the redox state affects melt structure (Mysen, 1988). The justification follows that of Giordano et al. (2008), that the effect of redox state likely does not improve the fit of the model.   The relationship between temperature and viscosity (log η) is modeled by the VFT equation (Vogel, 1921 and Fulcher, 1925): log 𝜂 = 𝐴 + 𝐵𝑇 𝐾 − 𝐶 where A, B and C are adjustable parameters. Respectively, these variables are a pre-exponential factor, pseudo-activation energy and the VFT-temperature. A is assumed to be an unknown constant based on the work of Myuller, 1955; Eyring et al., 1982; Angell, 1985; Russell et al., 2002; Giordano et al., 2008. B and C therefore are the only factors that can have a compositional control on viscosity.  3.1 Constant A rationale  The A parameter is theorized to be the viscosity (log η, Pa s) at infinite temperature (Russell et al., 2002, 2003, 2005). This implies A is the high-temperature limit that all silicate melts will approach with increasing temperature. A is hypothesized to be constant for all melts because at higher temperatures, liquids become highly dissociated and their chemical structure, apparent at lower temperatures is unraveled and their viscosities converge to a single value. This concept is supported by experimental observations of polymer melts and organic liquids (Agnell, 1991; Scopigno et al., 2003). In these cases, the glass transition temperature is sufficiently low such that it is feasible to measure viscosity at temperatures far above Tg. Both strong (log η is linearly proportional to 1/Tg) and fragile (non-linear relation between log η and Tg) liquids converge to a similar viscosity, ~ 10-5 Pa s; (Eyring et al., 1982; Angell, 1991, 1995; Russell et al., 2003; Scopigno et al., 2003).   8  More proof of this concept is apparent in the characteristic time scales of relaxation in melts (Eyring et al., 1982; Angell, 1991, 1995; Richet and Bottinga, 1995; Russell et al., 2003; Scopigno et al., 2003). The relaxation time scale of a melt (τ) is the time it takes to return to equilibrium after being perturbed. An applied stress over a time period greater than τ will result in viscous deformation, whereas if tstress < τ, brittle deformation will occur. The lower limit of melt viscosity (ηo) can be determined by a relationship between the bulk sheer modulus (G∞) and τ. The Maxwell equation states τ = ηo/ G∞, where G∞ is the bulk sheer modulus at infinite frequency, ~ 1010 Pa (Dingwell and Webb, 1989; Toplis, 1998), and τ is quasilattice vibration time period (~10-14 s) between sustained attempts surpass the energy barriers to melt rearrangement (Angell, 1991; Toplis, 1998). Using these values, the lower limit of viscosity (ηo) is approximately 10-4 Pa s (Giordano, et al., 2008). Including uncertainty, the range of lowest viscosity, and therefore A, is between 10-3.5 and 10-5.5 Pa s (Angell, 1991; Toplis, 1998). The findings of Giordano, et al., 2008; the theoretical basis of this work, of A = -4.55±0.21 Pa s is well within these theoretical constraints.   3.2 Modelling procedure  The goal of this research was to determine the A parameter that best describes melts of all compositions and to analyse the variation of the other two parameters, B and C, over empirical and compositional measures. To this end, the following procedure was followed: 1. Compile database, 2. Assess quality of experimental data, 3. Determine unique A, B and C parameters for each base and hydrated composition, 4. Using these independent parameters as a foundation, determine a global A, and dependent B and C values for each composition, 5. Assess the quality of the model fit against the preliminary independent parameters, experimental observations, and the model of Misiti et al., (2011), 6. Assess relationships between modeling parameters, empirical measures (SM, NBO/T) and compositional components (SiO2, H2O). Points 1 and 2 are discussed above (Experimental Database) and points 5 and 6 are discussed below, (Model Assessment and Discussion). The following is a discussion of modeling parameterization.  The first step of model parameterization was to determine independent A, B and C values for each base composition and its associated volatile-enriched syntheses. In all 9 cases where the base compositions were enriched with volatiles, there were more experiments done on the nominally dry base (max: 26, min: 11, mean: ~17) than enriched samples (max: 7 min: 2, mean:   9 ~4). Using the rationale of a common A, the A parameter was then determined using the better constrained dry composition but each variation of H2O on the base was given its own unique B and C. This was done by solving a non-linear optimization problem using the Newton – Raphson Method to control iterative the iterative search routine (methodology after Russell et al., 2003). All 3 parameters were allowed to vary for the dry composition but A would be fixed for hydrous compositions with only B and C varying. For the other 7 compositions without volatile enrichment there was only one set of parameters calculated. The result of this parameterization is assumed to be the best possible fit as the variables describe a closely related subset of data, despite A not being unique for all volatile variations. This preliminary parameterization provided a benchmark that subsequent attempts could be assessed against. The B and C values were also used to constrain the subsequent parameterization of a global A. Once the independent parameters had been calculated, they could then be used to focus the search for a single A that satisfactorily describes all melts along with unique B’s and C’s constrained by the global A. As before, each composition and volatile content would have a unique B and C that best described the experimental observations. The difference is that this model would solve for a single A whereas the previous stage has a unique A for each anhydrous base composition. As an example, figure 5 shows the comparison between the preliminary model and the new model.  The range of unique A values calculated from the first stage was -3.67 to -7.12 Pa s., whereas the theorized high temperature viscosity limit is between 10-3.5 and 10-5.5 Pa s. The discrepancy between the lowest possible viscosities implied that the other parameters (B and C) would be forced to change, in some cases drastically (when A << ~-4.5), in order to still adequately describe the observed data. The same Newton – Raphson methodology was employed to constrain the parameters. The global A was determined to be -4.74, well within the theoretical range and similar to that of Giordano et al., 2008. All parameters are show in Fig. 6 and Table 2.  4. Model assessment   The success of this research should be assessed on: 1. Its ability to reliably reproduce experimental data across reasonable, naturally-occurring temperatures, 2. Exhibit higher    10  precision than existing models, 3. Provide a solid foundation for fuller parameterization of a global viscosity model. The first two points are empirically discussed here, an evaluation of the third may only be done later.  At the very least, the goal of any model should be to adequately recreate the original data on which it was based and then, hopefully, provide valid predictions based on new inputs. This  new model should be noted for its ability to calculate estimates of viscosity that are well within  104/T(K)4 6 8 10 12 14 16 18 20Log [η(Pas)]-202468101214Global A: -4.7389Total No. of Experiments: 28Chi-Sqaure Spread: 0.13 - 47.35V_1631_WB: 8525C: 415B: 8823C: 232B: 7807C: 227B: 7410C: 225Fig. 5. An example of the comparison between the preliminary model and the new model for composition V_1631_W. The solid blue lines show predicted viscosity for a global A (-4.7389), where as the dashed black lines show the prediction of the preliminary model.   11 the range of uncertainty of the original observations. However, the scope of this research and time constraints precluded the development of a predictive function. Using the global A and compositionally dependent B and C parameters, the viscosity at a given temperature could be calculated. This calculated viscosity is easily compared to the original experimental observation at the same temperature (Fig. 7). Shown on the figure are all 437 experimental measures of viscosity and the predicted viscosity based on the parameters for each composition. The dashed lines shows ±0.25 log unit variation on log η [Measured] = log η [Predicted]. This 0.25 log unit range is a result of uncertainty in the original measurements.   	B Parameter0 2000 4000 6000 8000 10000 12000 14000 16000 18000A Parameter-7.5-7-6.5-6-5.5-5-4.5-4-3.5C Parameter-100 0 100 200 300 400 500 600 700 800A Parameter-7.5-7-6.5-6-5.5-5-4.5-4-3.5C Parameter0 2000 4000 6000 8000 10000 12000 14000 16000 18000B Parameter-1000100200300400500600700800Fig. 6. A comparison of parameters for the initial model with a unique A for each composition. Open black symbols denote anhydrous compositions and filled blue symbols, hydrous.   12  No. Label 1 Label 2Bvft Cvft Tg (K) m1 AMS_D1 AMS_D1_dry 10824.56 273.68 920.35 23.822 AMS_D1 AMS_D1_643 9892.65 199.20 790.20 22.383 AMS_D1 AMS_D1_641 8586.34 221.08 734.04 23.954 AMS_D1 AMS_D1_640 8683.15 192.72 711.46 22.965 AMS_D1 AMS_D1_639 6940.47 248.99 663.62 26.796 AMS_B1 AMS_B1_dry 10822.82 283.55 930.11 24.087 AMS_B1 AMS_B1_642 10475.18 185.65 811.45 21.708 AMS_B1 AMS_B1_638 9441.88 200.46 764.53 22.699 AMS_B1 AMS_B1_636 9927.22 165.81 758.88 21.4210 AMS_B1 AMS_B1_637 6990.70 244.71 662.34 26.5511 V_1631_W V_1631_W_dry 8525.02 415.08 924.38 30.3812 V_1631_W V_1631_W_640 8822.68 231.89 758.97 24.1013 V_1631_W V_1631_W_643 7807.16 227.06 693.47 24.8914 V_1631_W V_1631_W_642 7409.81 224.76 667.43 25.2415 V_1631_G V_1631_G_dry 8739.49 418.52 940.63 30.1616 V_1631_G V_1631_G_637 7821.39 295.68 762.94 27.3317 V_1631_G V_1631_G_638 7253.33 273.35 706.67 27.3018 V_1631_G V_1631_G_639 7942.50 191.07 665.56 23.4819 MNV 10768.78 287.03 930.37 24.2120 MNV 12633.54 17.59 772.33 17.1321 MNV 11723.34 41.10 741.47 17.7222 MNV 10323.45 71.69 688.42 18.6823 MNV 4894.37 358.24 650.63 37.2524 IGC 9118.79 476.94 1021.71 31.3925 IGC 10088.96 199.51 802.24 22.2826 IGC 7794.02 302.59 768.21 27.6227 IGC 9141.16 179.31 725.41 22.2428 IGC 3797.92 487.11 714.00 52.6829 IGC 6599.66 279.51 673.78 28.6130 MST 8140.00 464.49 950.78 32.7331 STB 6305.36 555.74 932.42 41.4332 Fra 7562.60 518.15 969.94 35.9433 CI_OF 9963.05 398.38 993.59 27.9434 SLP 5084.52 629.82 933.57 51.4535 MRP 6978.14 535.24 952.12 38.2336 MDV 11989.03 345.60 1061.84 24.8237 FRd_1 7562.63 516.76 968.56 35.8838 FRd_1 6839.11 465.30 873.88 35.8039 FRd_1 5243.49 564.45 877.70 46.9040 FRd_1 5520.38 541.35 871.15 44.2241 MINad_1 6649.37 540.97 938.21 39.5342 MINad_1 2795.18 698.40 865.39 86.7543 MINad_1 1509.85 737.51 827.71 153.6044 FR FR_dry 7755.76 514.09 977.42 35.3145 FR FR_1.6 7693.67 323.59 783.21 28.5246 FR FR_2.7 6687.49 315.16 714.67 29.9447 FR FR_3.8 6547.59 290.04 681.20 29.1548 FR FR_6.3 6059.28 279.84 641.83 29.6849 FR FR_I_CO2 7257.76 388.37 821.96 31.7350 FR FR_II_CO2 11750.73 135.14 837.14 19.9651 FR FR_III_CO2 9767.07 252.92 836.41 23.99Predicted by model (Avft = -4.74)Table 2. Summary of new model fit parameters.   13  Fig. 7. Measured vs. Model (predicted) viscosities calculated using the model.  Most predicted values are within acceptable range of the original measurement and accurately recreate the experimental data (Fig. 8.). Yet there are 14 calculated viscosities > ±0.2 log units different than the observed value and 9 > ±0.25 log units. The latter anomalous data points are from experiments on samples V_1631_G, Fra, FR and FRd_1. The range of SiO2 for all 16 base compositions is between 45.76 – 79.43 Wt%, but for these cases is 53.14 – 56.63 Wt%. For all except for one measurement (0.30 Wt%. H2O), the compositions are all nominally anhydrous (Wt%. H2O ≤ 0.02). Furthermore, all anomalies are from the beginning or end of experimental series, either at high temperatures or low. That is to say, if an experimental run on a single composition has several experimental measurements above and below the aforementioned melt modification range (~6 < log η < ~8), the anomalies are found in the last experiments at high temperature, low viscosity or the start of the low temperature, high viscosity measures. Figure 8 shows the experimental series with predictions greater than ± 0.25 log units. log η [Measured]0 2 4 6 8 10 12log η [Model]024681012  14   A possible explanation for the seemingly systemic anomaly is the quality of the experimental data. Idealized trend lines for high and low temperature observations have been added to Frd_1 (0.01 Wt% H2O) (Fig. 9.). Graphically, it is impossible to connect the two segments without a concave-down portion. The implication of a concave-down trend is that there is a temperature threshold beyond which the system exhibits different behaviour. Critical temperature limits are not observed in naturally occurring compositions, and therefore must be the result of imprecise measurement. Given the long timescales of measurement for low temperature, high viscosity measurements, there is greater potential for processes like vesiculation to effect the observations. As a result, it is likely that the low temperature observations are responsible for the errors and not the faster to measure high temperature experiments. The effect of these few potentially erroneous observations on the determination of the global A parameter is slight as they constitute a very small part of the experimental database used for its calculation (9 of 437 observations). Additionally, the global A parameter is more responsive to the relatively higher precision, high temperature experiments than it is to the less precise, low temperature ones. As a result, the effects of imprecise measurements are mostly confined to the B and C parameters as they are unique to each composition.   			104/T(K)4 6 8 10 12 14Log [η(Pas)]-202468101214Total No. of Experiments: 24MINad_1104/T(K)4 6 8 10 12 14Log [η(Pas)]-202468101214Total No. of Experiments: 18MNVFig. 8. Examples of good model fits for Arrhenian (linear) - MNV and non-Arrhenian (exponential) - MINad_1. Blue line is model prediction with global A.   15    Although the magnitude of discrepancy between observed and predicted viscosity is small (maximum < 0.31 log units), and therefore the effect on B and C, these suspect parameters constitute a larger portion of all parameters (6 of 102). The relationships between calculated parameters, A, B and C, are only qualitatively analyzed so these small variations are likely insignificant to the following discussion. However, if a more quantitative approach is taken to determining the compositional control, these observations may need to be removed from consideration.  4.1 Comparison against Misit et al., 2011 Another measure of success of a model is how it compares to previous attempts. The Phlegraen Fields is a volcanologically active region close to a major urban center. As a result, Fig. 9. Compositions with predicted viscosity >± 0.25 log units than measured values. Blue line is model prediction with global A. Pink line for Frd_1 (0.01 wt% H2O)  shows trend line for high temperature (lower left  and low temperature (upper right) observations. 			104/T(K)4 6 8 10 12 14Log [η(Pas)]-202468101214Total No. of Experiments: 26Frd_1 (0.01 wt% H2O)104/T(K)4 6 8 10 12 14Log [η(Pas)]-202468101214Total No. of Experiments: 27Fra104/T(K)4 6 8 10 12 14Log [η(Pas)]-202468101214Total No. of Experiments: 14V_1631_G_dry  16 much effort has been expended on understanding the complex volcanic system. This has culminated in numerous studies of melts (Di Genova et al., 2014; Misiti et al., 2006; Piochi et al., 2008; Romano et al., 2003; Vona et al., 2013) and a temperature – composition – viscosity model by Misiti et al. (2011).  The results of this new model are compared against those of Misiti et al. over two compositions. The aim of Misiti et al. was to create a general viscosity model for the Phlegraen Fields based on new experimental data over a range of temperatures at atmospheric pressure and at 0.5 GPa. Their 10 parameter model:   log 𝜂 = 	−𝑎 + /(123) + 5(126) ∙ exp	(𝑔 ∙ <1) predicts viscosity (log η) where T is absolute temperature, w is H2O Wt. % and a, b, c, d, e, g are compositionally dependent fit parameters. Two base sample compositions FRd_1 (Latite) and MINad_1 (Shoshonite), and associated hydrated synthesises were used to calibrate their model and also included in this experimental database. A comparison of the two models are presented in figure 10.   Starting with a few general observations of both figures. By and large, the fit of both models is within the 0.25 log unit uncertainty limits. At low viscosities (0 < log η < 4), both models show a minor systematic trend from over-estimate at log η ~ 0-1 to under-estimate at log η ~ 3-4. The spread at higher viscosities, lower temperatures, is also greater than at low viscosity. This difference in the quality of fit between high and low viscosities could be due to the difficulty in taking reliable measurements at low temperatures (The length of time required for measurement are such that it is relatively easy to introduce experimental error). Looking at FRd_1, the difference between models is slight. At higher viscosities, the predictions of this new model are marginally better but essentially the same at lower viscosities. As stated before, this difference could be due to experimental error more than to a more accurate prediction. The value of the new model is more apparent when comparing the predictions of MINad_1 viscosity. The spread of high viscosity data is equivalent to that of FRd_1 but the quality of fit of the new model is appreciably better. All of the predicted viscosities are within limits yet 4 point from Misiti et al. lie outside. This apparent improvement in fit should however be qualified by the limited data and used for this comparison.    17                         						Fig. 10. Comparison of Measured vs Predicted viscosity for new model and Misiti et al. 2011. Top pane shows Latite, FRd_1 and lower shows Shoshonite - MINad_1.   18 5. Discussion   In this new model, all the compositional controls are found in the B and C parameters. Therefore, an analysis of these parameters compared against compositional measures (SiO2 and H2O) and empirical properties (SM and NBO/T) should form the basis of an attempt at determining their compositional dependence. The following section will discuss the observed trends, and how they relate to theoretical predictions.  5.1 B vs. C  As seen in Fig. 11 and Table 2, calculated B parameters range from ~ 1500 to 12600 and C from ~ 15 to 740. There is a strong negative linear correlation between the two parameters with C dramatically decreasing with increasing B. The is also minimal overlap between the two, with parameters for anhydrous compositions lying to the right of hydrous compositions. That is, the numerical magnitude of hydrous composition parameters are lower than those of the B Parameter0 2000 4000 6000 8000 10000 12000 14000C Parameter0100200300400500600700800Fig. 11. Comparison of B and C parameters. Open symbols denote anhydrous compositions and the filled blue symbols, hydrous.   19 anhydrous. Additionally, the range of values for anhydrous parameters is smaller than that of hydrous. The quasi-linear relationships between parameters B and C for hydrous and anhydrous samples is a strong indication of their compositional dependence. Increased volatile content should decrease melt activation energy, roughly proportional to B, as it become increasingly depolymerized (Richet and Bottinga, 1995; Mysen, 1988).  Conversely, increasing volatile content increases the number of network-modifying molecules and the VFT temperature, proportional to C (Richet and Bottinga, 1995). This relation can be seen in Figure 11, the anhydrous B and C parameters all plot above those of hydrous compositions. The affect on B of increasing H2O is of greater magnitude than the affect on C. If the opposite was true, the roughly linear trends of hydrous and anhydrous parameters would cross over. It follows that as increasing H2O content decreases viscosity at a given temperature, the only way to account for this in the VFT equation is to decrease B and increase C (Dingwell, 1998). The sum of these modified parameters should be lower than those of the sum of the anhydrous values; this is observed in the figure.   5.2 B and C vs. SiO2, H2O, NBO/T, SM When looking only B or C in relation to other measures, the apparent trends can be far less clear (Fig. 12 & 13). Anhydrous B and C parameters show noticeable, yet opposite relations to increasing SiO2. Generally, B increases with increasing silica where as C decreases. Increasing silica increases polymerization, and thus melt activation energy (B) but also decreases the VFT  temperature (C). The affect of H2O on these relationships is ambiguous, however it mostly serves to decrease both parameters. NBO/T is an empirical ratio of the number of Non-Bridging Oxygen per Tetrahedral cation that reflects the degree of polymerization. NBO/T = 0 represents a fully polymerized melt and NBO/T = 2 is fully dissociated. Again, using the rationale of Richet and Bottinga, 1995, B decreases relative to increasing NBO/T as activation energy decreases. C increases with increasing NBO/T, although this is most clearly seen in anhydrous parameters. Finally, SM is another empirical parameter, the sum of all the structure modifying oxides (Giordano and Dingwell, 2003a). The trends in this parameter are the most obscured, with anhydrous B decreasing and C increasing with increasing SM. Hydrous B seems to follow the     20                               															Fig. 12. A comparison of B parameters against SiO2 (top left), H2O (top right), NBO/T (bottom left), SM (bottom right). Open symbols denote anhydrous compositions and filled blue symbols, hydrous. Fig. 13. A comparison of C parameters against SiO2 (top left), H2O (top right), NBO/T (bottom left), SM (bottom right). Open symbols denote anhydrous compositions and filled blue symbols, hydrous.   21 trend of its anhydrous counterparts, however the seems to be very little relation between hydrous C and SM.   5.3 Glass transition temperature and fragility The measures of glass transition temperature (Tg) and fragility (m) the are important determinants of transport properties and their relationship warrants further analysis. Tg is the absolute temperature that separates liquid behavior from brittle (glassy), and is taken to be where η = 1012 Pa s (Angell, 1995; Dingwell et al., 1993). It is calculated from rearranging the VFT equation, where  𝑇= = 𝐶 + 𝐵(12 − 𝐴)  and A, B, C are parameters determined by the new model. Fragility is a measure of how sensitive a liquid’s viscosity is to changes in temperature and has two end behaviors: “Strong” liquids show a linear relationship (Arrhenian) between viscosity and inverse temperature, “Fragile” liquids on the other hand are non-linear (non-Arrhenian) (Agnell, 1985). m, the “steepness index” is common measure of fragility and is used to characterize strong and fragile melts (Plazek and Ngai, 1991). It is calculated from: 𝑚 = 𝐵𝑇=(1 − 𝐶 𝑇=)A  where B, C again are model parameters and Tg is take at η = 1012 Pa s. The steepness index can be thought of as the tangent to the viscosity – temperature slope at Tg. It follows that low values of m correspond to strong melts and high values to fragile melts.    Figure 14 shows the calculated values of Tg and m for all melts in the database. The fragility of melts ranges from strong to moderately fragile and the Tg of anhydrous melts shows a weak negative correlation with m. The addition of H2O dramatically reduces the glass transition temperature for all melts, in accordance with experimental studies (Hess and Dingwell, 1996; Giordano et al., 2004a,b). It also produces a minor decrease in fragility. Generally, increasing the amount of network-modifying molecules (NBO/T), increases the fragility of    22 melts. Yet water can conversely cause a depolymerization in silicate melts and decrease NBO/T, the exact nature of this relationship is still under investigation (Kohn, 2000).  In summary, the accordance of relationships between model parameters and those both experimentally determined and theoretically predicted implies the new model can provide an adequate representation of real-world phenomena. However, the nature of the experimental data used to construct this model introduces a high degree of variability on to generally supported trends.  6. Recommendations    This work is a solid attempt at a viscosity model for the melts within the Phlegraen Fields, yet more work is required. Although beyond the scope of this research, the ability to calculate the model parameters, and therefore viscosity, using a new sample composition would dramatically increase the real-world applicability of the model. As is, important melt transport Fragility (m)15 20 25 30 35 40 45 50 55 60Tg (K)60070080090010001100MINad_10.5 Wt% H2O: [865, 87]2.43 Wt% H2O: [828, 154]Fig. 14. Comparison of glass transition temperature and fragility. Open symbols are anhydrous and filled blue symbols, hydrous.   23 measures such as Tg and m can be calculated using this model. These can be used to better constrain the nature of previous eruptive episodes and to provide an estimate of future events. However, if transport properties of yet un-erupted melts could be estimated, the increased accuracy of risk assessments for Napoli and the surrounding areas would be profound.   The first step in adding a compositional dependence to the model might be a closer analysis of the relationships between the B and C parameters, and chemical components. Silica content strongly controls the viscosity of melts and is correlated with both anhydrous B and C. When the model parameters are compared against the empirical metrics NBO/T and SM, relationships are often less clear, perhaps due to the complex interactions between compositional components on which they are constructed. One comparison stands out however, that of NBO/T and B. In this case, both anhydrous and hydrous parameters are negatively correlated with increasing NBO/T. The general trend in these comparisons has been for either anhydrous or hydrous parameters to vary in response to another measure, yet rarely together. This anomaly may be a good place to start.   It is hoped that this research provides insight in to how viscosity is affected by temperature, using data collected from the Phlegraen Fields. Volcanic systems can be incredibly complex and this is only an approximation of the multifaceted system. Much more work is still required to determine a global model for silicate melt viscosity.             24 7. References  Angell, C.A., 1995., Relaxations in Complex Systems (U.S. Department of Commerce National Technical Information Service, ed. K.L. Ngai and G.B. Wright, 1985). pp. 3–11. Angell, C.A., 1991. Relaxation in liquids, polymers and plastic crystal-strong/fragile patterns and related problems. J. Non-Cryst. Solids 131–133, 13–31. Costa, A., Dell’Erba, F., Di Vito, M. A., Isaia, R., Macedonio, G., Orsi, G., Pfeiffer, T. 2009. Tephra fallout hazard assessment at the Campi Flegrei caldera (Italy). Bulletin of Volcanology 71, 259-273. Di Genova, D., Romano, C., Alletti, M., Misiti, V., Scarlato, P., 2014. The effect of CO2 and H2O on Etna and Fondo Riccio (Phlegrean Fields) liquid viscosity, glass transition temperature and heat capacity. Chemical Geology 377, 72–86.  Dingwell, D.B., 1998. The glass transition in hydrous granitic melts. Physics of the Earth and Planetary Interiors 107, 1-8. Dingwell, D.B., Bagdassarov, N.S., Bussod, G.Y., Webb, S.L., 1993. Magma rheology. Experiments at high pressures and application to the earth's mantle. Mineral. Assoc. Canada Short Course Handbook, vol. 21, pp. 233–333. Eyring, H., Henderson, D., Stover, B.J., Eyring, E.M. Statistical Mechanics and Dynamics, John Wiley eds, Second edition, NY, 1982. 785 pp (ISBN: 0471370428). Giordano, D., D.B. Dingwell, D.B., 2003. Non-Arrhenian multicomponent melt viscosity: a model. Earth Planet. Sci. Lett. 208, 337–349. Giordano, D., Russell, J.K., Dingwell, D.B., 2008. Viscosity of magmatic liquids: A model. Earth and Planetary Science Letters 271, 123–134.  Giordano, D., Romano, C., Papale, P., Dingwell, D.B., 2004a. The viscosity of trachytes, and comparison with basalts, phonolites, and rhyolites. Chemical Geology 213, 49–61.  Giordano, D., Romano, C., Poe, B., Dingwell, D.B., Behrens, H., 2004b. The combined effects of water and fluorine on the viscosity of silicic magmas. Geochim. Cosmochim. Acta 68, 5159–516. Giordano, G., De Rita, D., Cas, R., Rodani, S., 2002. Valley pond and ignimbrite veneer deposits in the small-volume phreatomagmatic ‘Peperino Albano’ basic ignimbrite, Lago Albano maar, Colli Albani volcano, Italy: influence of topography. Journal of Volcanology and Geothermal Research 118, 131-144. Giordano, D., Mangiacapra, A., Potuzak, M., Russell, J.K., Romano, C., Dingwell, D.B., Di Muro, A., 2006. An expanded non-Arrhenian model for silicate melt viscosity: A treatment for metaluminous, peraluminous and peralkaline liquids. Chemical Geology 229, 42–56. Fulcher, G.S., 1925. Analysis of recent measurements of the viscosity of glasses. J. Am. Ceram. Soc. 8, 339-335. Hess, K.U, Dingwell, D.B., 1996. Viscosities of hydrous leucogranitic melts: A non-Arrhenian model. Am. Mineral. 81, 1297–1300. Hui, H., Zhang, Y., 2007. Towards a general viscosity equation for natural anhydrous and hydrous silicate melts. Geochimica et Cosmochimica Acta 71, 403-416. Kohn, S.C., 2000. The dissolution mechanisms of water in silicate melts: A synthesis of recent data. Mineral. Mag. 64, 389–408.    25 Misiti, V., Vetere, F., Freda, C., Scarlato, P., Behrens, H., Mangiacapra, A., Dingwell, D.B., 2011. A general viscosity model of Campi Flegrei (Italy) melts. Chemical Geology 290, 50–59. Misiti, V., Freda, C., Taddeucci, J., Romano, C., Scarlato, P., Longo, A., Papale, P., Poe, B.T., 2006. The effect of H2O on the viscosity of K-trachytic melts at magmatic temperatures. Chemical Geology 235, 124–137.  Mysen, B.O., 1988. Structure and properties of silicate melts. Elsevier, Amsterdam. 354 pp. Myuller, R.L., 1955. A valence theory of viscosity and fluidity for high-melting glass-forming materials in the critical temperature range. Zh. Prikl. Khim. 28, 1077–1087. Orsi, G., De Vita, S., di Vito, M., 1996. The restless, resurgent Campi Flegrei nested caldera (Italy): constraints on its evolution and configuration. Journal of Volcanology and Geothermal Research 74, 179-214. Piochi, M., Polacci, M., De Astis, G., Zanetti, A., Mangiacapra, A., Vannucci, R., Giordano, D., 2008. Texture and composition of pumices and scoriae from the Campi Flegrei caldera (Italy): Implications on the dynamics of explosive eruptions. Geochem. Geophys. Geosyst. 9, n/a–n/a. Plazek, D.J., Ngai, K.L., 1991. Correlation of polymer segmental chain dynamics with temperature-dependent time-scale shifts. Macromolecules 24, 1222–1224 Polacci, M., Papale, P., Del Seppia, D., Giordano, D., Romano, C., 2004. Dynamics of magma ascent and fragmentation in trachytic versus rhyolitic eruptions. Journal of Volcanology and Geothermal Research 131, 93–108. Richet, P., Y. Bottinga, Y., 1995. Rheology and configurational entropy of silicate melts. In: Stebbins, J.F., McMillan, P.F., Dingwell, D.B. (Eds.), Structure, Dynamics and Properties of Silicate Melts. Romano, C., Giordano, D., Papale, P., Mincione, V., Dingwell, D.B., Rosi, M., 2003. The dry and hydrous viscosities of alkaline melts from Vesuvius and Phlegrean Fields. Chemical Geology 202, 23–38. Russell, J.K., Giordano, D., 2005. A model for silicate melt viscosity in the system CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8. Geochimica et Cosmochimica Acta 69, 5333–5349. Russell, J.K., Giordano, D., Dingwell, D.B., K.U. Hess, K.U., 2002. Modelling the non-Arrhenian rheology of silicate melts: Numerical considerations. Eur. J. Mineral. 14, 417–427. Russell, J.K., Giordano, D., Dingwell, D.B., 2004. High-temperature limits on viscosity of non-Arrhenian silicate melts. American Mineralogist 88, 1390–1394.  Vogel, D.H., 1921. Temperaturabhängigkeitsgesetz der Viskosität von Flüssigkeiten. Phys. Z. 22, 645–646. Vona, A., Romano, C., Giordano, D., Russell, J.K., 2013. The multiphase rheology of magmas from Monte Nuovo (Campi Flegrei, Italy). Chemical Geology 346, 213 - 227.      

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