Interrelated structural chemical model to predict and calculate viscosity of magmatic melts and water diffusion in a wide range of compositions and T-P parameters of the Earth’s crust and upper mantle

Abstract

A new physicochemical model is proposed to predict and calculate the viscosity of magmatic melts and water diffusion as functions of the following parameters: Ptot.; Pfl.; T; melt composition, including volatiles (H2O, OH−, CO2, CO32−, F−, Cl−); cation ratios: Al3+/(Si4+ + Al3+), Al3+/(Na+ + K+ + Ca2+ + Mg2+ + Fe 2+), Fe2+/(Fe2+ + Fe3+), and a volume content of crystals and bubbles (up to 0.45, as applied to magma viscosity). The new model is specified by: (1) structural chemical approach; (2) ultimate simplicity of analytical dependences; (3) high accuracy of the prediction (±30 rel.%), which is consistent with the uncertainties of the experimental data on viscosity and water diffusion, especially at high pressures. The generalized equations suggested for calculating and predicting concentration, temperature, and pressure dependences of the viscosity of magmas and water diffusion are as follows: Viscosity:ηTP=η0exp(EXP/RT), where η0 is a pre-exponent constant for the viscosity of liquids at T → ∞ (η0 = 10−3.5±100.1 dPa·s, or poises); T is the temperature in K; EXP is the activation energy of viscous flow (cal/mole), which is a function of melt composition, including volatile components, and pressure; R = 1.987 (cal/mole·K) is universal gas constant; and ηTP is melt viscosity at the given temperature and pressure, in dPa·s. Water diffusivity: log D(H2O) = –(0.69 log η + 3.74) (depolymerized melts: andesite, basalt), log D(H2O) = –(0.29 log η + 5.35) (polymerized melts: rhyolite, obsidian, albite, dacite), where D(H2O) is the coefficient of water diffusion in cm2/s, η is melt viscosity in dPa·s. A simple computer program developed for calculating the viscosity of magmatic melts and water diffusivity is recommended for modeling magmatic and volcanic processes as well as their dynamics.

Change in the viscosity of kimberlite and basaltic magmas during their origin and evolution (prediction)

“…The criterion for comparison is the total basicity of such melts, which has a decisive influence on their viscosity and is quantified by a structure-chemical parameter (degree of depolymerization or basicity coefficient K = 100⋅NBO/T), rather than the contents of the main rock-forming components of the melts. basaltic melt corresponds to the range of mafic magmas (17 ≤ K ≤ 100), whereas K = 340 for the selected kimberlite melt corresponds to the range of ultramafic magmas (200 < K ≤ 400) (Persikov, 1998;Persikov and Bukhtiyarov, 2009), almost coinciding with the K values for the calculated compositions of primary kimberlite melts (Table 1). Viscosity of kimberlite and basaltic magmas during their evolution.…”

“…Viscosity of kimberlite and basaltic magmas during their evolution. To determine the viscosity of kimberlite and basaltic magmas under a wide range of TP-conditions, the structure-chemical model for the calculation and prediction of the viscosity of magmatic melts was applied (Persikov, 2007;Persikov and Bukhtiyarov, 2009). The model has made it possible to calculate and predict the viscosity of near-liquidus magmatic melts as a function of the following parameters: temperature; lithostatic and fluid pressures; the composition of melt, including volatiles and the forms of their dissolution (H 2 O, OH -, CO 2 , CO 3 2-, F -, and Cl -); relationships of cations in the melts: Al 3+ /(Al 3+ + Si 4+ ), Fe 2+ /(Fe 2+ + Fe 3+ ), Al 3+ /(Na + + K + + Ca 2+ + Mg 2+ + Fe 2+ ); and the volume fraction of crystals and bubbles (up to 45 vol.%).…”

“…The model has made it possible to calculate and predict the viscosity of near-liquidus magmatic melts as a function of the following parameters: temperature; lithostatic and fluid pressures; the composition of melt, including volatiles and the forms of their dissolution (H 2 O, OH -, CO 2 , CO 3 2-, F -, and Cl -); relationships of cations in the melts: Al 3+ /(Al 3+ + Si 4+ ), Fe 2+ /(Fe 2+ + Fe 3+ ), Al 3+ /(Na + + K + + Ca 2+ + Mg 2+ + Fe 2+ ); and the volume fraction of crystals and bubbles (up to 45 vol.%). The main equation for the calculation and prediction of the viscosity of magmatic melts depending on chemical composition, temperature, and pressure is the modified Arrhenius-Frenkel-Eyring theoretical equation (Frenkel', 1975;Persikov and Bukhtiyarov, 2009):…”

“…The influence of the volume fraction of fluid bubbles (V fl ≤ 0.45 or 45 vol.%) on the effective viscosity of subliquidus magmas is taken into account in the model with the use of equation (3) (Pal, 2003;Persikov and Bukhtiyarov, 2009;Persikov et al, 1987;Shaw et al, 1968;Stein and Spera, 2002;Uhira, 1980):…”

“…In the present paper, the structure-chemical model for calculation and prediction of the viscosity of magmas (Persikov, 2007;Persikov and Bukhtiyarov, 2009) and its improved version are used to predict the principle features of the viscosity of basaltic and kimberlite magmas in the processes of their origin in the mantle, evolution during ascent to the crust, and volcanic eruptions.…”