Toward a general viscosity equation for natural anhydrous and hydrous silicate melts

A new and empirical viscosity equation for anhydrous and hydrous natural silicate melts has been developed using the following formulation:logη=A+BT+expC+DT,where η is the viscosity, T is the temperature in K, and A, B, C, and D are linear functions of mole fractions of oxide components except for H2O. The formulation is applied successfully to fit the temperature and compositional dependence of viscosity for some binary systems. Furthermore, our model with eight parameters fits the compositional and temperature dependence of the viscosity data of anhydrous natural silicate melts better than 10-parameter model in literature. The main purpose of this work is to fit the entire high- and low-temperature viscosity database (1451 data points) of all “natural” silicate melts using this empirical formulation. The general viscosity equation has 37 parameters and is as follows: logη=[-6.83XSiO2-170.79XTiO2-14.71XAl2O3ex-18.01XMgO-19.76XCaO+34.31X(Na,K)2Oex-140.38Z+159.26XH2O-8.43X(Na,K)AlO2]+[18.14XSiO2+248.93XTiO2+32.61XAl2O3ex+25.96XMgO+22.64XCaO-68.29X(Na,K)2Oex+38.84Z-48.55XH2O+16.12X(Na,K)AlO2]1000/T+exp{[21.73XAl2O3ex-61.98X(Fe, Mn)O-105.53XMgO-69.92XCaO-85.67X(Na,K)2Oex+332.01Z-432.22XH2O-3.16X(Na,K)AlO2]+[2.16XSiO2-143.05XTiO2-22.10XAl2O3ex+38.56X(Fe, Mn)O+110.83XMgO+67.12XCaO+58.01X(Na,K)2Oex+384.77XP2O5-404.97Z+513.75XH2O]1000/T},logη=[-6.83XSiO2-170.79XTiO2-14.71XAl2O3ex-18.01XMgO-19.76XCaO+34.31X(Na,K)2Oex-140.38Z+159.26XH2O-8.43X(Na,K)AlO2]+[18.14XSiO2+248.93XTiO2+32.61XAl2O3ex+25.96XMgO+22.64XCaO-68.29X(Na,K)2Oex+38.84Z-48.55XH2O+16.12X(Na,K)AlO2]1000/T+exp{[21.73XAl2O3ex-61.98X(Fe, Mn)O-105.53XMgO-69.92XCaO-85.67X(Na,K)2Oex+332.01Z-432.22XH2O-3.16X(Na,K)AlO2]+[2.16XSiO2-143.05XTiO2-22.10XAl2O3ex+38.56X(Fe, Mn)O+110.83XMgO+67.12XCaO+58.01X(Na,K)2Oex+384.77XP2O5-404.97Z+513.75XH2O]1000/T},where η is the viscosity in Pa s, T is the temperature in K, Xi means mole fraction of oxide component i  , and Z=(XH2O)1/[1+(185.797/T)]Z=(XH2O)1/[1+(185.797/T)]. Al2O3exAl2O3ex or (Na,K)2Oex mean excess oxides after forming (Na,K)AlO2. The 2σ deviation of the fit is 0.61 log η units. This general model is recommended for viscosity calculations in modeling magma chamber processes and volcanic eruptions.