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: [GRAPHICS] where eta 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 H(2)O. 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: log eta = 1-6.83X(SiO2), - 170.79X(TiO2) - 14.71X(Al2O3ex) - 18-01X(MgO) - 19.76X(CaO) + 34.31X((Na,K)2Oex) -140.38Z + 159.26X(H2O) - 8.43X((Na,K)AlO2)] + [18.14X(SiO2) + 248-93X(TiO2) + 32.61X(Al2O3ex) + 25.96X(MgO) + 22.64X(CaO)- 68.29X((Na,K)2Oex) + 38.84Z - 48.55X(H2O) + 16.12X((Na,K)AlO2)]1000/T + exp{[21.73X(Al2O3ex) - 61.98X((Fe, Mn)O) - 105.53X(MgO) - 69.92X(CaO) - 85.67X((Na,K)2Oex) + 332.01Z - 432.22X(H2O) - 3-16X((Na,K)AlO2)] + [2.16X(SiO2) - 143.05X(TiO2) - 22.10X(Al2O3ex) + 38.56X((Fe, Mn)O) + 110.83X(Mgo) + 67.12X(CaO) + 58-01X((Na,K)2Oex) + 384.77X(P2O5) - 404.97Z + 513.75X(H2O)]1000/T}, where eta is the viscosity in Pa s, T is the temperature in K, X(i) means mole fraction of oxide component i, and Z = (X(H2O))(l/[1+(185.797/T)]). Al(2)O(3ex) or (Na,K)(2)O(ex) mean excess oxides after forming (Na,K)AlO(2). The 2 sigma deviation of the fit is 0.61 log eta units. This general model is recommended for viscosity calculations in modeling magma chamber processes and volcanic eruptions. (c) 2006 Elsevier Inc. All riahts reserved.