Granitic melt viscosities; empirical and configurational entropy models for their calculation

Newly measured viscosities of a low H₂O-content granitic melt and a low H₂O-content albitic melt have been combined with viscosity data from the literature to create two new models for the calculation of granitic melt viscosities at crustal pressures and temperatures between 700 and 900 °C; one model is purely empirical, and the other is based on configurational entropy theory. When the molecular weight of the anhydrous melt is calculated on the basis of eight O atoms, or assumed to be 260 gram formula weight (gfw), and the total H₂O concentration is expressed by its mole fraction, the viscosity, η, of per- and metaluminous granitic melts, ∼70-76 wt% SiO₂, can be calculated from the following empirical equations: For $XH2Otot≤0.25$, and for $XH2Otot>0.25$, where viscosity is in pascal-seconds, and temperature, T, is in kelvins. The first equation expresses the effects of H₂O addition on melt viscosity at low H₂O contents where the predominant H₂O species in the melt is OH⁻ (as demonstrated in previous studies) and small additions of H₂O have large effects on melt viscosity; above $XH2Otot≈0.25$, molecular H₂O is the dominant species of H₂O, the addition of which has only modest effects on melt viscosities. This empirical model is applicable to granitic melts with total H₂O contents between 0.3 and 12.3 wt%. Following configurational entropy theory, viscosities of the same hydrous granitic melts can be calculated by modeling the viscosities as ternary mixtures of various mole fractions of molecular H₂O, XH₂O, OH⁻, X_OH⁻, and silicate melt, X_{silicate melt}: ln η = −15.398 + [181.622/{T[S_conf(X_{silicate melt}) − R(CH₂OXH₂O ln XH₂O + C_OH⁻X_OH⁻ ln X_OH⁻ + C_{silitate melt}X_{silicate melt} ln X_{silicate melt})]}], where S_conf, the configurational entropy calculated from the viscosity measurements, is 4.567 × 10⁻³ J/(mol·K); R is the gas constant, 8.314 J/(mol·K); CH₂O is −1.899 × 10⁻³; C_OH⁻ is −1.531 × 10⁻³; and C_{silicate melt} is 4.913 × 10⁻³. Mole fractions of H₂O and OH⁻ are estimated from previously published measurements of species abundances in quenched rhyolitic glasses, and the molecular weight of the silicate melt is 260 gfw. Application of this model is limited to melts with a maximum of approximately 6 wt% total H₂O because XH₂O−X_OH⁻ speciation information is not available at higher H₂O contents. Numerical values in the above equation are not considered to have any physical or chemical significance. Calculated granitic melt viscosities deviate on average from measured viscosities by −0.03 log units for the empirical model and −0.2 log units for the configurational entropy model. At H₂O concentrations below 4 wt% and above 7 wt%, these models for viscosity estimation are significantly better than previous models, which can be in error by one to two orders of magnitude. Using either of these new models, the viscosities of granitic melts with 1-3 wt% H₂O are calculated to be up to two orders of magnitude lower than previously thought. This results in a one to two order-of-magnitude increase in the viscosities of melt extraction from source regions, transport of melts through the crust, and Stokes settling of crystals.