Viscosity of magmatic liquids: A model

The viscosity of silicate melts controls magma transport dynamics, eruption style and rates of physicochemical processes (e.g., degassing, crystallization) in natural magmas. Thus a comprehensive viscosity model for magmatic liquids has long been a goal of earth scientists. Here we present a model that predicts the non-Arrhenian Newtonian viscosity of silicate melts as a function of T and melt composition, including the rheologically important volatile constituents H2O and F. Our model is based on > 1770 measurements of viscosity on multicomponent anhydrous and volatile-rich silicate melts. The non-Arrhenian T-dependence of viscosity is accounted for by the VFT equation [log η = A + B / (T(K) − C)]. The optimization assumes a common, high-T limit (A) for silicate melt viscosity and returns a value for this limit of − 4.55 (+ 0.2) (e.g., log η ~ 10− 4.6 Pa s). All compositional dependence is ascribed to the parameters B and C and is accounted for by an additional 17 model coefficients. Our model is continuous in composition- and temperature-space and predicts the viscosity of natural volatile-bearing silicate melts (SiO2, Al2O3, TiO2, FeOtot, CaO, MgO, MnO, Na2O, K2O, P2O5, H2O, F2O− 1) over fifteen log units of viscosity (10− 1– 1014 Pa s). The model for viscosity can also predict other transport properties including glass transition temperatures (Tg) and melt fragility (m). We show strong systematic decreases in Tg and m with increasing volatile content. This pattern has implications for predicting styles of volcanic eruption and understanding silicate melt structure. Our model transforms a quarter-century of experimental study of melt viscosities, into a parameterisation having a predictive capacity that makes it relevant to diverse fields of research including: volcanology, geophysics, petrology and material sciences.