Modelling the viscosity of anhydrous and hydrous volcanic melts

The viscosity of volcanic melts is a dominant factor in controlling the fluid dynamics of magmas and thereby eruption style. It can vary by several orders of magnitude, depending on temperature, chemical composition, and water content. The experimentally accessible temperature range is restricted by melt crystallization and gas exsolution. Therefore, modeling viscosity as a function of temperature and water content is central to physical volcanology. We present a model that describes these dependencies by combining a physically motivated equation for temperature dependence of viscosity and a glass transition temperature (urn:x-wiley:15252027:media:ggge22604:ggge22604-math-0001) model for the effects of water. The equation uses the viscosity at infinite temperature urn:x-wiley:15252027:media:ggge22604:ggge22604-math-0002, urn:x-wiley:15252027:media:ggge22604:ggge22604-math-0003, and the steepness factor urn:x-wiley:15252027:media:ggge22604:ggge22604-math-0004 as fitting parameters. We investigate the effect of leaving urn:x-wiley:15252027:media:ggge22604:ggge22604-math-0005 free as a parameter and fixing its value, by fitting anhydrous viscosity data of 45 volcanic melts using the temperature dependent model. Both approaches describe experimental data well. Using a constant urn:x-wiley:15252027:media:ggge22604:ggge22604-math-0006 therefore provides a viable route for extrapolating viscosity from data restricted to small temperature intervals. Our model describes hydrous data over a wide compositional range of terrestrial magmas (26 data sets) with comparable or better quality than literature fits. With urn:x-wiley:15252027:media:ggge22604:ggge22604-math-0007 constrained, we finally apply our model to viscosities derived by differential scanning calorimetry and find—by comparing to viscometry based data and models—that this approach can be used to reliably describe the dependence of viscosity on temperature and water content. This introduces important implications for modeling the effects of nanostructure formation on viscosity.