A Simple Model for the Viscosity of Rhyolites as a Function of Temperature, Pressure and Water Content: Implications for Obsidian Flow Emplacement

Understanding the dynamics of rhyolitic conduits and lava flows, requires precise knowledge of how viscosity (η) varies with temperature (T), pressure (P) and volatile content (X). In order to address the paucity of viscosity data for high-silica rhyolite at low water contents, which represent water saturation at near-surface conditions, we made 245 viscosity measurements on Mono Craters (California) rhyolites containing between 0.01 and 1.1 wt.% H₂O, at temperatures between 796 and 1774 K using parallel plate and concentric cylinder methods at atmospheric pressure. We then developed and calibrated a new empirical model for the log of the viscosity of rhyolitic melts, where non-linear variations due to temperature and water content are nested within a linear dependence of log η on P. The model was fitted to a total of 563 data points: our 245 new data, 255 published data from rhyolites across a wide P-T-X space, and 63 data on haplogranitic and granitic melts under high P-T conditions. Statistically insignificant parameters were eliminated from the model in an effort to increase parsimony and the final model is simple enough for use in numerical models of conduit or lava flow dynamics:

log η = -5.142+(13080-2982log⁡(w+0.229))/(T-(98.9-175.9 log⁡(w+0.229)))- P(0.0007-0.76/T )

where η is in Pa s, w is water content in wt.%, P is in MPa and T is in K. The root mean square deviation (rmsd) between the model predictions and the 563 data points used in calibration is 0.39 log units. Experimental constraints have led previously to spurious correlations between P, T, X and η in viscosity data sets, so that predictive models may struggle to correctly resolve the individual effects of P, T and X, and especially their cross-correlations. The increasing water solubility with depth inside a simple isothermal sheet of obsidian suggests that viscosity should decrease by ~1 order of magnitude at ~20m depth and by ~2 orders of magnitude at ~100m depth. If equilibrium water contents are maintained, then deformation in spreading obsidian flows should be strongly partitioned into the deeper parts of the flow. Kinetically inhibited degassing, or recycling of degassed crust into a flow interior (e.g. by caterpillar-tread motion) could lead to strong lateral variations in viscosity within a flow, affecting flow evolution and morphology.