An experimentally-validated numerical model of diffusion and speciation of water in rhyolitic silicate melt

The diffusion of water through silicate melts is a key process in volcanic systems. Diffusion controls the growth of the bubbles that drive volcanic eruptions and determines the evolution of the spatial distribution of dissolved water during and after magma mingling, crystal growth, fracturing and fragmentation, and welding of pyroclasts. Accurate models for water diffusion are therefore essential for forward modelling of eruptive behaviour, and for inverse modelling to reconstruct eruptive and post-eruptive history from the spatial distribution of water in eruptive products. Existing models do not include the kinetics of the homogeneous species reaction that interconverts molecular () and hydroxyl () water; reaction kinetics are important because final species distribution depends on cooling history. Here we develop a flexible 1D numerical model for diffusion and speciation of water in silicate melts. We validate the model against FTIR transects of the spatial distribution of molecular, hydroxyl, and total water across diffusion-couple experiments of haplogranite composition, run at 800–1200°C and 5 kbar. We adopt a stepwise approach to analysing and modelling the data. First, we use the analytical Sauer-Freise method to determine the effective diffusivity of total water as a function of dissolved water concentration and temperature for each experiment and find that the dependence of on is linear for wt.% and exponential for wt.%. Second, we develop a 1D numerical forward model, using the method of lines, to determine a piece-wise function for that is globally-minimized against the entire experimental dataset. Third, we extend this numerical model to account for speciation of water and determine globally-minimized functions for diffusivity of molecular water and the equilibrium constant for the speciation reaction. Our approach includes three key novelties: 1) functions for diffusivities of and , and the speciation reaction, are minimized simultaneously against a large experimental dataset, covering a wide range of water concentration ( wt.%) and temperature (), such that the resulting functions are both mutually-consistent and broadly applicable; 2) the minimization allows rigorous and robust analysis of uncertainties such that the accuracy of the functions is quantified; 3) the model can be straightforwardly used to determine functions for diffusivity and speciation for other melt compositions pending suitable diffusion-couple experiments. The modelling approach is suitable for both forward and inverse modelling of diffusion processes in silicate melts; the model is available as a Matlab script from the electronic supplementary material

Rheology of three-phase suspensions determined via dam-break experiments

Three-phase suspensions, of liquid that suspends dispersed solid particles and gas bubbles, are common in both natural and industrial settings. Their rheology is poorly constrained, particularly for high total suspended fractions (0.5). We use a dam-break consistometer to characterize the rheology of suspensions of (Newtonian) corn syrup, plastic particles and CO2 bubbles. The study is motivated by a desire to understand the rheology of magma and lava. Our experiments are scaled to the volcanic system: they are conducted in the non-Brownian, noninertial regime; bubble capillary number is varied across unity; and bubble and particle fractions are 0 ≤ φgas ≤ 0.82 and 0 ≤ φsolid ≤ 0.37, respectively. We measure flow-front velocity and invert for a Herschel–Bulkley rheology model as a function of φgas, φsolid, and the capillary number. We find a stronger increase in relative viscosity with increasing φgas in the low to intermediate capillary number regime than predicted by existing theory, and find both shear-thinning and shear-thickening effects, depending on the capillary number. We apply our model to the existing community code for lava flow emplacement, PyFLOWGO, and predict increased viscosity and decreased velocity compared with current rheological models, suggesting existing models may not adequately account for the role of bubbles in stiffening lavas