Abstract
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 (H2Om) and hydroxyl (OH) 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 DH2Ot as a function of dissolved water concentration CH2Ot and temperature T for each experiment and find that the dependence of DH2Ot on CH2Ot is linear for CH2Ot≲1.8 wt.% and exponential for CH2Ot≳1.8 wt.%. Second, we develop a 1D numerical forward model, using the method of lines, to determine a piece-wise function for DH2OtCH2Ot,T 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 DH2OmCH2Ot,T and the equilibrium constant K for the speciation reaction. Our approach includes three key novelties: (1) functions for diffusivities of H2Ot and H2Om, and the speciation reaction, are minimized simultaneously against a large experimental dataset, covering a wide range of water concentration (0.25≤CH2Ot≤7 wt.%) and temperature (800°C≤T≤1200°C), 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.
Highlights
The diffusion of water through silicate melts is one of the most important processes in volcanic systems
Volcanic eruptions are driven by the buoyancy arising from bubbles that grow when volatiles that are dissolved in the magma diffuse into them (Blower et al, 2001; McBirney and Murase, 1970; Sparks, 1978)
We develop the first 1D numerical model for water diffusion and speciation reaction in silicate melts, which we validate against data from diffusion-couple experiments
Summary
The diffusion of water through silicate melts is one of the most important processes in volcanic systems. Suites of samples quenched after different dwell times are analysed and the spatial distribution of water used to reconstruct diffusivity (Fanara et al, 2013; Nowak and Behrens, 1997; Zhang and Ni, 2010) These studies rarely propagate uncertainties through to the resulting diffusivity models. (2) Those seeking validated and internally-consistent models for diffusivity of molecular water and the equilibrium constant of the speciation reaction, with well-constrained confidence intervals, are directed to Section 5, and Eqs. (3) Those seeking a flexible numerical model that can be used to forward model diffusion and speciation, to inverse model the spatial distributions of water species in natural or experimental samples, and to design experiments and analyse the resulting samples, are directed to section 5, and to the online electronic supplement, where a downloadable MATLAB implementation is available
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