Diffusion of Water in Silicate Melts

Abstract

The transport of water in silicate melts is examined from a theoretical point of view, taking into account the presence of both H_2O and OH^- species. It was assumed that only H_2O molecules may diffuse and that a constitutive relationship between the number density nH_2O of H_2O molecules and the total water content (n_Σ) exists such that nH_2O = g(n_Σ). This is related to dissociation or to chemical reactions such as H_2O molecular (melt) + Oxygen (melt) ⇌ 2 OH (melt). This approach leads to diffusion transport equations that are intrinsically nonlinear. Three regions are naturally defined: (I) high water content with a normal linear diffusion equation an: ∂n_Σ/∂t = DV^2n_Σ, where D is the intrinsic diffusion coefficient of a H_2O molecule in the silicate; (II) an intermediate or transitional region where the transport equation is ∂n_Σ/∂t = DV^2g(n_Σ); and (III) a region of low water concentration where the transport equation is an: ∂n_Σ/∂t = D^*V^2n^2_Σ. In the latter region, the equation is strongly nonlinear. D^* is a constant diffusion coefficient related to D. It follows that the dissociation of water molecules to form OH^- in silicates automatically implies a nonlinear transport behavior due to the storage of dissociated water molecules in immobile sites. This study of the kinetics of transport will aid in our understanding of speciation and structure in silicate melts.

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