Geological Notes Diffusion of Water in Silicate Melts

The transport of water in silicate melts is examined from a theoretical point of view, taking into account the presence of both H20 and OH species. It was assumed that only H20 molecules may diffuse and that a constitutive relationship between the number density nH 0 of H20 molecules and the total water content (n:E) exists such that nH,o = g(n:E) . This is related to dissociation or to chemical reactions such as H20 molecular ~me.lt) . + Oxyge~ (melt) +:t 2 0~ (melt) . This approach leads to diffusion transport equations that are mtnnstcally nonhnear. Three reg10ns are naturally defined: (I) high water content with a normal linear diffusion equation an:Eiirr = DV2n:!:, where D is the intrinsic diffusion coefficient of a H20 molecule in the silicate; (I~) an intermediate or transitional region where the transport equation is an:!:/a-r = DV2g(n:E) ; and (III) a reg10n of low water concentration where the transport equation is an:!:/a-r = D*V 2n3;. 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 .