Diffusive crystal dissolution

Abstract

Crystal dissolution may include three component processes: interface reaction, diffusion and complications due to convection. We report here a theoretical and experimental study of crystal dissolution in silicate melt without convection. A reaction-diffusion equation is developed and numerically solved. The results show that during non-convective crystal dissolution in silicate melt, the interface melt composition reaches a constant or stationary “saturation” composition in less than a second, hence interface reaction is not the rate-determining step and crystal dissolution in silicate melt is usually diffusion-controlled. Crystal dissolution experiments (designed to suppress convection) show that the concentration profiles of all components propagate into the melt according to the square root of run duration, and that the dissolution distance is also proportional to the square root of run duration. Thus our experiments confirm that the dissolution is diffusion controlled, which is consistent with our numerical calculations. For some principal equilibrium-determining components, concentration profiles conform approximately to the analytical solution of the diffusion equation with a constant effective binary diffusion coefficient. Diffusive dissolution rates (which are inversely proportional to square root of time) can thus be predicted from the phase equilibria and the effective binary diffusion coefficients. To predict steady-state convective dissolution rates, the thickness of the boundary layer must be known. If the convective compositional boundary layer thickness around a dissolving crystal aggregate or near the wall of a magma chamber during convection is about 2 cm or larger, then convective dissolution would rarely result in any significant alteration of original melt. Our dissolution experiments also illustrate the complexity of the diffusion process. Uphill diffusion is common, especially during olivine dissolution into andesitic melt where a majority of the components show the effect of diffusion up their own concentration gradients. Uphill diffusion has implications to the understanding of crystal zoning, and suggests caution is required in applying least squares mass balance analysis to magmatic rocks affected by processes involving diffusion.