A MODIFIED EFFECTIVE BINARY DIFFUSION-MODEL

Uphill diffusion, the diffusion of a component up its own concentration gradient, has often been observed in experimental studies of diffusion in synthetic multicomponent systems and natural silicate melts. To apply experimental data to natural processes, it is necessary to quantify this effect. A modified effective binary diffusion model is developed in this paper. The diffusive flux of a component is assumed to be proportional to its activity gradient (instead of concentration gradient). The activity coefficient is related to its concentration at quasi-equilibrium distribution in a compositional continuum with the help of the two-liquid partition concept. The concentration at quasi-equilibrium distribution is approximately expressed as a simple function of SiO2 or SiO2+Al2O3 concentration. The diffusion of SiO2 or SiO2+Al2O3 is assumed to be effectively binary. With these assumptions, diffusion of a major or trace component can be described by two adjustable parameters, D (the intrinsic effective binary diffusivity) and Cf (a parameter related to two-liquid partition coefficients). The simple model fits well the experimental uphill diffusion profiles produced by diffusive crystal dissolution into an andesitic melt using constant diffusivities when compositional variation across the whole profile is small. The parameters fit to the profiles are generally physically meaningful. The model is able to predict the direction of diffusion (occurrence or absence of uphill diffusion) in previous experiments and can be used to simulate the development of chemical concentration and isotopic ratio profiles during diffusion. When compositional dependence of diffusivities is allowed, the model may be applied to systems with greater compositional variation. This model can be tested in several ways and should be useful in studying diffusion in a variety of natural systems.