Nonparabolic diffusion in ternary solutions

The generalized Darken method (GDM) of interdiffusion is based on the concept of separation of diffusional and drift flows. Together with the equation of mass conservation it gives the conventional diffusion equation in the case of binary solutions. The Darken concept applied to the general case of diffusional transport in r-component solution results in the system of r-partial differential equations and the equation of state. Here GDM is applied to simulate the interdiffusion in ternary solutions. We present the evolution of component distributions in closed systems and for specific initial distributions. These results are presented to bring out classical diffusional structures and diffusion paths observed for ternary systems (parabolic diffusion). It has been shown that if the GDM is parabolic in a generalized sense, then the spatially averaged deviations of mole fractions of the mixture components from their means decrease monotonically to zero as time approaches infinity. In this work we analyze a class of the GDM's in which this decreasing behaviour is not valid (nonparabolic diffusion). By selecting an appropriate set of the initial concentrations of the components and their intrinsic diffusivities we show the nonparabolic diffusion in ternary system. The presented example of a ternary system yielding the nonparabolic diffusion was constructed by imposing extra conditions on the model parameters to reduce their number and simplify the relationships between them. A computer program was developed to follow this approach for the presented example of a ternary system. Interpretation of such unusual nonparabolic diffusion is presented.