This work examines diffusion in ternary non-ideal systems and derives coupled non-linear equations based on a non-equilibrium thermodynamic approach in which an explicit expression for the free energy is substituted into standard diffusion equations. For ideal solutions, the equations employ four mobility parameters (Maa, Mab, Mba, and Mbb), and uphill diffusion is predicted for certain initial conditions and combinations of mobilities. For the more complex case of ternary Simple Mixtures, two non-ideality parameters (χac and χbc) that are directly related to the excess free energy of mixing are introduced. The solution of the equations is carried out by means of two different numerical schemes: (1) spectral collocation and (2) finite element. An error minimization technique is coupled with the spectral collocation method and applied to diffusional profiles to extract the M and χ parameters. The model satisfactorily reproduces diffusional profiles from published data for silicate melts. Further improvements in numerical and experimental techniques are then suggested.
Bibliographical noteFunding Information:
The authors thank the Marie Curie Individual Fellowship Programme (A.C.) and British Petroleum International for financial support (S.E. and B.B.).
- Non-ideal solutions
- Silicate melts
- Ternary mixtures
- Uphill diffusion