Modelling of the multi-component concentration-dependent diffusion

Diffusion in a dense multi-component mixture needs a special approach for proper mathematical description, because the traditional system of the diffusion equations with the diagonal matrix ignores interaction between the mixture components. Thus in dense liquid or solid media it may be used at best as an initial approximation. At the same time it is important to keep the positivity of concentrations, which may be easily violated in case of a constant non-diagonal diffusion matrix, even if it is kept symmetric and positively defined. Therefore, the multi-component diffusion matrix should be not constant. A promising approach consists in using the cell-jump formalism, which provides the concentration-dependent diffusion matrix. In this paper we apply it to the description of two different admixtures that diffuse simultaneously from two sides of a tube. We compare the numerical results, obtained by the traditional and the cell-jump models, with the analytical solutions in both cases and prove the advantages of the cell-jump description. In spite of tending to the same final concentration distribution, the models demonstrate different types of evolution and remarkably different characteristic times. The obtained results may be applied in modelling various lithium salts diffusion in polyethylene oxide medium, which is important for the development of lithium-ion batteries.