Form of multicomponent Fickian diffusion coefficients matrix

The form of multicomponent Fickian diffusion coefficients matrix in thermodynamically stable mixtures is established based on the form of phenomenological coefficients and thermodynamic factors. While phenomenological coefficients form a symmetric positive definite matrix, the determinant of thermodynamic factors matrix is positive. As a result, the Fickian diffusion coefficients matrix has a positive determinant, but its elements — including diagonal elements — can be negative. Comprehensive survey of reported diffusion coefficients data for ternary and quaternary mixtures, confirms that invariably the determinant of the Fickian diffusion coefficients matrix is positive.

► Irreversible thermodynamics establishes form of multicomponent diffusion coefficients.
► Phenomenological coefficients and thermodynamic factors affect sign of diffusion coefficients.
► Negative diagonal elements of diffusion coefficients matrix can occur in non-ideal mixtures.
► Eigenvalues of the matrix of Fickian diffusion coefficients may not be all real.