Multicomponent phenomenological coefficients

The principles of irreversible thermodynamics may be used to study the species mass and heat conduction transport. In this approach, the diffusion coefficients are defined in terms of the Onsager [102, 103] phenomenological coefficients. For a q component gas mixture, the linearity postulate in irreversible thermodynamics can be employed to obtain the multicomponent mass fiux vectors (Hirschfelder et al. [55], p. 714 Curtiss and Bird [26, 27]) ... 

Thus, the Maxwell-Stefan diffusion coefficients satisfy simple symmetry relations. Onsager s reciprocal relations reduce the number of coefficients to be determined in a phenomenological approach. Satisfying all the inequalities in Eq. (6.12) leads to the dissipation function to be positive definite. For binary mixtures, the Maxwell-Stefan dififusivity has to be positive, but for multicomponent system, negative diffusivities are possible (for example, in electrolyte solutions). From Eq. (6.12), the Maxwell-Stefan diffusivities in an -component system satisfy the following inequality... 

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