Onsager Reciprocal Relations for Stefan−Maxwell Diffusion

The choice of diffusional driving forces and fluxes such that a sum of their products yields the entropy generation rate does not generally lead to a system with a symmetric transport matrix. One can apply Onsager's fluctuation theory to a mass-transfer system with various driving forces, such as gradients of mole fraction, concentration, or chemical potential, and obtain a proper reciprocal relation among the transport properties so defined. Although Stefan−Maxwell coefficients are generally not symmetric, 𝒟 ij ≠ 𝒟 ji, Onsager's theory still supplies the reciprocal relation. This work employs these principles to derive the reciprocal relation among Stefan−Maxwell coefficients for isothermal, isobaric mass diffusion, with an illustration for ideal solutions.