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, Dij not equal Dji, 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
Monroe, CW., & Newman, J. (2006). Onsager reciprocal relations for Stefan-Maxwell diffusion. Industrial & Engineering Chemistry Research, 45(15), 5361-5367.