Theoretical model of thermal diffusion factors in multicomponent mixtures

Unlike molecular diffusion, neither measured thermal diffusion coefficients nor the theoretical framework exist for the estimation of thermal diffusion coefficients in nonideal multicomponent mixtures. This work derives a theoretical model for thermal diffusion coefficients in ideal and nonideal multicomponent mixtures, based on the thermodynamics of irreversible processes and the molecular kinetic approach incorporating explicit effects of nonequilibrium properties such as the net hear of transport and molecular diffusion coefficients, and of equilibrium properties of the mixture, which are determined by the Peng-Robinson equation of stare. An interesting feature of this model is that in nonideal multicomponent mixtures thermal diffusion coefficients depend on molecular diffusion coefficients, while in binary mixtures they do not. The model successfully describes thermal diffusion factors of binary mixtures for which experimental data are available, even those in extreme nonideal conditions and close to the critical point. Since experimental data on thermal diffusion factors in multicomponent hydrocarbon mixtures are not available, testing the model's accuracy was not possible. The model, however, successfully predicted spatial variation of composition in a ternary mixture of nC(24)/nC(16)/nC(12), providing an indirect verification. The situ-component mixture of C-1/C-3/nC(5)/nC(10)/nC(16)/C-12 shows significant dependency of thermal diffusion factors on the distance to the critical point. A also demonstrates for the first time that there is no need to adopt a sign convention for thermal diffusion coefficients in binary and higher mixtures. The thermodynamic stability analysis shows that when the thermal diffusion coefficient is positive the component should go to the cold region in a binary mixture.