On the thermal diffusion in polymer solutions: Case study on bicomponent film drying

Abstract This paper aims to theoretically explain experimental observations regarding the thermal diffusion of polymers in polymer solutions. 3D governing equations for mass and heat diffusion in polymer solutions were derived in the framework of classical irreversible thermodynamics using local equilibrium hypothesis, Onsager reciprocal relations and Prigogine's theory in systems in mechanical equilibrium. The mutual diffusion coefficient, thermal diffusion coefficient and thermal conductivity enter the governing equations as functions of thermodynamic variables and phenomenological coefficients that are bounded to some theoretical constraints. It was shown that the derivative of the linear combination of chemical potentials of polymer and solvent with respect to temperature plays an important role in thermal diffusion in polymer solutions. Thermal diffusion coefficient derived in the model can qualitatively explain the experimental observations in the literature regarding the dependence of thermal diffusion of polymers to molecular weight, polymer chain rigidity and viscosity of the solvent. Numerical simulation of the governing equations for a 1D drying process of polymer solutions indicates that the model is able to capture the effect of thermal diffusion. This effect manifests itself as an increase in local concentration of the solvent on the warm side of a temperature gradient during a solution casting process.