Multi-component diffusion in polymer solutions

In the present work a comprehensive methodology is proposed for calculating the Fickian diffusion coefficients in a multi-component solvents-polymer system as a function of the solvents self-diffusion coefficients, the constituent chemical potentials and the process conditions. This methodology is based on the application of well-established principles such as the Gibbs-Duhem theorem for diffusing systems along with the friction coefficient concepts. The case of constant friction coefficient ratios is re-examined leading to a screening of the existing theories for multi-component polymer systems. Finally, the described methodology is applied to the formamide-acetone-cellulose acetate (CA) system which is used in the asymmetric membrane manufacture. The acetone evaporation process from this system is studied as a one-dimensional numerical experiment. For this purpose, the evaporation process is modeled as a coupled heat and mass transfer problem with a moving boundary. The Galerkin finite element method is used to simultaneously solve the non-linear governing equations. All the model parameters were estimated from literature measurements leading to a fully predictive model. The model predictions are in excellent agreement with experimental data for polymer solution weight and surface temperature vs. time thus validating the applied methodology for the calculation of friction coefficients.