Direct determination of the concentration dependence of diffusivities using combined model-based Raman and NMR experiments

Diffusion in liquids can still be predicted only with high uncertainty due to a lack of sufficient experimental data. Diffusion experiments are complex and time-consuming. Furthermore, the determination of the concentration dependence of the diffusion coefficients requires usually several experiments even for binary mixtures. A powerful model identification framework based on two fast experimental techniques is presented here. Raman inter-diffusion experiments in combination with a novel incremental identification technique establish the concentration dependence directly from the data without requiring a priori specification of the model structure. In regions where this technique is sensitive to error noise, it is complemented with NMR intra-diffusion measurements. Models describing the concentration dependence are identified in two steps. Based on the combined data suitable model candidates are proposed and initialized through basic curve fitting in the first identification step. A statistically sound dynamic optimization step yields the final model parameters. The methodology is exemplarily used to determine the diffusion coefficient in the mixture ethyl acetate–cyclohexane in the full concentration space.