Do ternary liquid mixtures exhibit negative main Fick diffusion coefficients?†
Experimental data on Fick diffusion coefficients of ternary and higher mixtures depend on the reference frame; those which are in common use are associated with the average velocity either with respect to volume, mass or mole number. In this study, the dependence of diffusion coefficients on the reference frame is thoroughly analyzed for three ternary mixtures of different types. The first one, tetralin–isobutylbenzene–dodecane, can almost be considered as ideal, the second one, cyclohexane–toluene–methanol, exhibits liquid–liquid phase separation and the third one, water–ethanol–triethylene glycol, contains three associating species and is also strongly non-ideal. Experimental diffusion coefficient data sampled in the volume reference frame are transformed to the molar and mass reference frames. The required partial molar volumes are derived from present density measurements. Four additional mixtures are considered along a single or two composition paths. A highlight of this study is the existence of a strong similarity of the main diffusion coefficients in the volume and mass reference frames for all considered mixtures. When the excess volume is small, the coefficients in the molar reference frame are also similar. However, for the mixture with a large excess volume (containing water), the diffusion coefficients in the molar reference frame differ significantly, even indicating negative main diffusion coefficients. It is shown that negative main diffusion coefficients appear due to relatively large experimental uncertainties of cross diffusion coefficients, which are propagated and amplified by frame transformation.