(34i) Transport Properties in Ternary Liquid-Liquid Systems

In chemical engineering extraction plays a crucial role for the purification of products ranging from bulk products to biopharmaceuticals. For the extraction, the mass transfer of the target product across the interface is essential as it determines the residence time and so the dimensions of the extraction unit. The nature of the interface between two fluids has been the subject of science since Young, Laplace and Gauss in the 1800 [1]. All three have the assumption of an interface between two fluids as a surface of zero thickness. On this surface there would be unsteadiness in all physical properties. The idea of an interface with a non-zero thickness was developed in detail by Lord Rayleigh and van der Waals proposing gradient theories for the interface based on thermodynamic principles [1]. Based on the ideas of the gradient theory by Van der Waals, Cahn and Hilliard developed the density gradient theory (DGT), which can be used to calculate interfacial properties in equilibrium and the mass transfer across the interface in non-equilibrium [2]. In contrast to other mass transfer models, the thermodynamics can be directly considered by the inclusion of the Helmholtz free energy in the DGT. Up to now the DGT was used in binary system for the calculations of the mass transfer across the interface [3].

In this work this approach was expanded to ternary mixtures. First, the mass transfer across the interface was experimentally determined using a Nitsch-Cell [4] for the systems toluene-acetone-water (System 1) and heptane-hexane-methanol (System 2). Afterwards the phase equilibra were successfully described by the Koningsveld-Kleintjens model and the interfacial tensions of these systems were modeled by adjusting the influence parameters of the DGT to experimental data of interfacial tension for each system. In addition to the interfacial tension, also the concentration profiles of the components across the interface could be modelled. As a result a strong accumulation of acetone in the interface of System 1 could be observed, but there was only a light accumulation of hexane in System 2. The problem is that this accumulation cannot be verified experimentally. Moreover, the experimental results show, that System 1 shows three times longer equilibration times than System 2. By the modelling of the mass transfer across the interface, it could be shown, that the DGT in combination with Koningsveld-Kleintjens approach can be used to model the mass transfer in good agreement with experimental data.  Hereby, the so called mobility coefficients have to be adjusted to experimental mass transfer data. Comparing the resulting mobility coefficients, it can be seen that in both systems the mobility coefficients are in the same range even though there is a large difference in the equilibration times. This can be a hint for the accumulation at the interface and that it forms a resistance for the mass transfer.

Here, the DGT in combination with a thermodynamic model was firstly compared to experimental data.

References

[1]    D. M. Anderson, G. B. McFadden, A. A. Wheeler “Diffuse-interface methods in fluid mechanics”, Annual review of fluid mechanics 1998, 30, 139-165.

[2]    J. W. Cahn, J. E. Hilliard “Free energy of a nonuniform system. I. Interfacial free energy”, The Journal of chemical physics 1958, 28, 258-267.

[3] A. Kulaguin Chicaroux, A. Gorak, T. Zeiner “ Demixing of Behaviour of binary Polymer Mixtures”, Journal of Molecular Liquids, 2015, 209, 42-49.

[4] Plucinski, P., W. Nitsch, „Mechanism of mass transfer between aqueous phase and water-in-oil microemulsion” Langmuir, 1994, 10, 371-376.