Modeling the transport of low molecular weight metal complexes across the liquid–liquid interface during extraction in a synthetic boundary cell by using the finite differences method

Abstract

We determine transport parameters such as the diffusion coefficient, D, the integral mass flux and the transfer coefficient across the liquid–liquid interface, α, in solvent extraction systems by using analytical ultracentrifugation, emphasizing extraction systems with chemical reaction at the liquid–liquid interface. If this reaction is fast, the transport process is diffusion-limited. The experimental data of dichromate extraction by tertiary amine represent such diffusion-limited transport. They can be described according to the second transport law with the parameters D, c, α and K _D by applying the model of Scott and Drickamer of diffusion-limited transport. However, by solving the second transport law by Laplace transformation as previously, we cannot take into account any chemical reaction kinetics, which plays an important role in many other systems, such as the extraction of Re(VII), which is also reported here. In order to be able to describe the transport across interfaces where chemical reactions take place, we developed a numeric solution based on finite differences.

Acknowledgements. We appreciate the discussion about the role of the interfacial reaction and on coupled transport phenomena with Prof. Dr. W. Nitsch (TU München). We also highly appreciate the help of Dr. B. Plewinsky (on leave from BAM Berlin) in providing relevant literature concerning analytical ultracentrifugation. Support for this project by the DFG (reference no. Lu 573/5-1+2 in terms of SPP 1105) is highly appreciated. R.L. appreciates a grant by the Stiftung Industrieforschung as well as support by the Fonds der chemischen Industrie.