Development of a model for the Description of Intra-diffusion in Homogeneous Liquid Lennard–Jones Mixtures

Abstract

A model for calculation of intra-diffusion coefficients of homogeneous liquid 1-centre Lennard–Jones (LJ) mixtures is proposed. As starting point for deriving this model we have chosen the model of Liu et al. [Chem. Eng. Sci. 53, (1998), 2403–2422] suggested for calculation of the self-diffusion coefficients of pure LJ model fluids. This model was extended to liquid mixtures by introducing suitable combining and mixing rules for description of different characteristics of the mixture components. The five parameters of the model were determined from data obtained by molecular-dynamics (MD) simulations performed in this work. To generate a database for intra-diffusion coefficients the method of optimal experiment design is employed. This method is applied to plan simulations in such a way as to obtain optimal estimates of the model parameters. The parameters were determined based on the range of temperatures 90 < T<350 K and mass densities 200 < ρ ^M<2580 kg/m³ with the total average absolute deviation of 5.56%. The suggested model was tested on the data available in literature concerning intra-diffusivities of 1-centre LJ liquid mixtures. The prediction accuracy of 42 data points is 13.08%. Further work will be directed at further optimisation of model structure and model parameters.

Keywords:

• Intra-diffusion
• Homogeneous liquid mixture
• Lennard–Jones mixture
• Molecular-dynamics

Acknowledgements

We are grateful for the support for implementation of the procedure of experimental design by Dipl.–Ing André Bardon of the chair of process systems engineering at the RWTH Aachen University. This project was funded by the German Science foundation in the framework of the collaborative research center 540 ‘model-based experimental analysis of kinetic phenomena in fluid multi-phase reactive systems’.