Modelling the viscosity of simple fluids based on Enskog theory


R. Umla1, V. Vesovic1 and N. Riesco1

1Imperial College London, Qatar Carbonates and Carbon Storage Research Centre (QCCSRC), Department of Earth Science & Engineering, South Kensington Campus, London, U.K.

Keywords: Enskog
property: viscosity
material: simple fluids

Industrial process design creates a considerable demand for reliable values of the viscosity of a wide variety of fluid mixtures over extensive ranges of density and temperature. The economic case for improving the accuracy with which viscosity is determined is strong. There is, therefore, a clear need for predictive methods that are accurate, reliable, internally consistent and, as far as possible, based on a solid theoretical understanding of the underlying molecular interactions.

For dense fluids, one has to rely on more approximate approaches, as the lack of rigorous kinetic theory precludes more fundamental developments. Invariably, the starting point of a number of approaches is Enskog formulation [1], that characterizes molecules by a hard sphere diameter. As the Enskog formulation relies on a number of approximations, it is necessary to make use of an effective temperature-dependent diameter to adequately mimic the behaviour of real fluids. However, even then, the Enskog equation lacks correlative power and fails to represent real viscosity data, especially over large density intervals.

 In this work, we propose a new model to compute the viscosity of simple fluids. It is based on Enskog theory and it makes use of two effective diameters to represent two aspects of molecular interactions, namely static and dynamic. The new 2-sigma model outperforms previous approaches based on Enskog theory in terms of correlative power. Molecular dynamics corrections to Enskog theory have also been incorporated to extend the 2-sigma model to very high densities. Moreover, by relating the model parameters to Lennard-Jones parameters, the model can be used to predict the viscosity of real fluids. It is envisaged that the 2-sigma model will be able to provide the viscosity of pure species at conditions where no experimental data exists or where a number of species are grouped as pseudo-components. As such, it would provide an ideal input viscosity data for the VW-method [2-3] that calculates mixture viscosity.

References
  1. S. Chapman and T. Cowling, The Mathematical Theory of Non-uniform Gases (Cambridge University Press, 1970)

  2. V.Vesovic and W.A.Wakeham, Int. J. Thermophys. 10, 125 (1989)

  3. D.D. Royal, V. Vesovic, J.P.M. Trusler, W.A. Wakeham, Mol. Phys. 101, 339 (2003)

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