- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Thermodynamic approach to momentum transport in dense fluids

Christopher Devik Fjeldstad1,*, Jonas Bueie2,†, and Astrid S. de Wijn1,‡

  • *Contact author: christopher.fjeldstad@ntnu.no
  • †Contact author: jonas.bueie@ntnu.no
  • ‡Contact author: astrid.dewijn@ntnu.no
PDF

Phys. Rev. Research 8, 043132 – Published 5 November, 2026

DOI: https://doi.org/10.1103/5z8g-qwyf

Abstract

We present a framework for extending Chapman-Enskog theory beyond the hard-sphere fluid model. Rather than relying on effective hard-sphere diameters, the approach makes use of an exchange function that can be related to the thermodynamic properties of the system. We show that two existing extensions, including modified Enskog theory (MET), fit into this framework. Based on our approach, we propose an alternative to MET that takes into account the potential interaction energy associated with the interparticle interactions in the fluid. The proposed expression is applied to predicting the shear viscosity of several different simulated fluid models across a wide set of densities 0.05≤ρ*≤0.8 and temperatures 1.5≤T*≤4.0 in Lennard-Jones (LJ) units. The fluid models considered include both the Weeks-Chandler-Andersen (WCA) fluid and the LJ fluid. At low and intermediate densities, here taken to be ρ*≤0.3, we report mean relative prediction errors between 2% and 4% for both of these. Across all densities considered, the largest mean relative errors reported are 4.4% and 8.1% for the WCA fluid and LJ fluid, respectively. We also investigate other interaction models, including a diatomic molecular model, in order to better understand the limitations of our approach.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (33)

  1. S. Chapman and T. G. Cowling, The Mathematical Theory of Nonuniform Gases, 3rd ed. (Cambridge University Press, Cambridge, 1970).
  2. J. G. Kirkwood, The statistical mechanical theory of transport processes I. General theory, J. Chem. Phys. 14, 180 (1946).
  3. J. Dymond, Corrections to the Enskog theory for viscosity and thermal conductivity, Physica B+C 144, 267 (1987).
  4. E. Yusibani, Y. Takata, Z. Suud, and D. Irwanto, The prediction of helium gas viscosity under high pressure and high temperature with the Chapman-Enskog solution and excess viscosity, J. Phys.: Conf. Ser. 799, 012008 (2017).
  5. J. G. Kirkwood, F. P. Buff, and M. S. Green, The statistical mechanical theory of transport processes. III. The coefficients of shear and bulk viscosity of liquids, J. Chem. Phys. 17, 988 (1949).
  6. A. S. de Wijn, V. Vesovic, G. Jackson, and J. P. M. Trusler, A kinetic theory description of the viscosity of dense fluids consisting of chain molecules, J. Chem. Phys. 128, 204901 (2008).
  7. R. Umla, N. Riesco, and V. Vesovic, Viscosity of pure fluids—Enskog-2σ model, Fluid Phase Equilib. 334, 89 (2012).
  8. R. Umla and V. Vesovic, Viscosity of liquids—Enskog-2σ model, Fluid Phase Equilib. 372, 34 (2014).
  9. M. Robles and L. I. Uruchurtu, Theoretical scheme for the shear viscosity of Lennard-Jones fluids, J. Chem. Phys. 124, 094112 (2006).
  10. V. G. Jervell and Ø. Wilhelmsen, Revised Enskog theory for Mie fluids: Prediction of diffusion coefficients, thermal diffusion coefficients, viscosities, and thermal conductivities, J. Chem. Phys. 158, 224101 (2023).
  11. K. M. Dyer, B. M. Pettitt, and G. Stell, Systematic investigation of theories of transport in the Lennard-Jones fluid, J. Chem. Phys. 126, 034502 (2007).
  12. K. Meier, A. Laesecke, and S. Kabelac, Transport coefficients of the Lennard-Jones model fluid. I. Viscosity, J. Chem. Phys. 121, 3671 (2004).
  13. H. J. M. Hanley, R. D. McCarty, and E. G. D. Cohen, Analysis of the transport coefficients for simple dense fluid: Application of the modified Enskog theory, Physica 60, 322 (1972).
  14. J. D. Weeks, D. Chandler, and H. C. Andersen, Role of repulsive forces in determining the equilibrium structure of simple liquids, J. Chem. Phys. 54, 5237 (1971).
  15. J. E. Lennard-Jones, Cohesion, Proc. Phys. Soc. 43, 461 (1931).
  16. Theory and Simulation of Hard-Sphere Fluids and Related Systems, edited by Á. Mulero, Lecture Notes in Physics Vol. 753 (Springer, Berlin, 2008).
  17. J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids, 3rd ed. (Academic Press, Burlington, MA, 2006).
  18. N. F. Carnahan and K. E. Starling, Equation of state for nonattracting rigid spheres, J. Chem. Phys. 51, 635 (1969).
  19. L. Boltzmann, Lectures on Gas Theory (Dover Publications, New York, 1995), Vol. 1, originally published by the University of California Press, Berkeley, 1964.
  20. H. Van Beijeren and M. H. Ernst, The non-linear Enskog-Boltzmann equation, Phys. Lett. A 43, 367 (1973).
  21. M. L. de Haro, E. G. D. Cohen, and J. M. Kincaid, The Enskog theory for multicomponent mixtures. I. Linear transport theory, J. Chem. Phys. 78, 2746 (1983).
  22. F. Pousaneh and A. S. de Wijn, Kinetic theory and shear viscosity of dense dipolar hard sphere liquids, Phys. Rev. Lett. 124, 218004 (2020).
  23. S. Pieprzyk, A. C. Brańka, D. M. Heyes, and M. N. Bannerman, Revised Enskog theory and molecular dynamics simulations of the viscosities and thermal conductivity of the hard-sphere fluid and crystal, Phys. Rev. E 109, 054119 (2024).
  24. P. H. Lee and B. M. Ladanyi, Structural and dielectric properties of dipolar hard sphere mixtures: Reference hypernetted chain and pertubation theory results, J. Chem. Phys. 91, 7063 (1989).
  25. M. Thol, G. Rutkai, A. Köster, R. Lustig, R. Span, and J. Vrabec, Equation of state for the Lennard-Jones fluid, J. Phys. Chem. Ref. Data 45, 023101 (2016).
  26. G. Mie, Zur kinetischen Theorie der einatomigen Körper, Ann. Phys. 316, 657 (1903).
  27. A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in 't Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, and S. J. Plimpton, lammps—A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales, Comput. Phys. Commun. 271, 108171 (2022).
  28. F. Müller-Plathe, Reversing the perturbation in nonequilibrium molecular dynamics: An easy way to calculate the shear viscosity of fluids, Phys. Rev. E 59, 4894 (1999).
  29. G. Bussi, D. Donadio, and M. Parrinello, Canonical sampling through velocity rescaling, J. Chem. Phys. 126, 014101 (2007).
  30. P. D. Neufeld, A. R. Janzen, and R. A. Aziz, Empirical equations to calculate 16 of the transport collision integrals Ω(l,s)* for the Lennard-Jones (12–6) potential, J. Chem. Phys 57, 1100 (1972).
  31. S. Stephan, J. Staubach, and H. Hasse, Review and comparison of equations of state for the Lennard-Jones fluid, Fluid Phase Equilib. 523, 112772 (2020).
  32. A. P. Thompson, S. J. Plimpton, and W. Mattson, General formulation of pressure and stress tensor for arbitrary many-body interaction potentials under periodic boundary conditions, J. Chem. Phys. 131, 154107 (2009).
  33. L. Onsager, The effects of shape on the interaction of colloidal particles, Ann. N. Y. Acad. Sci. 51, 627 (1949).

Outline

Information

Phys. Rev. Research 8, 043132– Published 5 November, 2026
  • Received 9 June 2026
  • Accepted 9 October 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation