A general formulation of the reversible stress tensor for a nonlocal fluid

Jiujiang Zhu*, John W. Crawford, John W. Palfreyman

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)


    The nonlocal stress tensor is an indispensable constitutive equation required to close the thermodynamic system of nonlocal fluid dynamics. A nonlocal functional variational principle is employed to derive a general expression for the thermodynamically reversible stress tensor for a two-phase, single component, nonlocal fluid. The Euler–Lagrange equation and Noether’s current are used to obtain the general form of the stress tensor, which is then used to derive a wide range of functional forms found in the literature. We also clarify some existing ambiguities. The general form of the nonlocal stress tensor is able to represent micro scale intermolecular interactions, and provides an efficient mesoscale numerical tool for multi-scale analysis using Lattice Boltzmann simulation.
    Original languageEnglish
    Pages (from-to)124-134
    Number of pages11
    JournalInternational Journal of Engineering Science
    Early online date29 May 2013
    Publication statusPublished - Sept 2013


    • Nonlocal fluid dynamics
    • Generalized stress tensor
    • Nonlocal functional variational principle
    • Intermolecular interaction


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