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.
Zhu, J., Crawford, J. W., & Palfreyman, J. W. (2013). A general formulation of the reversible stress tensor for a nonlocal fluid. International Journal of Engineering Science, 70, 124-134. https://doi.org/10.1016/j.ijengsci.2013.03.014