Symmetry of the pressure tensor in macromolecular fluids

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Abstract
For molecules possessing internal angular momentum, irreversible thermodynamics shows that the relaxation of the internal angular momentum occurs via the antisymmetric component of the pressure tensor. Yet it is common in fluid dynamics, even for fluids of orientable molecules, to assume that the pressure tensor is symmetric. An attempt to clarify this anomaly for solutions of macromolecules was made by Curtiss, Bird, and Hassager [Adv. Chem. Phys. 35, 31 (1976)]. They found in their kinetic theory treatment, that after making several approximations common in polymer theory, the pressure tensor is symmetric. The purpose of this paper is to show that within the usual question of uniqueness, their conclusion regarding the symmetry of the pressure tensor depends on only two things: (i) that the interatomic (between ’’beads’’) potential is spherical and (ii) that the fluid’s densities (of mass and momentum) are localized at the bead points. If instead, the densities are localized at the polymer center of mass, there arises an inherently antisymmetric component of the pressure tensor. This localization is considered to be more in keeping with the molecular nature of such systems.