Shear viscosity for fluids of hard ellipsoids: A kinetic theory and molecular dynamics study

The frequency‐dependent shear viscosity η(ω) and the shear‐orientation coupling parameter R are calculated for fluids of hard prolate ellipsoids of revolution, using kinetic theory and molecular dynamics. Two effects which contribute to the shear viscosity are considered. First, the D ∞h particle symmetry influences both the spectrum of the collision operator and the multi‐Lorentzian decay of η(ω). These multiple decays are most important at low densities for elongated particles. Second, coupling between the stress tensor and the collective molecular orientation leads to a minimum in η(ω) between its zero‐frequency limit η and its infinite‐frequency plateau value η∞. At densities approaching the transition to a nematic phase, the zero‐frequency shear viscosity is predicted to be dominated by its infinite‐frequency plateau value, i.e., η/η∞∼1. Molecular dynamics simulations, extended to longer times than those previously reported, confirm the existence of the dip in η(ω) and the importance of stress‐orientation coupling in determining the value of η. Discrepancies previously thought to exist between simulation and theory are attributed to this coupling between the stress and slow collective reorientation; we now obtain good agreement between simulation and theory at low and moderate densities. The kinetic theory predicts the position of the dip quite well, but underestimates its magnitude for elongated particles at medium and high densities. The theory also predicts a weak density dependence of the shear‐orientation coupling parameter R, and a decrease in this parameter with increasing elongation, whereas the simulations show a steady increase in R with both density and elongation. Moreover, the ratio η/η∞ falls below unity, rather than approaching unity, as the density increases, in several of the cases studied. The Stokes–Einstein relation and the Stokes–Einstein–Debye relation are investigated, and a consistent picture emerges of a crossover between a regime in which kinetic theory is accurate (at low density and elongation) to one in which a hydrodynamic description with slip boundary conditions applies (at high density and elongation). The change to hydrodynamic behavior is more apparent for the rotational motion than for the translational motion.