Power-law exponents for the shear viscosity of non-Newtonian simple fluids

Nonequilibrium molecular-dynamics simulations are performed to compute the shear viscosities of a simple Lennard-Jones fluid across a wide range of densities and temperatures that span the liquid phase. It is found that the standard mode-coupling value of beta = 0.05 for the exponent of the strain rate power-law dependence (eta = eta0-eta1gammabeta) is only applicable in a very narrow region of the thermodynamic state-space. More generally, the exponent is a remarkably simple linear function of temperature and density, analogous to the linear relationship that exists for the scaling exponents of the pressure and energy found previously by Ge et al. [Phys. Rev. E 67, 061201 (2003)], and ranges between approximately 0.2 and 1.6. It is also found that the parameters eta0 and eta1 are steep functions of increasing density for any particular temperature and can be represented by a stretched exponential of the density.