Theory of Nonlinear Transport Processes: Nonlinear Shear Viscosity and Normal Stress Effects

Formally exact equations of motion satisfied by the gross variables of a macroscopic system valid far from thermal equilibrium are obtained with the aid of the new projection operator in nonequilibrium statistical mechanics. These equations are used to study nonlinear shear viscosity and normal stress effects of a model incompressible fluid in the presence of a shear flow which is not necessarily small. We find that the mode-coupling mechanism responsible for the long-time tails in time-correlation functions becomes very important here also and that a simple power-series expansion in the rate of shear $D$ therefore fails. The part of shear viscosity dependent upon the rate of shear and the normal stress effect are found to vary as ${\mathrm{}\left|D\right|\mathrm{}}^{\frac{1}{2}}$ and ${\mathrm{}\left|D\right|\mathrm{}}^{\frac{3}{2}}$, respectively.