Theory of the nonequilibrium structure of dense simple fluids: Effects of shearing

The nonequilibrium canonical distribution function of the generalized Boltzmann equation entails a nonequilibrium Kirkwood hierarchy of integral equations for dynamic correlation functions. A sheared simple fluid at constant density and temperature is considered. Shear effects appear in the nonequilibrum potential as additional contributions to the intermolecular potential. Approximations are introduced into the hierarchy to derive a closed integral equation for the dynamic pair-correlation function that reduces identically to the Percus-Yevick integral equation as the shear rate vanishes. Two exact results are obtained: the dynamic pair-correlation function is proven to possess the symmetry of the nonequilibrium potential, and the corresponding structure factor is shown to be positive definite for all wave-number vectors. The dynamic pair-correlation function is expanded in terms of the spherical harmonics, and the equations for coupled radial components are solved numerically. The shear rate and angular dependences of the dynamic pair-correlation function and structure factor are shown. In the low-shear-rate limit, the shear stress ${\mathit{P}}_{\mathit{x}\mathit{y}}$, pressure difference p(γ¯)-p(0), and normal-stress differences ${\mathit{P}}_{\mathit{y}\mathit{y}}$-${\mathit{P}}_{\mathit{z}\mathit{z}}$ and ${\mathit{P}}_{\mathit{y}\mathit{y}}$-${\mathit{P}}_{\mathit{z}\mathit{z}}$ obey power laws with exponents 1, 2, and 2 respectively; ${\mathit{P}}_{\mathit{x}\mathit{x}}$-${\mathit{P}}_{\mathit{y}\mathit{y}}$ is zero identically.