Distribution functions of a simple fluid under shear: low shear rates

Anisotropic pair distribution functions for a simple, soft sphere fluid at moderate and high density under shear have been calculated by nonequilibrium molecular dynamics, by equilibrium molecular dynamics with a nonequilibrium potential, and by a nonequilibrium distribution function theory [H. H. Gan and B. C. Eu, Phys. Rev. A 45, 3670 (1992)] and some variants. The nonequilibrium distribution function theory consists of a nonequilibrium Ornstein-Zernike relation, a closure relation, and a nonequilibrium potential and is solved in spherical harmonics. The distortion of the fluid structure due to shear is presented as the difference between the nonequilibrium and equilibrium pair distribution functions. From comparison of the results of theory against results of equilibrium molecular dynamics with the nonequilibrium potential at low shear rates, it is concluded that, for a given nonequilibrium potential, the theory is reasonably accurate, especially with the modified hypernetted chain closure. The equilibrium molecular-dynamics results with the nonequilibrium potential are also compared against the results of nonequilibrium molecular dynamics and suggest that the nonequilibrium potential used is not very accurate. In continuing work, a nonequilibrium potential better suited to high shear rates [H. H. Gan and B. C. Eu, Phys. Rev. A 46, 6344 (1992)] is being tested.