Theory of the nonequilibrium structure of dense simple fluids. II. High-shear-rate effects.

Abstract

The integral equation for the dynamic pair correlation function derived previously from the modified moment method is solved for a non-Newtonian soft-sphere fluid undergoing a plane Couette flow. In this approach, the dynamic pair correlation function is a functional of the shear stress, which determines the macroscopic state of the nonequilibrium fluid. The distortions of the structure factor at high shear rates are examined for a non-Newtonian fluid. Normal stress effects are included in the study presented. It is found that as the shear rate increases, the structure factor fractures into domains of high intensity in the xy (shear), xy, and yz planes in the wave-vector space. At packing fractions in the range of \ensuremath{\eta}=0.3--0.45, the structure factor exhibits a plateau behavior at reduced shear rates \ensuremath{\gamma}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\ge}100, and this behavior is seen to be directly related to the thixotropy of the fluid. In all planes considered, the structure factor suggests, essentially, a distorted-fluid-like structure, although there is evidence indicating that the approach to an ordered phase is also a probable interpretation. These effects are in qualitative agreement with the observations made on colloidal suspensions and low-shear-rate molecular-dynamics simulation results. In the presence of normal stresses, the structure factor in the xy plane is rotated in the direction of the shear flow. The angle of rotation is determined by the magnitude of the primary normal stress difference and also by the thermodynamic state of the fluid. The structure factor in the yz plane is similar to the case without normal stresses, and the xz plane is undistorted.