Pair-correlation function of a fluid undergoing a simple shear flow: Solution of the Kirkwood-Smoluchowski equation

Point of departure is an extended Kirkwood-Smoluchowski (K-S) equation for the pair-correlation function (PCF) which is applicable to a rather large range of shear rates. A solution procedure for the K-S equation in a stationary plane Couette-flow (simple shear flow) is outlined where the vorticity of the flow field is taken into account exactly and a perturbation calculation is made with respect to the deformation rate associated with the symmetric traceless part of the velocity gradient field. The first order solution is obtained explicitly and discussed in details. To obtain specific results, the intermolecular potential is assumed to consist of a hard core and a soft attractive force. Especially for hard spheres we obtain a completely explixit expression for the PCF, which is displayed graphically for some typical cases. It shows the ellipsoidal distrotion of the PCF (or the structure factor) observed by experiments1,2) at lower shear rates and a twisted distortion at higher shear rates.