Microscopic theory for the pair correlation function of liquidlike colloidal suspensions under shear flow

We present a theoretical framework to investigate the microscopic structure of concentrated hard-sphere colloidal suspensions under strong shear flows by fully taking into account the boundary-layer structure of convective diffusion. We solve the pair Smoluchowski equation with shear separately in the compressing and extensional sectors of the solid angle, by means of matched asymptotics. A proper, albeit approximate, treatment of the hydrodynamic interactions in the different sectors allows us to construct a potential of mean force containing the effect of the flow field on pair correlations. We insert the obtained pair potential in the Percus-Yevick relation and use the latter as a closure to solve the Ornstein-Zernike integral equation. For a wide range of either the packing fraction eta and the Peclet (Pe) number, we compute the pair correlation function and extract scaling laws for its value at contact. For all the considered values of Pe, we observe a very good agreement between theoretical findings and numerical results from the literature, up to rather large values of eta. The theory predicts a consistent enhancement of the structure factor S(k) at k 0, upon increasing the Pe number. We argue this behavior may signal the onset of a phase transition from the isotropic phase to a nonuniform one, induced by the external shear flow.