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

Abstract

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 equationwith 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 η and the Péclet (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 η. 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.