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

TL;DR

This paper develops a microscopic theoretical framework to analyze the structure of concentrated colloidal suspensions under shear flow, incorporating hydrodynamic interactions and boundary-layer effects to predict pair correlations and potential phase transitions.

Contribution

It introduces a novel approach combining matched asymptotics and integral equations to accurately model shear-induced structural changes in colloidal suspensions.

Findings

Good agreement with numerical results for pair correlation functions.

Predicts enhancement of the structure factor at zero wavevector with increasing shear.

Suggests possible shear-induced phase transition from isotropic to non-uniform phases.

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 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 P\'eclet ($\textrm{Pe}$) number, we compute the pair correlation function and extract scaling laws for its value at contact. For all the considered value of $\textrm{Pe},$ we observe a very good agreement between theoretical findings and numerical results from literature, up to rather large values of $\eta.$ The theory predicts a consistent enhancement of the structure factor $ S(k)$ at $k \to 0,$ upon increasing the $\textrm{Pe}$ number. We argue this behaviour may signal the onset of a phase transition from the isotropic phase to a non-uniform one, induced by the external shear flow.