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 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 Péclet ($\text{Pe}$) number, we compute the pair correlation function and extract scaling laws for its value at contact. For all the considered value of $\text{Pe},$ 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 $\text{Pe}$ 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.

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Cited by in corpus (4)

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• Generalized Langevin equation with shear flow and its fluctuation-dissipation theorems derived from a Caldeira-Leggett Hamiltonian
• Machine Learning-Informed Scattering Correlation Analysis of Sheared Colloids
• Superadiabatic dynamical density functional theory for colloidal suspensions under homogeneous steady-shear