Implementation of Lees-Edwards periodic boundary conditions for direct numerical simulations of particle dispersions under shear flow

TL;DR

This paper introduces a numerical method for simulating particle dispersions under shear flow using Lees-Edwards boundary conditions, solving fluid dynamics in oblique coordinates, and validating against experimental viscosity data across various conditions.

Contribution

It presents a novel approach combining oblique coordinate Navier-Stokes solutions with a smoothed profile method for particle-fluid interactions under shear flow.

Findings

Method accurately reproduces experimental viscosity data.

Effective in simulating nonlinear shear-thinning regimes.

Validates the approach across wide volume fractions and shear rates.

Abstract

A general methodology is presented to perform direct numerical simulations of particle dispersions in a shear flow with Lees-Edwards periodic boundary conditions. The Navier-Stokes equation is solved in oblique coordinates to resolve the incompatibility of the fluid motions with the sheared geometry, and the force coupling between colloidal particles and the host fluid is imposed by using a smoothed profile method. The validity of the method is carefully examined by comparing the present numerical results with experimental viscosity data for particle dispersions in a wide range of volume fractions and shear rates including nonlinear shear-thinning regimes.