Prediction of shear-thickening of particle suspensions in viscoelastic fluids by direct numerical simulation

TL;DR

This study uses direct numerical simulations to understand shear-thickening in particle suspensions within viscoelastic fluids, highlighting the importance of normal stress differences and microstructure effects for accurate predictions.

Contribution

The paper introduces a detailed numerical approach to predict shear-thickening in suspensions using an Oldroyd-B fluid model, aligning simulations with experimental data.

Findings

Quantitative agreement with experimental shear-thickening behavior.

Normal stress differences are crucial for accurate predictions.

Microstructure influences suspension viscosity and flow patterns.

Abstract

To elucidate the key factor for the quantitative prediction of the shear-thickening in suspensions in viscoelastic fluids, direct numerical simulations of many-particle suspensions in a multi-mode Oldroyd-B fluid are performed using the smoothed profile method. Suspension flow under simple shear flow is solved under periodic boundary conditions by using Lees--Edwards boundary conditions for particle dynamics and a time-dependent oblique coordinate system that evolves with mean shear flow for fluid dynamics. Semi-dilute many-particle suspensions up to a particle volume fraction of 0.1 are investigated. The presented numerical results regarding the bulk rheological properties of the shear-thickening behavior agree quantitatively with recent experimental results of semi-dilute suspensions in a Boger fluid. The presented result clarifies that an accurate estimation of the first normal stress difference of the matrix in the shear-rate range where the shear-thickening starts to occur is crucial for the quantitative prediction of the suspension shear-thickening in a Boger fluid matrix at around the Weissenberg number $\rm{Wi}=1$ by an Oldroyd-B model. Additionally, the effect of suspension microstructures on the suspension viscosity is examined. The paper concludes with a discussion on how the flow pattern and the elastic stress development change with the volume fraction and Weissenberg number.