Interface-resolved simulations of particle suspensions in Newtonian, shear thinning and shear thickening carrier fluids

TL;DR

This study uses interface-resolved simulations to analyze how particles behave in various non-Newtonian fluids under shear, revealing effects of inertia, microstructure, and shear rate distributions on suspension rheology.

Contribution

It introduces detailed numerical simulations of particle suspensions in non-Newtonian fluids, highlighting the impact of inertia and microstructure on effective viscosity and shear stress.

Findings

Inertia causes deviations in effective viscosity from Stokesian suspensions.

Particle layering occurs near walls, influenced by confinement and volume fraction.

Local shear rate distributions are broad and depend on volume fraction and Reynolds number.

Abstract

We present a numerical study of noncolloidal spherical and rigid particles suspended in Newtonian, shear thinning and shear thickening fluids employing an Immersed Boundary Method. We consider a linear Couette configuration to explore a wide range of solid volume fractions ($0.1\le \Phi \le 0.4$) and particle Reynolds Numbers ($0.1\le Re_p \le 10$). We report the distribution of solid and fluid phase velocity and solid volume fraction and show that close to the boundaries inertial effects result in a significant slip velocity between the solid and fluid phase. The local solid volume fraction profiles indicate particle layering close to the walls, which increases with the nominal $\Phi$. This feature is associated with the confinement effects. We calculate the probability density function of local strain rates and compare their mean value with the values estimated from the homogenization theory of \cite{Chateau08}, indicating a reasonable agreement in the Stokesian regimes. Both the mean value and standard deviation of the local strain rates increase primarily with the solid volume fraction and secondarily with the $Re_p$. The wide spectrum of the local shear rate and its dependency on $\Phi$ and $Re_p$ points to the deficiencies of the mean value of the local shear rates in estimating the rheology of these noncolloidal complex suspensions. Finally, we show that in the presence of inertia, the effective viscosity of these noncolloidal suspensions deviates from that of Stokesian suspensions. We discuss how inertia affects the microstructure and provide a scaling argument to give a closure for the suspension shear stress for both Newtonian and power-law suspending fluids. The stress closure is valid for moderate particle Reynolds numbers, $ O(Re_p)\sim 10$.