Predictions of microstructure and stress in planar extensional flows of a dense viscous suspension

TL;DR

This paper models the microstructure and stress in dense viscous suspensions under extensional flow, combining theoretical analysis with Stokesian dynamics simulations to predict particle trajectories and stress-strain relationships.

Contribution

It introduces a novel approach linking microstructural particle distributions to stress predictions using force balances and simulations in extensional flows.

Findings

Predicted stress depends on particle microstructure and strain rate.

Validated theoretical predictions with numerical simulations.

Identified the role of higher moments of particle distribution in stress tensors.

Abstract

We consider extensional flows of a dense layer of spheres in a viscous fluid and employ force and torque balances to determine the trajectory of particle pairs that contribute to the stress. In doing this, we use Stokesian dynamics simulations to guide the choice of the near-contacting pairs that follow such a trajectory. We specify the boundary conditions on the representative trajectory, and determine the distribution of particles along it and how the stress depends on the microstructure and strain rate. We test the resulting predictions using the numerical simulations. Also, we show that the relation between the tensors of stress and strain rate involves the second and fourth moments of the particle distribution function.