Multifluid simulation of shear-induced migration in pressure-driven suspension flows

TL;DR

This study develops a multi-fluid simulation model for shear-induced migration in suspension flows, incorporating microstructure effects and comparing different stress closure models, achieving good agreement with experimental data.

Contribution

It introduces a novel MF-roughness model that captures microstructure effects in shear-induced migration and compares it with existing phenomenological models.

Findings

The MF-roughness model accurately reproduces benchmark distributions.

Optimized models show similar results and align with experimental data.

Microstructure-informed modeling improves understanding of suspension flow behavior.

Abstract

The present study simulates shear-induced migration (SIM) in semi-dilute pressure-driven Stokes suspension flows using a multi-fluid (MF) model. Building on analysis from a companion paper (Harvie, 2024), the specific formulation uses volume-averaged phase stresses that are linked to the binary hydrodynamic interaction of spheres and suspension microstructure as represented by an anisotropic, piece-wise constant pair-distribution function (PDF). The form of the PDF is chosen to capture observations regarding the microstructure in sheared suspensions of rough particles, as reported in the literature. Specifically, a hydrodynamic roughness value is used to represent the width of the anisotropic region, and within this region the concentration of particles is higher in the compression zone than expansion zone. By numerically evaluating the hydrodynamic particle interactions and calculating the various shear and normal viscosities, the stress closure is incorporated into Harvie's volume-averaged MF framework, referred to as the MF-roughness model. Using multi-dimensional simulations the roughness and compression zone PDF concentration are then globally optimised to reproduce benchmark solid and velocity distributions reported in the literature for a variety of semi-dilute monodisperse suspension flows occurring within rectangular channels. For comparison, two different versions of the phenomenological stress closure by Morris and Boulay (1999) are additionally proposed as fully tensorial frame-invariant alternatives to the MF-roughness model. Referred to as MF-MB99-A and MF-MB99-B, these models use alternative assumptions for partitioning of the mixture normal stress between the solid and fluid phases. The optimised solid and velocity distributions from all three stress closures are similar and correlate well with the experimental data.