A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration

Abstract

A constitutive equation for computing particle concentration and velocity fields in concentrated monomodal suspensions is proposed that consists of two parts: a Newtonian constitutive equation in which the viscosity depends on the local particle volume fraction and a diffusion equation that accounts for shear-induced particle migration. Particle flux expressions used to obtain the diffusion equation are derived by simple scaling arguments. Predictions are made for the particle volume fraction and velocity fields for steady Couette and Poiseuille flow, and for transient start-up of steady shear flow in a Couette apparatus. Particle concentrations for a monomodal suspension of polymethyl methacrylate spheres in a Newtonian solvent are measured by nuclear magnetic resonance (NMR) imaging in the Couette geometry for two particle sizes and volume fractions. The predictions agree remarkably well with the measurements for both transient and steady-state experiments as well as for different particle sizes.

Hydrodynamic particle migration in a concentrated suspension undergoing flow between rotating eccentric cylinders

“…We have modeled the suspension following the technique presented by Phillips et al (1992). Here, we expanded the model expression to twodimensions by describing the flow in terms of the strain rate tensor and the migration in terms of gradients in the generalized shear rate.…”

“…Except for Zhang and Acrivos (1994), who studied the flow of nonneutrally buoyant particles in pipe flow, these models have been compared to data only from one-dimensional flows. Here, we compare the NMR data from the two-dimensional bearing flow to numerical predictions using a model expression previously used successfully to describe one-dimensional flows by Phillips et al (1992). The model expression consists of two parts: a Newtonian constitutive equation in which the viscosity depends on the local solids volume fraction and a diffusion equation that accounts for shear-induced particle migration.…”

“…Other investigators have proposed mechanisms to model the suspended particle migration caused by the presence of nonuniform shear gradients (Phillips et al 1992, Koch 1989, Leighton and Acrivos 1987, Nott and Brady 1994, Zhang and Acrivos 1994. Except for Zhang and Acrivos (1994), who studied the flow of nonneutrally buoyant particles in pipe flow, these models have been compared to data only from one-dimensional flows.…”

“…A model, originally proposed by Phillips et al (1992) is generalized to two dimensions. The coupled equations of motion and particle migration are solved numerically using an explicit pseudo-transient finite volume formulation.…”

“…The suspensions consists of large, noncolloidal spherical particles suspended in a viscous Newtonian liquid. Nuclear magnetic resonance (NMR) imaging is used to measure the time evolution of concentration and velocity profiles as the flow induces particle migration from the initial, well-mixed state.A model, originally proposed by Phillips et al (1992) is generalized to two dimensions. The coupled equations of motion and particle migration are solved numerically using an explicit pseudo-transient finite volume formulation.…”