The rheology of hard sphere suspensions at arbitrary volume fractions: An improved differential viscosity model

TL;DR

This paper introduces a new continuum-based model for predicting the viscosity of hard sphere suspensions across all volume fractions, effectively capturing experimental data at various shear rates and frequencies.

Contribution

It presents an improved differential viscosity model that incorporates geometrical effects via an effective volume fraction, extending applicability to arbitrary concentrations.

Findings

Model accurately predicts viscosity across volume fractions.

Excellent agreement with experimental data at different shear rates.

Effective at high-frequency limits.

Abstract

We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method that assumes a hierarchy of relaxation times. Geometrical information of the system is introduced through an effective volume fraction that approaches the usual filling fraction at low concentrations and becomes one at maximum packing. The agreement of our expression for the viscosity with experiments at low- and high-shear rates and in the high-frequency limit is remarkable for all volume fractions.