Macroscopic behavior of bidisperse suspensions of noncolloidal particles in yield stress fluids

TL;DR

This study investigates the rheological properties of bidisperse suspensions in yield stress fluids, revealing how particle size heterogeneity influences elastic modulus and yield stress, and proposing simple predictive models based on packing and volume fraction.

Contribution

It provides new experimental and theoretical insights into how bidispersity affects suspension rheology and introduces closed-form estimates for elastic modulus and yield stress.

Findings

Bidisperse suspensions have lower elastic modulus and yield stress than monodisperse ones at same solid volume.

The yield stress relates to elastic modulus and volume fraction via established rheological equations.

Packing models effectively describe the influence of particle size heterogeneity on suspension behavior.

Abstract

We study both experimentally and theoretically the rheological behavior of isotropic bidisperse suspensions of noncolloidal particles in yield stress fluids. We focus on materials in which noncolloidal particles interact with the suspending fluid only through hydrodynamical interactions. We observe that both the elastic modulus and yield stress of bidisperse suspensions are lower than those of monodisperse suspensions of same solid volume fraction. Moreover, we show that the dimensionless yield stress of such suspensions is linked to their dimensionless elastic modulus and to their solid volume fraction through the simple equation of Chateau et al.[J. rheol. 52, 489-506 (2008)]. We also show that the effect of the particle size heterogeneity can be described by means of a packing model developed to estimate random loose packing of assemblies of dry particles. All these observations finally allow us to propose simple closed form estimates for both the elastic modulus and the yield stress of bidisperse suspensions: while the elastic modulus is a function of the reduced volume fraction $\phi/\phi_m$ only, where $\phi_m$ is the estimated random loose packing, the yield stress is a function of both the volume fraction $\phi$ and the reduced volume fraction.