Homogenization approach to the behavior of suspensions of noncolloidal particles in yield stress fluids

TL;DR

This paper develops a homogenization method to predict the behavior of suspensions of rigid particles in yield stress fluids, providing estimates for their overall properties that align well with experimental data.

Contribution

It introduces a nonlinear homogenization approach to model suspensions in non-Newtonian fluids, specifically Herschel-Bulkley fluids, capturing their effective yield stress and flow properties.

Findings

Estimates for suspension yield stress match experimental data.

Modeling as Herschel-Bulkley fluid with same exponent is effective.

Provides practical estimates for large strain rate behavior.

Abstract

The behavior of suspensions of rigid particles in a non-Newtonian fluid is studied in the framework of a nonlinear homogenization method. Estimates for the overall properties of the composite material are obtained. In the case of a Herschel-Bulkley suspending fluid, it is shown that the properties of a suspension with overall isotropy can be satisfactory modeled as that of a Herschel-Bulkley fluid with an exponent equal to that of the suspending fluid. Estimates for the yield stress and the consistency at large strain rate levels are proposed. These estimates compare well to both experimental data obtained by Mahaut et al [J. Rheol. 52, 287-313 (2008)] and to experimental data found in the literature.