A discrete model for the apparent viscosity of polydisperse suspensions including maximum packing fraction

TL;DR

This paper introduces a novel discrete model for the apparent viscosity and maximum packing fraction of polydisperse suspensions, integrating existing theories and validated against experimental data, with implications for improved suspension modeling.

Contribution

The paper presents the first unified model that consistently describes polydisperse volume fractions and maximum packing fraction, incorporating asymptotic matching and generalized equations.

Findings

Model aligns well with experimental data.

Replaces the empirical Sudduth model for large diameter ratios.

Provides a basis for future extension to small size ratios.

Abstract

Based on the notion of a construction process consisting of the stepwise addition of particles to the pure fluid, a discrete model for the apparent viscosity as well as for the maximum packing fraction of polydisperse suspensions of spherical, non-colloidal particles is derived. The model connects the approaches by Bruggeman and Farris and is valid for large size ratios of consecutive particle classes during the construction process, appearing to be the first model consistently describing polydisperse volume fractions and maximum packing fraction within a single approach. In that context, the consistent inclusion of the maximum packing fraction into effective medium models is discussed. Furthermore, new generalized forms of the well-known Quemada and Krieger equations allowing for the choice of a second-order Taylor coefficient for the volume fraction ($\phi^2$-coefficient), found by asymptotic matching, are proposed. The model for the maximum packing fraction as well as the complete viscosity model are compared to experimental data from the literature showing good agreement. As a result, the new model is shown to replace the empirical Sudduth model for large diameter ratios. The extension of the model to the case of small size ratios is left for future work.