Viscosity of Suspensions of Hard and Soft Spheres

TL;DR

This paper reanalyzes literature data to reveal a sharp dynamic crossover in the viscosity of suspensions of hard and soft spheres, indicating different regimes of concentration dependence and a transition from polymer-like to hard-sphere behavior.

Contribution

It identifies a precise concentration-dependent crossover in suspension viscosity and compares behaviors of soft and hard spheres, providing new insights into their rheological properties.

Findings

Viscosity exhibits a sharp crossover from stretched exponential to power law at a critical volume fraction.

Crossover occurs at a volume fraction of about 0.41 and relative viscosity of 11.

Soft spheres transition from polymer-like to hard-sphere behavior as they become more rigid.

Abstract

From a reanalysis of the published literature, the low-shear viscosity of suspensions of hard spheres is shown to have a dynamic crossover in its concentration dependence, from a stretched exponential at lower concentrations to a power law at elevated concentrations. The crossover is sharp, with no transition region in which neither form applies, and occurs at a volume fraction (ca. 0.41) and relative viscosity (ca. 11) well below the sphere volume fraction and relative viscosity (0.494, 49, respectively) of the lower phase boundary of the hard sphere melting transition. For soft spheres -- taking many-arm star polymers as a model -- with increasing sphere hardness $\eta(\phi)$ shows a crossover from random-coil polymer behavior toward the behavior shown by true hard spheres.