A Continuum Model for Complex Flows of Shear Thickening Colloidal Solutions

Joseph Green,Daniel Ryckman,Michael Cromer

doi:10.3390/fluids4010021

Abstract

Colloidal shear thickening fluids (STFs) have applications ranging from commercial use to those of interest to the army and law enforcement, and the oil industry. The theoretical understanding of the flow of these particulate suspensions has predominantly been focused through detailed particle simulations. While these simulations are able to accurately capture and predict the behavior of suspensions in simple flows, they are not tractable for more complex flows such as those occurring in applications. The model presented in this work, a modification of an earlier constitutive model by Stickel et al. J. Rheol. 2006, 50, 379–413, describes the evolution of a structure tensor, which is related to the particle mean free-path length. The model contains few adjustable parameters, includes nonlinear terms in the structure, and is able to predict the full range of rheological behavior including shear and extensional thickening (continuous and discontinuous). In order to demonstrate its capability for complex flow simulations, we compare the results of simulations of the model in a simple one-dimensional channel flow versus a full two-dimensional simulation. Ultimately, the model presented is a continuum model shown to predict shear and extensional thickening, as observed in experiment, with a connection to the physical microstructure, and has the capability of helping understand the behavior of STFs in complex flows.

Highlights

IntroductionColloidal fluids are approximately Newtonian, with increasing concentrations they show complex rheological behavior including shear thinning or thickening and glass-like relaxation states
Colloidal solutions consist of a liquid, Newtonian or viscoelastic, in which solid particles are suspended, so that the particles are large compared to the lengthscale of the fluid microstructure, but small enough to be affected by Brownian motion.At low concentrations, colloidal fluids are approximately Newtonian, with increasing concentrations they show complex rheological behavior including shear thinning or thickening and glass-like relaxation states
The primary goal of this work is to provide a constitutive model that describes the microstructure of a colloidal solution and its shear thickening behavior, and is suitable for complex flow simulations

Summary

Introduction

Colloidal fluids are approximately Newtonian, with increasing concentrations they show complex rheological behavior including shear thinning or thickening and glass-like relaxation states. At these higher concentrations the complex rheological responses are due to hydrodynamic interactions between particles at high flow rates. Colloidal shear thickening fluids (STFs) have exciting applications ranging from commercial use (e.g., polymeric binders for paints) to those of interest to the army and law enforcement (e.g., soft body armor) and more [1]. It has been shown experimentally through ballistics tests [2] and “stabbing” tests [3] that, in the application to body armor [4], the frequency response of certain shear thickening fluids (STFs) allows a fabric interwoven with an STF to stop a projectile or prevent the piercing of a knife while being light and flexible enough to provide full body protection

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