A Continuum Model for Complex Flows of Shear Thickening Colloidal Solutions

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.