Modeling stress relaxation in dense, fine-particle suspensions

Abstract

In this work, we examine the predictions of the constitutive model proposed in Baumgarten and Kamrin [Baumgarten and Kamrin, Proc. Natl. Acad. Sci. U.S.A. 116, 20828–20836 (2019)], as it relates to the transient relaxation of shear stresses in dense, fine-particle suspensions such as water-cornstarch or water-poly(methyl methacrylate) mixtures. Such mixtures are known to exhibit dramatic increases in viscosity when impacted or sheared, and in rate-controlled experiments, these mixtures are also observed to support shear stresses long after all macroscopic flow has stopped. We show that the experimental observations of substantially longer stress decay in these mixtures compared with standard Newtonian fluids can be captured by the model through its evolution of the internal state variable, f, which reflects the fraction of frictional contacts at the microscale. Analysis of the behavior of f suggests that the presence of system spanning granular contact networks and the associated rate of decay of the elastic energy stored in these networks is responsible for the observed phenomena.