Abstract
There is a growing consensus that shear thickening of concentrated dispersions is driven by the formation of stress-induced frictional contacts. The Wyart-Cates (WC) model of this phenomenon, in which the microphysics of the contacts enters solely via the fraction f of contacts that are frictional, can successfully fit flow curves for suspensions of weakly polydisperse spheres. However, its validity for "real-life", polydisperse suspensions has yet to be seriously tested. By performing systematic simulations on bidisperse mixtures of spheres, we show that the WC model applies only in the monodisperse limit and fails when substantial bidispersity is introduced. We trace the failure of the model to its inability to distinguish large-large, large-small and small-small frictional contacts. By fitting our data using a polydisperse analogue of f that depends separately on the fraction of each of these contact types, we show that the WC picture of shear thickening is incomplete. Systematic experiments on model shear-thickening suspensions corroborate our findings, but highlight important challenges in rigorously testing the WC model with real systems. Our results prompt new questions about the microphysics of thickening for both monodisperse and polydisperse systems.
Highlights
Shear thickening, the increase in viscosity Z with shear stress s or rate g_, is ubiquitous in concentrated suspensions.[1]
By performing systematic simulations on bidisperse mixtures of spheres, we show that the WC model applies only in the monodisperse limit and fails when substantial bidispersity is introduced
At x = 0.2, for example, a large–large contact contributes over an order of magnitude more than a large–small one; while, the effect of forming a small–small contact is negligible (D22 E 0); i.e., small particles are largely redundant for stress transmission
Summary
The increase in viscosity Z with shear stress s or rate g_, is ubiquitous in concentrated suspensions.[1] Its microscopic origin has been hotly debated.[2] Recent experiments,[3,4,5,6,7] simulations[8,9] and theoretical modelling[10] point to a s-dependent transition from frictionless (sliding) to frictional (rolling) interparticle contacts. A phenomenological model by Wyart and Cates[10] (WC) predicts thickening based on a single microphysical parameter, the fraction of frictional contacts, f. It fits well the rheology of model systems;[3,5] its validity for complex industrial suspensions remains untested. We systematically explore the conditions under which the WC model breaks down for one kind of complexity: size polydispersity, and reveal important shortcomings in our current understanding of shear thickening
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