# Testing the Wyart-Cates model for non-Brownian shear thickening using bidisperse suspensions

## TL;DR

This study tests the Wyart-Cates shear thickening model on bidisperse suspensions, revealing its limitations beyond monodisperse systems and suggesting the need for a more comprehensive microphysical understanding.

## Contribution

The paper demonstrates that the Wyart-Cates model fails for bidisperse suspensions and introduces a polydisperse extension to better capture shear thickening behavior.

## Key findings

- The WC model applies only to monodisperse suspensions.
- The model fails when bidispersity is introduced.
- A polydisperse contact fraction improves modeling accuracy.

## 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.