# Force transmission and the order parameter of shear thickening

## TL;DR

This paper develops a force distribution model based on the q-model to explain the order parameter of shear thickening, predicting deviations under different contact constraints and extending understanding of shear thickening mechanisms.

## Contribution

It introduces a force distribution model using the q-model to predict the order parameter behavior in shear thickening suspensions, including effects of rolling friction and bidispersity.

## Key findings

- Model explains f(σ) for sliding friction contacts.
- Predicts broadening of shear thickening with rolling friction.
- Extends to systems with bidispersity.

## Abstract

The origin of the abrupt shear thickening observed in some dense suspensions has been recently argued to be a transition from frictionless (lubricated) to frictional interactions between immersed particles. The Wyart-Cates rheological model, built on this scenario, introduced the concept of fraction of frictional contacts $f$ as the relevant order parameter for the shear thickening transition. Central to the model is the "equation-of-state" relating $f$ to the applied stress $\sigma$, which is directly linked to the distribution of the normal components of non-hydrodynamics interparticle forces. Here, we develop a model for this force distribution, based on the so-called $q$-model that we borrow from granular physics. This model explains the known $f(\sigma)$ in the simple case of sphere contacts displaying only sliding friction, but also predicts strong deviation from this "usual" form when stronger kinds of constraints are applied on relative motion. We verify these predictions in the case of contacts with rolling friction, in particular a broadening of the stress range over which shear thickening occurs. We finally discuss how a similar approach can be followed to predict $f(\sigma)$ in systems with other variations from the canonical system of monodisperse spheres with sliding friction, in particular the case of large bidispersity.