Kinetic theory of discontinuous shear thickening

TL;DR

This paper proposes a kinetic theory model that explains discontinuous shear thickening in suspensions, highlighting the roles of collision dynamics, environmental friction, and external temperature in the phenomenon.

Contribution

It introduces a simple kinetic model incorporating collision integral, environmental friction, and a thermostat to explain DST behavior.

Findings

Viscosity scales as shear rate squared at high shear rates.

DST is more prominent at lower densities and external temperatures.

Model captures transition from Newtonian to shear thickening behavior.

Abstract

A simple kinetic theory to exhibit a discontinuous shear thickening (DST) is proposed. The model includes the collision integral and the friction from environment as well as a thermostat term characterized by $T_{\rm ex}$. The viscosity of this model is proportional to $\dot\gamma^2$ for large shear rate $\dot\gamma$, while it is Newtonian for low $\dot\gamma$. The emergence of the DST is enhanced for lower density and lower nonzero $T_{\rm ex}$.