Kinetic theory of discontinuous shear thickening

¹ Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
² Department of Physics, Kyoto University, Kyoto University, Kyoto 606-8502, Japan

^* e-mail: hisao@yukawa.kyoto-u.ac.jp
^** e-mail: takada.satoshi.3s@kyoto-u.ac.jp

Published online: 30 June 2017

Abstract

A simple kinetic theory to exhibit a discontinuous shear thickening (DST) is proposed. The model includes a collision integral, a drag from environment and an environmental temperature T_ex as well as a shear term. The viscosity of this model is proportional to $${\dot{\gamma }}^2$$ for large shear rate $$\dot{\gamma }$$, while it is independent of $$\dot{\gamma }$$ for low sheae rate. The emergence of the DST is enhanced for lower density and lower nonzero T_ex.