Theory for the rheology of dense non-Brownian suspensions: divergence of viscosities and $\unicode[STIX]{x1D707}$ – $J$ rheology

A systematic microscopic theory for the rheology of dense non-Brownian suspensions characterized by the volume fraction $\unicode[STIX]{x1D711}$ is developed. The theory successfully derives the critical behaviour in the vicinity of the jamming point (volume fraction $\unicode[STIX]{x1D711}_{J}$ ), for both the pressure $P$ and the shear stress $\unicode[STIX]{x1D70E}_{xy}$ , i.e. $P\sim \unicode[STIX]{x1D70E}_{xy}\sim \dot{\unicode[STIX]{x1D6FE}}\unicode[STIX]{x1D702}_{0}\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D711}^{-2}$ , where $\dot{\unicode[STIX]{x1D6FE}}$ is the shear rate, $\unicode[STIX]{x1D702}_{0}$ is the shear viscosity of the solvent and $\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D711}=\unicode[STIX]{x1D711}_{J}-\unicode[STIX]{x1D711}>0$ is the distance from the jamming point. It also successfully describes the behaviour of the stress ratio $\unicode[STIX]{x1D707}=\unicode[STIX]{x1D70E}_{xy}/P$ with respect to the viscous number $J=\dot{\unicode[STIX]{x1D6FE}}\unicode[STIX]{x1D702}_{0}/P$ .