Theory for the rheology of dense non-Brownian suspensions: divergence of viscosities and $\mu$-$J$ rheology

Abstract

A systematic microscopic theory for the rheology of dense non-Brownian suspensions characterized by the volume fraction $\phi$ is developed. The theory successfully derives the critical behavior in the vicinity of the jamming point (volume fraction ${\phi }_J$), for both the pressure $P$ and the shear stress ${\sigma }_{xy}$, i.e. $P\sim {\sigma }_{xy}\sim \dot{\gamma }{\eta }_0\delta {\phi }^{-2}$, where $\dot{\gamma }$ is the shear rate, ${\eta }_0$ is the shear viscosity of the solvent, and $\delta \phi ={\phi }_J-\phi >0$ is the distance from the jamming point. It also successfully describes the behavior of the stress ratio $\mu ={\sigma }_{xy}/P$ with respect to the viscous number $J=\dot{\gamma }{\eta }_0/P$.

49 pages, 16 figures

References in corpus (2)

• Divergence of Viscosity in Jammed Granular Materials: A Theoretical Approach
• Kinetic theory of discontinuous shear thickening

Cited by in corpus (5)

• Enskog kinetic theory of rheology for a moderately dense inertial suspension
• Simulation of dense non-Brownian suspensions with the lattice Boltzmann method: Shear jammed and fragile states
• Rheology of granular liquids in extensional flows: Beyond the $\mu (\mathcal{I})$-law
• Kinetic theory of discontinuous shear thickening of a moderately dense inertial suspension of frictionless soft particles
• Early-stage impact dynamics in dense suspensions of millimeter-sized particles