Theory for the rheology of dense non-Brownian suspensions: divergence of viscosities and μ-J rheology*

A systematic microscopic theory for the rheology of dense non-Brownian suspensions characterized
by the volume fraction is developed. The theory successfully derives the critical behavior in the
vicinity of the jamming point, both the pressure P and the shear stress σ, diverge with the exponent -2
proportional to the deviation of the volume fraction from the jamming point.
It also successfully describes the behavior of the stress ratio μ = σ/P with respect to the viscous number J which is the dimensionless shear rate in terms of the solvent viscosity and the pressure.
The theory predicts the behavior of μ which approaches a constant in the jamming limit, and the contribution of the square root of J appears within the framework of the theory.
The theoretical predictions are consistent with our simulation, in particular, the value of μ in the jamming limit does not require any fitting parameter.
The theory is also consistent with previous experiments and simulation for dense non-Browninan suspension.