Universality of stress-anisotropic and stress-isotropic jamming of frictionless spheres in three dimensions: Uniaxial vs isotropic compression

Abstract

We numerically study a three dimensional system of athermal, overdamped, frictionless spheres, using a simplified model for a non-Brownian suspension. We compute the bulk viscosity under both uniaxial and isotropic compression as a means to address the question of whether stress-anisotropic and stress-isotropic jamming are in the same critical universality class. Carrying out a critical scaling analysis of the system pressure $p$, shear stress $\sigma$, and macroscopic friction $\mu=\sigma/p$, as functions of particle packing fraction $\phi$ and compression rate $\dot\epsilon$, we find good agreement for all critical parameters comparing the isotropic and anisotropic cases. In particular, we determine that the bulk viscosity diverges as $p/\dot\epsilon\sim (\phi_J-\phi)^{-\beta}$, with $\beta=3.36\pm 0.09$, as jamming is approached from below. We further demonstrate that the average contact number per particle $Z$ can also be written in a scaling form as a function of $\phi$ and $\dot\epsilon$. Once again, we find good agreement between the uniaxial and isotropic cases. We compare our results to prior simulations and theoretical predictions.