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 $\varphi$ 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 $p/\dot{\epsilon }\sim ({\varphi }_J-\varphi {)}^{-\beta }$, 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 $\varphi$ 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.

arXiv comment14 pages, 11 figures, updated to published version, changes to figures 3 and 5, minor changes to text

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• Comparison of compression vs shearing near jamming, for a simple model of athermal frictionless disks in suspension
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