Duality in Shearing Rheology Near the Athermal Jamming Transition

TL;DR

This paper investigates the rheological behavior of soft-core disks near the athermal jamming transition, revealing a duality that links the diverging viscosity below jamming to the Herschel-Bulkley exponent above jamming.

Contribution

It introduces a mapping from soft-core to hard-core particles that uncovers a duality relation connecting rheological exponents across the jamming transition.

Findings

Viscosity divergence below jamming is characteristic of the hard-core limit.

A mapping from soft to hard particles recovers critical behavior.

Derived a duality relation linking rheological exponents.

Abstract

We consider the rheology of soft-core frictionless disks in two dimensions in the neighborhood of the athermal jamming transition. From numerical simulations of bidisperse, overdamped, particles, we argue that the divergence of the viscosity below jamming is characteristic of the hard-core limit, independent of the particular soft-core interaction. We develop a mapping from soft-core to hard-core particles that recovers all the critical behavior found in earlier scaling analyses. Using this mapping we derive a duality relation that gives the exponent of the non-linear Herschel-Bulkley rheology above jamming in terms of the exponent of the diverging viscosity below jamming.