Viscous forces and bulk viscoelasticity near jamming

TL;DR

This study investigates how different viscous force laws affect the mechanical response of jammed soft sphere packings, revealing a sensitive dependence of viscoelastic properties on the specific damping interactions near jamming.

Contribution

It demonstrates that the complex shear modulus near jamming varies significantly with the viscous force law, highlighting the importance of damping mechanisms in viscoelastic behavior.

Findings

$G^*$ depends strongly on the viscous force law.

Dynamic critical scaling can be present or absent depending on the force law.

Scaling exponents of $G^*$ with frequency vary with damping mechanisms.

Abstract

When weakly jammed packings of soft, viscous, non-Brownian spheres are probed mechanically, they respond with a complex admixture of elastic and viscous effects. While many of these effects are understood for specific, approximate models of the particles' interactions, there are a number of proposed force laws in the literature, especially for viscous interactions. We numerically measure the complex shear modulus $G^*$ of jammed packings for various viscous force laws that damp relative velocities between pairs of contacting particles or between a particle and the continuous fluid phase. We find a surprising sensitive dependence of $G^*$ on the viscous force law: the system may or may not display dynamic critical scaling, and the exponents describing how $G^*$ scales with frequency can change. We show that this sensitivity is closely linked to manner in which viscous damping couples to floppy-like, non-affine motion, which is prominent near jamming.