Toward a microscopic description of flow near the jamming threshold

TL;DR

This paper develops an analytical model linking microscopic contact forces to macroscopic viscosity in suspensions near jamming, revealing how force distributions and flow modes diverge as the system approaches the jamming threshold.

Contribution

It introduces a tractable model that captures the negative selection of weak contacts and predicts scaling laws for viscosity and force distributions near jamming.

Findings

Viscosity diverges as (z_c - z)^{-(3+θ)/(1+θ)}.

Flow exhibits a low-frequency mode controlling viscosity divergence.

Force distribution scale f* vanishes near jamming as (z_c - z)^{1/(1+θ)}.

Abstract

We study the relationship between microscopic structure and viscosity in non-Brownian suspensions. We argue that the formation and opening of contacts between particles in flow effectively leads to a negative selection of the contacts carrying weak forces. We show that an analytically tractable model capturing this negative selection correctly reproduces scaling properties of flows near the jamming transition. In particular, we predict that (i) the viscosity {\eta} diverges with the coordination z as {\eta} ~ (z_c-z)^{-(3+{\theta})/(1+{\theta})}, (ii) the operator that governs flow displays a low-frequency mode that controls the divergence of viscosity, at a frequency {\omega}_min\sim(z_c-z)^{(3+{\theta})/(2+2{\theta})}, and (iii) the distribution of forces displays a scale f* that vanishes near jamming as f*/<f>\sim(z_c-z)^{1/(1+{\theta})} where {\theta} characterizes the distribution of contact forces P(f)\simf^{\theta} at jamming, and where z_c is the Maxwell threshold for rigidity.