Model for the Scaling of Stresses and Fluctuations in Flows near Jamming

TL;DR

This paper develops an analytical model for flows of soft, viscous spheres near jamming, revealing four distinct flow regimes with unique scaling exponents validated by simulations.

Contribution

It introduces a novel analytical model predicting multiple flow regimes and their scaling exponents near the jamming transition, differing from previous studies.

Findings

Four distinct flow regimes identified

Scaling exponents are rational-valued

Model validated with simulations

Abstract

We probe flows of soft, viscous spheres near the jamming point, which acts as a critical point for static soft spheres. Starting from energy considerations, we find nontrivial scaling of velocity fluctuations with strain rate. Combining this scaling with insights from jamming, we arrive at an analytical model that predicts four distinct regimes of flow, each characterized by rational-valued scaling exponents. Both the number of regimes and values of the exponents depart from prior results. We validate predictions of the model with simulations.