Length scales and self-organization in dense suspension flows

TL;DR

This paper investigates the microscopic mechanisms behind dense suspension flows near jamming, revealing a connection to rigidity transitions and identifying key length scales that influence flow properties.

Contribution

It introduces an analogy between suspension flows and rigidity transitions in floppy networks, deriving critical properties and numerically confirming the proximity of suspensions to this transition.

Findings

Velocity correlation length scales as p^{0.18}

Identifies a larger length scale l_r  1/rac{1}{rac{p}{}}

Discloses a vanishing strain  1/p associated with flow decorrelation.

Abstract

Dense non-Brownian suspension flows of hard particles display mystifying properties: as the jamming threshold is approached, the viscosity diverges, as well as a length scale that can be identified from velocity correlations. To unravel the microscopic mechanism governing dissipation and its connection to the observed long-range correlations, we develop an analogy between suspension flows and the rigidity transition occurring when floppy networks are pulled -- a transition believed to be associated to the stress-stiffening of certain gels. After deriving the critical properties near the rigidity transition, we show numerically that suspensions flows lie close to it. We find that this proximity causes a decoupling between viscosity and the correlation length of velocities \xi, which scales as the length l_c characterizing the response of the velocity in flow to a local perturbation, previously predicted to follow l_c\sim 1/\sqrt{z_c-z}\sim p^{0.18} where p is the dimensionless particle pressure, z the coordination of the contact network made by the particles and z_c is twice the spatial dimension. We confirm these predictions numerically, predict the existence of a larger length scale l_r\sim 1/\sqrt{p} with mild effects on velocity correlation and the existence of a vanishing strain \delta \gamma\sim 1/p that characterizes de-correlation in flow.