Effect of particle collisions in dense suspension flows

TL;DR

This paper investigates how particle collisions influence the velocity and force fields in dense suspension flows near jamming, providing a mechanistic understanding of the scaling laws governing viscosity and contact force distributions.

Contribution

It offers a mechanistic derivation of the scaling of viscosity with coordination deficit, linking local collision effects to global rheological properties in dense suspensions.

Findings

Collision effects significantly alter the velocity field within a diverging volume near jamming.

Contact force changes due to collisions are relatively modest compared to typical contact forces.

The derived scaling of viscosity with coordination deficit matches previous results, providing a mechanistic explanation.

Abstract

We study non-local effects associated with particle collisions in dense suspension flows, in the context of the affine solvent model known to capture various aspects of the jamming transition. We show that an individual collision changes significantly the velocity field on a characteristic volume $\Omega_c\sim 1/\delta z$ that diverges as jamming is approached, where $\delta z$ is the deficit in coordination number required to jam the system. Such an event also affects the contact forces between particles on that same volume $\Omega_c$, but this change is modest in relative terms, of order $f_{coll}\sim \bar{f}^{0.8}$, where $\bar{f}$ is the typical contact force scale. We then show that the requirement that coordination is stationary (such that a collision has a finite probability to open one contact elsewhere in the system) yields the scaling of the viscosity (or equivalently the viscous number) with coordination deficit $\delta z$. The same scaling result was derived in [E.~DeGiuli, G.~D\"uring, E.~Lerner, and M.~Wyart, Phys.~Rev.~E {\bf 91}, 062206 (2015)] via different arguments making an additional assumption. The present approach gives a mechanistic justification as to why the correct finite size scaling volume behaves as $1/\delta z$, and can be used to recover a marginality condition known to characterize the distributions of contact forces and gaps in jammed packings.