Effect of particle collisions in dense suspension flows

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.~Düring, 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.

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• Anomalous linear elasticity of disordered networks
• Critical Scaling of Compression-Driven Jamming of Athermal Frictionless Spheres in Suspension
• Non-Affine Displacements Below Jamming under Athermal Quasi-Static Compression
• Unifying Suspension and Granular flows near Jamming
• Universality of stress-anisotropic and stress-isotropic jamming of frictionless spheres in three dimensions: Uniaxial vs isotropic compression