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Length scales and self-organization in dense suspension flows

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 correlation length, we develop an analogy between suspension ﬂows and the rigidity transition occurring when ﬂoppy networks are pulled, a transition believed to be associated with the stress stiffening of certain gels. After deriving the critical properties near the rigidity transition, we show numerically that suspension ﬂows lie close to it. We ﬁnd that this proximity causes a decoupling between viscosity and the correlation length of velocities ξ , which scales as the length l c characterizing the response to a local perturbation, previously predicted to follow l c ∼ 1 / √ z c − z ∼ p 0 . 18 , where p is the dimensionless particle pressure, z is the coordination of the contact network made by the particles, and z c is twice the spatial dimension. We conﬁrm these predictions numerically and predict the existence of a larger length scale l r ∼ √ p with mild effects on velocity correlation and of a vanishing strain scale δγ ∼ 1 /p that characterizes decorrelation in ﬂow.