Analogy between strain-stiffening and jamming in dense flows

Dense granular and suspension flows display peculiar properties near the jamming threshold: the rheology is singular, and a diverging length scale can be identified from the velocity correlation of the particles, or from non-local effects affecting flow. In elastic networks a rigidity transition occurs when the coordination $z$ is increased toward some threshold $z_c$, but can also take place if a large strain is imposed as remarked early on by Maxwell. The latter phenomenon has been proposed to cause the ubiquitous stress-stiffening observed in gels of biopolymers. In my talk I will present the critical properties of a network immersed in a fluid approaching such a strain-induced rigidity transition. Then I will argue that this transition is at play in dense suspension flows, where it corresponds microscopically to the buckling of force chains. Our predictions include the existence of a vanishing strain $\gamma\sim 1/p$ in flow near jamming, where $p$ is the dimensionless particle pressure, and unravels the existence of two length scales affecting flow.