The macroscopic friction of particulate materials often weakens as the flow rate is increased, leading to potentially disastrous intermittent phenomena including earthquakes and landslides. We theoretically and numerically study this phenomenon in simple granular materials. We show that velocity weakening, corresponding to a nonmonotonic behavior in the friction law, μ(I), is present even if the dynamic and static microscopic friction coefficients are identical, but disappears for softer particles. We argue that this instability is induced by endogenous acoustic noise, which tends to make contacts slide, leading to faster flow and increased noise. We show that soft spots, or excitable regions in the materials, correspond to rolling contacts that are about to slide, whose density is described by a nontrivial exponent θs. We build a microscopic theory for the nonmonotonicity of μ(I), which also predicts the scaling behavior of acoustic noise, the fraction of sliding contacts χ, and the sliding velocity, in terms of θs. Surprisingly, these quantities have no limit when particles become infinitely hard, as confirmed numerically. Our analysis rationalizes previously unexplained observations and makes experimentally testable predictions.
The flow rate of granular materials through an orifice
