The global property of the dilute-to-dense transition of granular flows in a 2D channel

The dilute-to-dense transition of granular flow of particle size d ₀ is studied experimentally in a two dimensional channel (width D) with confined exit (width d). It is found that there exists a maximum inflow rate Q_c, above which the outflow changes from dilute to dense and the outflow rate Q(t) drops abruptly from Q_c to a dense flow rate Q _d. The re-scaled critical rate q_c(≡Q _c/(D/d₀)) is found to be a function of a scaling variable λ only, i.e. q_c ∼ F(λ), and λ ≡d/d₀ d d/D-d. This form of λ suggests that the dilute-to-dense transition is a global property of the flow; unlike the jamming transition, which depends only on d/d₀. The transition is found to occur when the area fraction of particles near the exit reaches a critical value 0.65±0.03.