Criticality of the dilute-to-dense transition in a 2D granular flow

Abstract

This work investigates the criticality of the dilute-to-dense transition in an inclined quasi-2D granular channel flow. At fixed inflow rate Q0 and exit opening size d, the waiting time t before the transition occurs after a dilute flow is initiated at t = 0 is recorded. The histogram f(t) of the number of times counted that the transition occurs at a time t is plotted as a function of t for each d. It is found that the probability function C(t) for the flow remaining dilute at a waiting time t decays exponentially, and its characteristic time α−1(d) can be fitted well to a power law a(dc−d)−γ with dc the critical opening size beyond which the transition will never occur.

External pressure dependence of granular orifice flow: Transition to Beverloo flow

“…For example, when an intruder approaching the solid bottom boundary of a granular medium, the penetration resistance near the boundary is found increasing exponentially with decreasing distance, which may be related to the characteristic length of "jamming" caused by the locally applied stress [31] . When studying the criticality of the dilute-to-dense transition in granular flow, it's found that the probability function for the flow remaining dilute decays exponentially with the waiting time [32] . The transition follows exponential decay and has a characteristic parameter that appears to be a property of granular media.…”

Numerical simulations in granular matter: The discharge of a 2D silo

“…In these containers jamming -that is, a complete arrest of the flow making the granular material behave like a solid -is known to appear as soon as the size of the exit hole is reduced to a few times the average diameter of the grains inside. Experimental work in both 2D and 3D hoppers [47,48] and silos [49][50][51][52][53] have shown that jamming depends only on the ratio between particle and exit hole sizes, as long as the diameter and height of the silo are large enough such that (1) the boundary effects of the walls can be neglected and (2) the pressure at the bottom of the silo saturates, following the Janssen effect [6].…”

Phase transition in peristaltic transport of frictionless granular particles

“…Here, we consider the peristaltic transport of dry and smooth granular particles, which is closely related to the transport of particles through a bottleneck [12,13], particularly the discharge of grains from a silo [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Through previous studies it has been established that there are three regimes depending on the linear size of the bottleneck, w. If w is sufficiently large, particles flow continuously [16][17][18][19][20].…”

“…It is also known that the mass flow rate Q satisfies the Beverloo law Q ∝ (w − w 0 ) B for an empirical value w 0 , where B is 3/2 and 5/2 for twoand three-dimensional systems under gravity, respectively [16][17][18], and B is 1 for disks on a conveyor belt [19,20]. With decreasing size of the bottleneck, the flow becomes intermittent owing to the formation and breakdown of an arch at the outlet [21][22][23][24], and finally the flow stops, i.e., jamming occurs [25][26][27][28][29]. Note, however, that the term jamming used in this context is slightly different from that in the jamming transition of granular matter discussed in recent studies [30][31][32][33][34][35][36][37].…”

“…Indeed, the jamming transition can be observed even for smooth, i.e., frictionless, granular particles, while the jamming of a granular flow at the bottleneck is due to the persistent arch formation by grains, which can be observed only for rough, or frictional, particles. What actually corresponds to the jamming transition in the discharge of grains appears to be the so-called dilute-to-dense transition [21][22][23], which is observed at a phase boundary between continuous and intermittent regimes.…”