The critical phenomena of the dilute-to-dense transition in two-dimensional granular flow

The criticality of the dilute-to-dense transition in an inclined two-dimensional(M) granular channel flow is investigated. The waiting time t before the transition occurs and after the flow is initiated is recorded. It is found that the probability function C(t) for the flow remaining dilute at time t decays exponentially with a characteristic time alpha(-1) (d). The characteristic time is found to be fitted well by a power law a(d(c) - d)(-gamma), where d(c) is the critical opening size: as for d > d(c), the transition will never happen. The existence of a critical opening size at the exit confirms that the dilute-to-dense transition in 2D granular flow is a critical transition.