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(2D) 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 α-1(d). The characteristic time is found to be fitted well by a power law a(dc-d)-γ, where dc is the critical opening size: as for d>dc, 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.