A Stochastic Description of TransitionBetween Granular Flow States

Abstract

Two-dimensional granular flow in a channel with small exit is studiedby molecular dynamics simulations. We firstly define a key area nearthe exit, which is considered to be the choke area of the system.Then we observe the time variation of the local packing fraction andflow rate in this area for several fixed inflow rate, and find thatthese quantities change abruptly when the transition from dilute flowstate to dense flow state happens. A relationship between the localflow rate and the local packing fraction in the key area is also given.The relationship is a continuous function under the fixed particlenumber condition, and has the characteristic that the flow rate has amaximum at a moderate packing fraction and the packing fraction isterminated at a high value with negative slope. By use of the relationship,the properties of the flow states under the fixed inflow rate conditionare discussed in detail, and the discontinuities and the complex timevariation behavior observed in the preexisting works are naturallyexplained by a stochastic process.