"Faster is Slower" Effect in Granular Flows

GAGO, PAULA A.; PARISI, DANIEL R.; PUGNALONI, LUIS A.

Moscu

Conferencia; TRAFFIC AND GRANULAR FLOW '11; 2011

The faster is slower (FIS) effect was predicted by using the social force model, for the scape of panicking pedestrians through a narrow door (Helbing et al., 2000). FIS refers to the existence of an optimum pedestrian desired velocity that yield the shortest mean evacuation time. This optimum is related with the appearance of blocking clusters (Parisi and Dorso, 2005). Even though blockages have been observed in real catastrophes, the faster is slower curve was not still measured for humans under laboratory conditions. In the present work, we found an analogous granular flow system that exhibits the FIS effect. It consist of a quasi two-dimensional hopper placed on a vibrating inclined plane. Increasing the angle of the plane (θ) leads to an increase in the component of the force of gravity parallel to it. This is similar to increasing the desired force in the social force model. The vibration is an aid to break blockages which otherwise would be stable and arrest the flow permanently (Mankoc et al., 2009). We placed a microphone below the exit such that particles leaving the hopper knock it and a signal can be registered for each realization for different angles (θ). Post-processing of these signals allows to obtain the time intervals between two successive particles (dt) and also the total discharge time (T). For narrow exits (3 particles diameters) the distribution of dt shows a long tail which is the main responsible for the total discharge time. This tail can be fitted by a power law (Janda et al., 2009) with a negative exponent α, were |α| < 2, indicating that the mean dt is not defined. As a consequence, the mean discharge time is not defined and depends on the number of discharges studied. Hence, we take α as a measure of the ability of the system not to develop long-lasting blockages. Small values of |α| indicate that the probability of having long flow interruptions (dt) is higher. It is observed that |α| decreases when the angle θ increases, indicating that the efficiency of the discharge gets worse for increasing angles (i.e. large desire forces) in the range studied. This is, to our knowledge, the first experimental evidence of the FIS effect in granular flows. Moreover, our results suggest that a different approach might be necessary to quantify the evacuation times for pedestrians since the mean of T may not be defined in such systems.