Anomalous behavior of granular particles falling through a funnel

Abstract

In this thesis, we show several surprising phenomena that occur in an extremely simple system of a single frictionless, inelastic, spherical particle falling under gravity through a symmetric funnel. One might naively expect that particles would fall through funnels with steeper sides more quickly, exert a smaller total impulse on the funnel walls and lose less energy. However, we show that there are special ranges of angles of the funnel walls for which exactly the opposite occurs. Typically, the particle will experience a sequence of collisions that is highly sensitive to the location that it enters the funnel and nearby particle trajectories become widely dispersed. However, in the special angular ranges this is not the case, and the particle can experience sequences of collisions that have a highly coherent structure. We provide a theoretical analysis that can predict and explain this surprising behavior. We further consider the system in which the side walls have friction, and find that when the coefficient of kinetic friction is relatively large, the particle will stay longer inside the system when the declined angle of funnel is larger than 45±. We also give a theoretical explanation to this phenomenon.