Waves And Flows In A Vertically Vibrated Annular Granular System

The granular materials are widespread in nature, and are closely related with industrial production and people’s daily life. Different from normal solid, liquid and gas, the granular materials are a special material state. In recent decades, with the development of experimental technique and computer simulation technique, many peculiar and interesting phenomena and unique motion laws, such as surface patterns, heaping, convection, soliton etc., are revealed constantly in the granular materials which present as an energy dissipation system under external excitation. These findings not only deepen our understanding of nonlinear discrete media but also play an important guiding role in many similar practical problems. In this paper, by experiment, we mainly study waves and flows in the granular materials within an asymmetric periodic structure under vertical vibration.We use a two-dimensional annular granular system which has an asymmetric sawtooth-shaped base and is vibrated vertically. We study the surface waves, the horizontal flow and the shock waves in the system. For the surface waves, a DV camera is used to record panoramic views of the granular system, and behaviors of the system under different driving parameters are observed by slow playback of videos of the panoramic views. For the horizontal flow and shock waves, a high-speed digital camera is used to record local regions of the granular system, and motions within the system are studied with the help of particle-tracking technique and by making statistical and average analyses on the behavior of granules in the measure window.In a large range of driving parameters, there are rich patterns forming on the surface of the annular granular system. These surface patterns include periodic subharmonic waves, kink pairs, superpositions of kink pair and subharmonic wave, bulk motions, multi-kink pairs and gas-liquid hybrid kink pairs in a thin granular layer, etc. We analyze in detail the formation and transition of different surface patterns, and discuss the effect of driving parameters and layer thickness on the pattern formation and transition. The velocity of kink pair as a function of driving parameters is measured, and a simple explanation is given.When there are surface patterns, the horizontal flow caused by the asymmetric sawteeth also exists in the granular system. We focus on the horizontal flow in the subharmonic wave and the arm region of kink pair. The variation of total horizontal flow with time indicates that there are positive and negative flows, and the variation of the flow is periodic. The total flow changes dramatically when the granular layer collides with the base, and changes slightly after the layer leaves the base. The variation of stratified horizontal flow with space and time indicates that there are positive and negative flows simultaneously in the layer at any moment. The variation of spatial distribution of the flow is also periodic in time, and the spatial distribution changes by collisions in the layer. The variation of time-averaged total flow with driving parameters indicates that the time-averaged total flow always increases first, then decreases, and then increases with driving acceleration. The first increment corresponds to the presence of a subharmonic wave, and the flow decreases with driving frequency. The second increment corresponds to the presence of a superposition of kink pair and subharmonic wave, and the flow increases with driving frequency. The variation of time-averaged total flow with driving parameters could be explained by ratchet effect and fluidization of the system. The surface wave and the internal flow are related, and the relationship between the velocity of kink pair and the velocity of flow is preliminarily explored.In order to compare with the horizontal flow in the granular system which has surface waves, we also study the horizontal flow in the system which has no surface waves. When there are no surface waves, the variation of the flow with time is also periodic. The variation of total flow with time indicates that there are positive and negative flows when the driving acceleration is low, and the negative flow gradually disappears as the driving acceleration increases. The effect of driving frequency on the total flow increases with driving acceleration. The variation of stratified horizontal flow with space and time indicates that there are positive and negative flows in the lower layer and the flow changes greatly. There is usually only positive flow in the upper layer and the flow changes little. The variation of time-averaged total flow with driving parameters indicates that the flow increases with driving acceleration, and is insensitive to driving frequency. The variation of the flow in the system with no surface waves is essentially different from the situation with surface waves.By analyzing the density fluctuation, the temperature and the Mach number in the granular system, we study the density wave and the shock wave within the system. When there are no surface waves, the density waves arise in the system are similar in two driving periods. The density wave is caused by the collision between the layer and the base, and propagates upward with a non-uniform velocity by collisions within the layer. During the propagation of the density wave, the compression and expansion of the layer often generate shock wave. We discuss in detail the space-time distribution of the shock wave. The shock wave arises in the temperature wave front regions caused by collisions, and disappears in the compression regions after collisions. The shock width decreases during the propagation, and the shock wave finally disappears in the top layer. The temperature increases with driving acceleration, and the Mach number is insensitive to driving acceleration. When there is a subharmonic wave, two density waves caused by two collisions between the trough and the base arise in a vibrating period. The two density waves are generally distinct. The two collisions also generate two shock waves, and the transition from vertical motion to horizontal motion happens in the system when the shock waves reach the upper layer, resulting in new crest and trough. When there is a kink pair, two totally different density waves caused by two collisions between the arm and the base arise in a vibrating period. The two density waves are decaying waves with a high speed. When the surface wave, the horizontal flow and the shock wave exist simultaneously, the situation is complex and interesting. We make an effort to explore the relation among the three different motions.