Sudden Chain Energy Transfer Events in Vibrated Granular Media

Abstract

In a mixture of two species of grains of equal size but different mass, placed in a vertically vibrated shallow box, there is spontaneous segregation. Once the system is at least partly segregated and clusters of the heavy particles have formed, there are sudden peaks of the horizontal kinetic energy of the heavy particles, that is otherwise small. Together with the energy peaks the clusters rapidly expand and the segregation is partially lost. The process repeats once segregation has taken place again. Depending on the experimental or numerical parameters, the energy bursts can occur either randomly or with some regularity in time. An explanation for these events is provided based on the existence of a fixed point for an isolated particle bouncing with only vertical motion. The horizontal energy peaks occur when the energy stored in the vertical motion is partly transferred into horizontal energy through a chain reaction of collisions between heavy particles. A necessary condition for the observed regularity of the events is that chain reactions involve most of the heavy particles. Fluidized granular media in a shallow geometry (quasi two dimensional) has attracted attention because it allows for a detailed analysis of both the collective behavior and the motion of individual grains [9][10][11][12]. The possibility of quantifying the system's dynamics at both scales may help building a mathematical model for the collective dynamics of granular media. Placing monodisperse inelastic spheres in a vertically vibrated shallow box of height less than two particles' diameters, a particular phase separation takes place: grains form solid-like regions surrounded by fluid-like ones, having high contrasts in density, local order and granular temperature [9]. This phase separation is driven by the negative compressibility of the effective two dimensional fluid [10]. For shallow systems the horizontal kinetic energy of the grains can be quite different from the vertical kinetic energy.Granular matter is usually polydisperse, with grains differing in mass, shape, size or mechanical properties. It is known that a mixture of two types of grains differing in some of these properties can mix or segregate when externally excited [7].In this letter we report an experimental and numerical study of a phenomenon that takes place when two particle species of equal size but different mass are put in a vertically vibrated

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