Effective Dimension Transition of the Dynamics of Granular Materials in the Pipe

Phase transition of strongly excited granular materials in 2D pipe is investigated numerically. By changing the ratio between width of the pipe and the height of the granular bed, we observe the transition between the 1 dimensional like state and the actual 2 dimensional state. Moreover, it is found that the character of the transition changes when the magnitude of dissipation passes through a critical value. PACS number(s): Granular materials exhibit some complex phenomena. These complex phenomena strongly depend on not only the character of external forces but also that of boundary condition. When granular materials in slim pipes with fluid (air, water, and so on) flow down or are fluidized by inducing fluid from the bottom, slugging is observed . In most of the investigations of such slugging in a slim pipe, the system’s effective dimension is regarded as 18–10. On the other hand, two or more dimensional phenomena, bubbling and channeling, occur when granular materials are in a wider vessel. The similar tendency is also observed for granular materials in a vibrating vessel3–6. When the width of the vessel is small, most of particles construct solid structure in bulk and only particles near side E-mail: [email protected] 1 walls flow down to the bottom. However, in a wide vessel, most of particles are strongly fluidized and construct multi-roll structure like Bernard convection From these facts, the behaviors of granular materials are extremely different between that in a slim vessel and that in a wide vessel. Then, an important problems appear; what quantity determines ’slim’ (one dimensional system) or ’wide’ (two or three dimensional system) for a given system? The purpose of this paper is to make a clear view on this problem. Here, we simulate following simplified situation. The system consists of two dimensional particles of mass 1 and diameter d in a two-dimensional box under uniform gravity. The width of the box is a, and the height of the box is infinite. We employ the following particle model which is one of the simplest model of granular materials. The equation of the motion of the ith particle is