南京大学学报(自然科学版) ›› 2011, Vol. 47 ›› Issue (2): 120–125.

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 垂直激励下颗粒物质系统中的质量环流与密度波*

 杨 帆, 丁 茫, 蔡 慧, 缪国庆**
  

  • 出版日期:2015-04-08 发布日期:2015-04-08
  • 作者简介: ( 南京大学声学研究所, 近代声学教育部重点实验室, 南京, 210093)
  • 基金资助:
     国家自然科学基金( 10674067)

 Mass flow and density wave in a vertically vibrated granular system

 Yang Fan, Ding Mang, Cai Hui, Miao Guo Qing   

  • Online:2015-04-08 Published:2015-04-08
  • About author: (Institute of Acoustics and Key Laboratory of Modern Acoustics of Ministry of Education,
    Nanjing University, Nanjing, 210093, China)

摘要: 以实验方法研究了底部为锯齿形的环形槽中, 二维颗粒物质系统在垂直激励下的运动. 环形 槽外径 19 cm, 内径 18 ? 3 cm, 高 12 cm. 实验中选用约 1 000 个直径为 3 mm 的铜球. 以 Br?el & Kj? r
4805 振动台以及 Br?el & Kj? r 1050 振动激励控制器激励环形槽作竖直振动. 高速照相机( Redlake MASD M otionScope PCI 2000sc) 用于记录颗粒运动. 以外加激励频率 f 和无量纲外加激励加速度 ?=
4? 2 f 2 A/ g ( A 为激励振幅, g 为重力加速度)作为控制参数. 当 ? 超过 1 ? 8 时, 颗粒层自上而下呈流体化 状态. 实验中观察到沿水平方向的质量环流, 以及逆质量环流方向的密度波. 质量环流的速度自下而上
单调减小并反向. 随激励频率的增加, 质量环流速度单调减小, 而密度波振幅在 18 Hz 处有一极大值. 形成质量环流的机制为槽底部锯齿的棘齿效应, 密度波的形成机制尚在研究之中.

Abstract:  We report the experimental findings on horizontal transport and density wave in granular materials in a vertically vibrated annular container with a sawtooth?shaped base. The inner and outer diameters of the container are
183 mm and 190 mm, respectively. T he container is excited by Br?el & Kj? r 4805, which is controlled by a vibration exciter control Br?el & Kj? r 1050. The driving frequency f and the dimensionless acceleration amplitude
?= 4? 2 f 2 A/ g ( A is the driving amplitude and g the gravitational acceleration) are used as two control parameters. The particles are copper spheres with a diameter of 3 mm. A high speed camera ( Redlake MASD MotionScope PCI
2000sc) is used to record the movements of all spheres. An image processing technique is used to track the locations of all particles. We use the vibrating container as the reference frame in image processing. Every chosen region of
the pictures is divided into three stripes uniformly in vertical direction. T he experimental results are obtained by anassembly average. As ? increases to and beyond a critical value ? c = 1 ? 8, the granular layer fluidizes from top to
lower parts. The velocity distribution of grains indicates that the horizontal granular flow appears, and the fitting curves of densities indicate that the density wave appears in the layer. We have observed that from bottom to top the
granular flow velocity decreases and the direction reverses, while the density wave propagates against the granular flow. As driving frequency is increased, the granular flow velocity decreases monotonically, while the amplitude of
density wave has a maximum at 18Hz. The mechanism for the granular flow is the ratchet effect of the sawtooth of bottom of the container, while the exploration on the mechanism for the density wave is underway.

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