杜童节^1a, 周 亮², 陈立范², 王宏杰², 陈 泉^1b, 孔 平²

（1. 上海理工大学a. 健康科学与工程学院, b. 光电信息与计算机工程学院, 上海200093; 2. 上海健康医学院协同科研中心, 上海201318）

引用格式：杜童节, 周亮, 陈立范, 等. 垂直振动颗粒系统气液相变的临界特征[J]. 中国粉体技术, 2023, 29(5): 40-48.

DU T J, ZHOU L, CHEN L F, et al. Critical characteristics of gas-liquid phase transition in vertical vibrating particle systems[J]. China Powder Science and Technology, 2023, 29(5): 40-48.

DOI：10.13732/j.issn.1008-5548.2023.05.006

收稿日期：2023-03-21,修回日期：2023-05-30，在线出版时间：2023-07-26 17：52。

基金项目：国家自然科学基金项目,编号:11902190。

第一作者简介：杜童节(1998—),男,硕士研究生,研究方向为振动颗粒气体。E-mail: f203592629@163.com。

通信作者简介：孔平(1979—),女,副教授,博士,硕士生导师,研究方向为智能信息处理。E-mail: kongp@sumhs.edu.cn 。

摘要：为了研究颗粒系统在外界能量驱动下体系内部的运动与结构变化,采用局部密度判断法和粒子图像测速法,测量垂直振动二维圆盘内均值粒径为2 mm的球型颗粒的局部概率密度分布和速度分布,探究气液相变过程中离散颗粒的空间分布特征和动力学特征;通过增加圆盘颗粒的填充密度和振动台的加速度,建立局部概率密度分布的特征参数K值、 均值密度φ和加速度Γ的关系模型。结果表明:当垂直振动颗粒系统处于气态时,颗粒系统中颗粒的速度分布满足指数分布,颗粒速度分布指数等于1.52。在改变φ和Γ的过程中,颗粒系统发生气液相变,气液相变过程中颗粒速度速度分布的临界条件是一致的,即当颗粒速度分布指数等于1.40时,垂直振动颗粒系统开始从气态向液态转变。

关键词：振动颗粒系统; 气液相变; 密度分布

Abstract：In order to study the internal motion and structural changes of the particle system driven by external energy, the local probability density distribution and velocity distribution of spherical particles with an average diameter of 2 mm in the vertical vibrating two-dimensional disk were measured by local density judgment method and particle image velocimetry method, and the spatial distribution characteristics and kinetic characteristics of discrete particles during gas-liquid phase transition were explored. By increasing the filling density of particles in the disk and the acceleration of the shaker, the relationship model of the characteristic parameters K, mean density φ and acceleration Γ of the local probability density distribution was established. The results show that when the vertical vibrating particle system is in the gas state, the velocity distribution of particles in the particle system satisfies the exponential distribution, and the particle velocity distribution index is equal to 1.52. In the process of φ and Γ of the particle system, the critical condition of the gas-liquid phase transition of the particle system and the velocity distribution of the particle velocity during the gas-liquid phase transition is consistent, that is, when the particle velocity distribution index is equal to 1.40, the vertical vibrating particle system begins to transform from the gaseous state to the liquid state.

Keywords：vibrationally particle system; gas-liquid phase change; density distribution

参考文献(References)：

[1]NOIRHOMMME M, LUDEWIG F, VANDEWALLE N, et al. Cluster growth in driven granular gases[J]. Physical Review: E, 2017, 95(2): 022905.

[2]BRILLIANTOV N, POSCHEL T. Kinetic theory of granular gases[M]. New York: Oxford University Press, 2004: 35-49.

[3]WANG W G, HOU M Y, CHEN K, et al. Experimental and numerical study on energy dissipation in the freely cooling granular gases under microgravity[J]. Chinese Physics B, 2018, 27(8): 084501.

[4]BREY J J, DE SORIA M I G, MAYNER P. Inhomogeneous cooling state of a strongly confined granular gas at low density[J]. Physical Review: E, 2019, 100(5): 052901.

[5]FREITAS N, ESPOSITO M. Information flows in macroscopic Maxwell’s demons[J]. Physical Review: E, 2023, 107(1): 014136.

[6]LUDING S, CLEMENT E, BLUMEN A. Studies of columns of beads under external vibrations[J]. Physical Review: E, 1994, 49(2): 1634.

[7]LOSERT W, COOPER D G, DLOUR J. Velocity statistics in excited granular media[J]. Chaos, 1999, 9(1): 682-690.

[8]王文广. 微重力下颗粒气体自由冷却及相转变现象的研究[D]. 北京: 中国科学院大学, 2018.

WANG W G. Study on free cooling and phase transition phenomenon of particulate gas under microgravity[D]. Beijing: University of Chinese Academy of Sciences, 2018.

[9]ROUYER F, MENON N. Velocity fluctuations in a homogeneous 2D granular gas in steady state[J]. Physical Review Letters, 2000, 85(17): 3676.

[10]SHAH S H, LIN Y C, HOU M Y. Effect of number density on velocity distributions in a driven quasi-two-dimensional granular gas[J]. Chinese Physics: B, 2010, 19(10): 108203.

[11]李睿, 戴伟, 张端明. 加热机制对粒径呈幂律分布的颗粒气体中能量均分失效行为的影响[J]. 四川大学学报(自然科学版), 2017, 54(5): 1073-1076.

LI R, DAI W, ZHANG D M. Effect of heating mechanism on energy equalization failure behavior in particle size power-law distribution of granular gases [J]. Journal of Sichuan University(Natural Science Edition), 2017, 54(5): 1073-1076.

[12]NOIRHOMMME M, CAZAUBIEL A, FALCON E, et al. Particle dynamics at the onset of the granular gas-liquid transition[J]. Physical Review Letters, 2021, 126(12): 128002.

[13]吴麒麟. 微重力下颗粒物质运动行为基础研究[D]. 北京: 中国科学院大学, 2020.

WU Q L. Basic research on motion behavior of particulate matter under microgravity[D]. Beijing: University of Chinese Academy of Sciences, 2020.

[14]KNIGHT C, O’SULLIVAN C, VAN WACHEM B. Computing drag and interactions between fluid and polydisperse particles in saturated granular materials[J]. Computers and Geotechnics, 2020, 117: 103210.

[15]XU M B. Background interference removal algorithm for PIV preprocessing based on improved local Otsu thresholding[J]. Chinese Journal of Biomedical Engineering, 2022, 31(4): 147-159.

[16]MEER D, REIMANN P. Temperature anisotropy in a driven granular gas[J]. Europhysics Letters, 2019, 74(3): 384-386.

[17]HOU M, LIU R, ZHAI G. Velocity distribution of vibration-driven granular gas in Knudsen regime in microgravity[J]. Microgravity Science and Technology, 2008, 20(2): 73-80.

[18]PRASADV V, DAS D, SABHAPANDIT S, et al. Velocity distribution of driven granular gases[J]. Journal of Statistical Mechanics: Theory and Experiment, 2019, 2019(6): 063201.

[19]ROVERE M, HEERMANN D W, BINDER K. Block density distribution function analysis of two-dimensional Lennard-Jones fluids[J]. Europhysics Letters, 1988, 6(7): 585-588.

[20]ROVERE M, HEERMANND W, BINDER K. The gas-liquid transition of the two-dimensional Lennard-Jones fluid[J]. Journal of Physics: Condensed Matter, 1990, 2(33): 709-714.

[21]HARTH K, TRITTEL T, WEGNER S, et al. Free cooling of a granular gas of rodlike particles in microgravity[J]. Physical Review Letters, 2018, 120(21): 214301.

[22]KAWARADA A, HAYAKAWA H. Non-Gaussian velocity distribution function in a vibrating granular bed[J]. Journal of the Physical Society of Japan, 2004, 73(8): 2037-2040.