基于Janssen连续介质模型的筒仓-颗粒-提拉棒系统临界深度研究  

Investigation into Critical Depth in Silo-Grains-Lifting Rod Systems Based on Janssen’s Continuum Model

作　　者：张兴刚 崔晋秦 何宁怀 汤燕 崔津赫 王烽 ZHANG Xinggang;CUI Jinqin;HE Ninghuai;TANG Yan;CUI Jinhe;WANG Feng(College of Physics,Guizhou University,Guiyang 550025,Guizhou,China)

机构地区：[1]贵州大学物理学院,贵州贵阳550025

出　　处：《华南理工大学学报(自然科学版)》2024年第12期87-92,共6页Journal of South China University of Technology(Natural Science Edition)

基　　金：贵州省基础研究(自然科学)项目(ZK2022148);贵州大学大学生创新项目(2022113,2023126);贵州大学本科教学成果奖培育项目(2024-2)。

摘　　要：颗粒物质广泛存在于自然界及人类的生产生活中,它有许多不同于常规固体和液体的力学性质。粮仓效应是一个重要的、展现颗粒物质独特静力学性质的效应,人们从理论模型、计算机模拟等方面对其进行了比较深入的研究。“筷子提米”是一个与粮仓效应密切相关的有趣物理现象,但现有研究缺乏对此现象的定量分析,特别是对临界深度的探讨。该文先将“筷子提米”所涉及的实际系统抽象简化为由筒仓、颗粒、提拉棒构成的系统,采用粮仓效应中的Janssen连续介质模型对该系统进行静力学分析,从理论上推导出一个关于临界深度的超越方程。然后,结合实验以及该超越方程的数值解,对实验中颗粒体系的转向系数、临界深度随有关物理量的变化进行了探究。结果表明:不同实验条件下的转向系数在平均值1.16附近有微小的涨落;提拉棒直径不变时,筒仓直径、筒仓质量的增大会导致颗粒与筒仓的总质量增加,临界深度随之增大;筒仓直径不变时,提拉棒直径的增大会导致颗粒与筒仓总质量的减小、提拉棒与颗粒接触面积的增大,临界深度随之减小;理论计算与实验测量结果基本吻合。Granular matter is widely present in nature and human production and life.It exhibits many mechanical properties that differ from those of conventional solids and liquids.Janssen effect is one of the important and well-known phenomena that demonstrates the unique static mechanical properties of granular matter.Researchers have conducted in-depth studies on this effect from various perspectives,including theoretical models and computer simulations.“Chopstick rice-lifting”is an interesting physical phenomenon closely related to the Janssen effect.However,existing research lacks a quantitative analysis of this phenomenon,particularly regarding the discussion of the critical depth.In this paper,the actual system involved in“chopstick rice-lifting”is simplified into a system composed of a silo,grains,and a lifting rod,and the Janssen continuum model is employed to conduct a static mechanical analysis of this system,leading to the theoretical derivation of a transcendental equation concerning the critical depth.Subsequently,by combining experimental data with the numerical solution of this transcendental equation,the authors explore how the Janssen coefficient and critical depth of the granular system in the experiment vary with relevant physical quantities.The results indicate that the Janssen coefficient under different experimental conditions fluctuates slightly around an average value 1.16;and that,when the diameter of the lifting rod is held constant,an increase in the diameter and mass of the silo results in a higher total mass of both the grains and the silo,thereby increasing the critical depth.Conversely,when the diameter of the silo is constant,an increase in the diameter of the lifting rod leads to a decrease in the total mass and an increase in the contact area between the lifting rod and the grains,resulting in a decrease in the critical depth.The theoretical calculation results are generally consistent with the experimental measurement results.

关 键 词：颗粒物质 Janssen连续介质模型 粮仓效应 临界深度 

分 类 号：O414.2[理学—理论物理]