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双分散颗粒体系在临界堵塞态的结构特征

张威 胡林 张兴刚

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双分散颗粒体系在临界堵塞态的结构特征

张威, 胡林, 张兴刚

Structural features of critical jammed state in bi-disperse granular systems

Zhang Wei, Hu Lin, Zhang Xing-Gang
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  • 堵塞行为是颗粒体系中一种常见的现象, 其力学性质与堆积结构的关联非常复杂. 本文采用离散元法研究了由两种不同半径颗粒组成的二维双分散无摩擦球形颗粒体系在临界堵塞态所呈现的结构特征, 讨论了大小颗粒粒径比与大颗粒百分比对临界堵塞态的影响. 数值模拟结果表明, 当粒径比 小于1.4时, 临界平均接触数与大颗粒百分比关系不大, 当粒径比 大于1.4时随着大颗粒百分比的增大临界平均接触数先减小再增大. 而临界体积分数在粒径比 小于1.8时随着大颗粒百分比的增加先减小后增大, 大于1.8时又基本不随大颗粒百分比而变化. 大颗粒百分比在接近0或1 时, 系统近似为单分散体系, 临界平均接触数与体积分数基本不随半径比的增大而变化; 在接近0.5时, 临界平均接触数随着半径比的增大逐渐减小, 而临界体积分数则是先减小后增大. 文中对大-小颗粒这一接触类型的百分比也进行了探讨, 其值随着大颗粒百分比的增大呈二次函数的变化趋势, 粒径比对这一变化趋势只有较小的影响.
    A jammed state is a common phenomenon in complex granular systems, in which the relationship between the mechanical properties and the geometric structures is very complicated. The critical jammed state in a two-dimensional particle system is studied by numerical simulation. The system is composed of 2050 particles with two different radii, whose distribution is random. Initially the particles with a smaller radius are of a looser distribution in the given space. When the radius increases, a transition from the looser state to the jammed state happens. The particle dimension-radius ratio and the percentage of large particles kB play primary roles in this system, which are discussed in detail based on the statistical analysis of the average contact number, packing fraction, and contact type. By analyzing the relationship between pressure and packing fraction of the granular system, the critical jammed point for the applied pressure to the boundary can be found. Numerical simulation result shows that no obvious connection exists between the average contact number and the percentage of large particles for the case that the particle dimension-radius ratio is less than 1.4. The average contact number approximate to 4 when = 1.4, which is consistent with previous conclusions. The average contact number first decreases and then increases when the percentage of large particles become larger in the case 1.4. A minimum value C = 0.84 is obtained when kB = 0.5. When the percentage of large particles increases, the critical packing fraction decreases first and then increases in the case 1.8, but it almost keeps constant for 1.8. When the percentage of large particles is close to either 0% or 100%, the granular system is approximately mono-disperse. In this case, the average contact number and packing fraction become constant. When the percentage is close to 50%, the critical average contact number decreases all the time with larger particles-radius ratio, while the critical packing fraction decreases first and then increases. The percentage of large-small contact type is also discussed. The value varies following a quadratic function with the increase of the percentage of large particles, while the particles-radius ratio has slight impact on this variation. Specifically, we have calculated the percentage of large-small contact type based on probabilistic method, and the result agrees well with the simulation results. We give the reason why previous researchers studied the case of = 1.4 :1 and kB = 0.5 on the basis of results in this paper, and find that the values of and kB have no influence on the power-law relation around the critical jammed state.
      Corresponding author: Hu Lin, hulin53@sina.com;sci.xgzhang@gzu.edu.cn ; Zhang Xing-Gang, hulin53@sina.com;sci.xgzhang@gzu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11264006) and the Introduced Talents of Scientific Research Foundation of Guizhou University, China (Grant No. 201334).
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    Zhang G H, Sun Q C, Huang F F, Jing F 2011 Acta Phys. Sin. 60 124502 (in Chinese) [张国华, 孙其诚, 黄芳芳, 金峰 2011 物理学报 60 124502]

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    Eric l. Corwin, Heinrich M. Jaeger 2005 Nature 03698 1075

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    Zhang X G, Hu L 2012 Chin. J. Comput. Phys. 29 627 (in Chinese) [张兴刚, 胡林 2012 计算物理 29 627]

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    Feng X, Zhang G H, Sun Q C 2013 Acta Phys. Sin. 62 184501 (in Chinese) [冯旭, 张国华, 孙其诚 2013 物理学报 62 184501]

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出版历程
  • 收稿日期:  2015-05-19
  • 修回日期:  2015-09-14
  • 刊出日期:  2016-01-20

双分散颗粒体系在临界堵塞态的结构特征

    基金项目: 国家自然科学基金(批准号: 11264006)和贵州大学引进人才科研基金(批准号:201334)资助的课题.

摘要: 堵塞行为是颗粒体系中一种常见的现象, 其力学性质与堆积结构的关联非常复杂. 本文采用离散元法研究了由两种不同半径颗粒组成的二维双分散无摩擦球形颗粒体系在临界堵塞态所呈现的结构特征, 讨论了大小颗粒粒径比与大颗粒百分比对临界堵塞态的影响. 数值模拟结果表明, 当粒径比 小于1.4时, 临界平均接触数与大颗粒百分比关系不大, 当粒径比 大于1.4时随着大颗粒百分比的增大临界平均接触数先减小再增大. 而临界体积分数在粒径比 小于1.8时随着大颗粒百分比的增加先减小后增大, 大于1.8时又基本不随大颗粒百分比而变化. 大颗粒百分比在接近0或1 时, 系统近似为单分散体系, 临界平均接触数与体积分数基本不随半径比的增大而变化; 在接近0.5时, 临界平均接触数随着半径比的增大逐渐减小, 而临界体积分数则是先减小后增大. 文中对大-小颗粒这一接触类型的百分比也进行了探讨, 其值随着大颗粒百分比的增大呈二次函数的变化趋势, 粒径比对这一变化趋势只有较小的影响.

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