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The phenomenon of granular capillary rising under vertical vibration provides a novel technical route for hoisting, transporting and collecting granular materials. However, there are still obvious deficiencies in the existing studies of the granular capillary rising behavior, especially the intensive investigation on the effects of gravitational acceleration, horizontal vibration component and particle size distribution are still lacking. To address these problems, the discrete element method is used to numerically simulate the granular capillary rising phenomenon under different operating conditions. The final capillary rising height and average capillary rising velocity of the granular matter are computed and analyzed based on the numerical simulations. The results show that the granular capillarity can also occur under low gravity conditions, and that the final capillary rising height and the average capillary rising velocity first increase and then decrease with the gravitational acceleration. It is also found that the final capillary rising height is insensitive to the variation of horizontal vibrational component, whereas the average capillary rising velocity increases with the augmentation of horizontal vibrational component. Compared with the mono-sized particles, the particles with the same mean size but having a Gaussian size distribution exhibit a maximal capillary rising height at a larger critical tube diameter. Meanwhile, the average capillary rising velocity of the particles having a Gaussian size distribution is faster in the tube diameter range where the granular capillary dynamics for both size distributions is dominated by the jamming effect.
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Keywords:
- granular matter /
- capillary effect /
- vertical vibration /
- discrete element method
[1] Xing Y, Zheng J, Li J D, Cao Y X, Pan W, Zhang J, Wang Y J 2021 Phys. Rev. Lett. 126 048002
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Zhao Y Z, Cheng Y, Zheng J Y 2009 Chin. J. Comput. Mech. 26 239
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图 1 颗粒系统示意图
Figure 1. Schematic diagram of granular system.
图 2 不同重力加速度下颗粒毛细上升动力学过程
Figure 2. Dynamic process of granular capillary rising under different gravitational accelerations.
图 3 毛细上升高度随时间的演变
Figure 3. Evolution of capillary rising height with time.
图 4 最终毛细上升高度和平均毛细上升速度随重力加速度的变化
Figure 4. Dependence of final capillary rising height and average capillary rising velocity on gravitational acceleration.
图 5 最终毛细上升高度和平均毛细上升速度随水平振动分量的变化
Figure 5. Dependence of final capillary rising height and average capillary rising velocity on horizontal vibrational component.
图 6 不同粒径分布下最终毛细上升高度和平均毛细上升速度随管径的变化
Figure 6. Dependence of final capillary rising height and average capillary rising velocity on tube diameter under different particle size distribution.
表 1 数值模拟参数
Table 1. Parameters used in numerical simulations
参数 符号 数值 容器内径/mm D 28.2 管内径/mm d 8 颗粒数目 Np 200000 管壁厚度/mm δ 0.6 管底面距容器底面的距离/mm L 30 颗粒密度/(kg⋅m–3) ρp 2500 杨氏模量/MPa Y 10 泊松比 υ 0.25 恢复系数 ε 0.5 颗粒间滑动摩擦系数 μpp,s 0.8 颗粒间滚动摩擦系数 μpp,r 0.1 颗粒-壁面间滑动摩擦系数 μpw,s 0.58 颗粒-壁面间滚动摩擦系数 μpw,r 0.05 振幅/mm Az 12.42 频率/Hz f 10 
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[1] Xing Y, Zheng J, Li J D, Cao Y X, Pan W, Zhang J, Wang Y J 2021 Phys. Rev. Lett. 126 048002
Google Scholar
[2] Li Z F, Zeng Z K, Xing Y, Li J D, Zheng J, Mao Q H, Zhang J, Hou M Y, Wang Y J 2021 Sci. Adv. 7 eabe8737
Google Scholar
[3] Then H Z, Sekiguchi T, Okumura K 2020 Soft Matter 16 8612
Google Scholar
[4] Kogane A, Kuwagi K, Mawatari Y, Mawatari Y, Davoren L, Seville J P K, Parker D J 2020 J. Phys. Commun. 4 075012
Google Scholar
[5] van Gerner H J, van der Weele K, van der Meer D, van der Hoef M A 2015 Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 92 042203
Google Scholar
[6] Sánchez I, Díaz A A, Guerrero B, Trosel Y, Rojas C 2015 Mech. Res. Commun. 67 1
Google Scholar
[7] 郭宇, 凡凤仙, 白鹏博, 刘举 2019 上海理工大学学报 41 409
Google Scholar
Guo Y, Fan F X, Bai P B, Lu J 2019 J. Univ. Shanghai for Sci. Technol. 41 409
Google Scholar
[8] Sánchez I, Darias J R, Paredes R, Lobb C J, Gutiérrez G 2009 Traffic Granular Flow 545
[9] Liu C P, Wu P, Wang L 2013 Soft Matter 9 4762
Google Scholar
[10] 张富翁, 王立, 刘传平, 吴平 2014 物理学报 63 014501
Google Scholar
Zhang F W, Wang L, Liu C P, Wu P 2014 Acta. Phys. Sin. 63 014501
Google Scholar
[11] Fan F X, Parteli E J R, Pöschel T 2017 Phys. Rev. Lett. 118 218001
Google Scholar
[12] 张华腾, 凡凤仙, 王志强 2020 力学学报 52 442
Google Scholar
Zhang H T, Fan F X, Wang Z Q 2020 Chin. J. Theo. Appl. Mech. 52 442
Google Scholar
[13] 凡凤仙, 王志强, 刘举, 张华腾 2019 力学学报 51 415
Google Scholar
Fan F X, Wang Z Q, Liu J, Zhang H T 2019 Chin. J. Theo. Appl. Mech. 51 415
Google Scholar
[14] Fan F X, Liu J, Parteli E J R, Pschel T 2017 EPJ Web of Conferences 140 16008
Google Scholar
[15] 刘举, 白鹏博, 凡凤仙, 胡晓红 2016 化工进展 35 1956
Google Scholar
Liu J, Bai P B, Fan F X, Hu X H 2016 Chem. Ind. Eng. Prog. 35 1956
Google Scholar
[16] Zhang F W, Cronin K, Lin Y H, Miao S, Liu C P, Wang L 2019 Powder Technol. 343 383
Google Scholar
[17] Zhang F W, Cronin K, Lin Y, Liu C, Wang L 2018 Powder Technol. 333 421
Google Scholar
[18] Zhang F W, Wang L, Liu C P, Wu P 2017 Adv Powder Technol. 28 356
Google Scholar
[19] Liu C P, Zhang F W, Wu P, Wang 2014 Powder Technol. 259 137
Google Scholar
[20] Kawamoto H, Kubo K, Kikumiya R, Adachi M 2021 J. Aerosp. Eng. 34 04021097
Google Scholar
[21] Liu Y, Zhao J H 2015 Chin. Phys. B 24 034502
Google Scholar
[22] Xu Y P, Musser J, Li T, Padding J T, Rogers W A 2017 Powder Technol. 320 304
Google Scholar
[23] Zhang N, Cheng B, Baoyin H 2019 Appl. Math. Mech. Engl. Ed. 40 127
Google Scholar
[24] Brilliantov N V, Spahn F, Hertzsch J M, Pöschel T 1996 Phys. Rev. E 53 5382
Google Scholar
[25] Cundall P A, Strack O D 1979 Géotechnique 29 47
Google Scholar
[26] Ai J, Chen J F, Rotter J M, Ooi J Y 2011 Powder Technol. 206 269
Google Scholar
[27] Kloss C, Goniva C, Hager A, Amberger S, Pirker S 2012 Prog. Comput. Fluid Dyn. 12 140
Google Scholar
[28] Shäfer J, Dippel S, Wolf D E 1996 J. Phys. I 6 5
Google Scholar
[29] 赵永志, 程易, 郑津洋 2009 计算力学学报 26 239
Zhao Y Z, Cheng Y, Zheng J Y 2009 Chin. J. Comput. Mech. 26 239
[30] Ng T T, Zhou W, Ma G, Chang X L 2014 J. Eng. Mech. 141 04014167
Google Scholar
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