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实验测量了重力驱动下的玻璃珠颗粒样品通过不同倾角和孔径的圆形孔洞的卸载流量.发现无论孔径大小,流量均与倾角的余弦呈良好的线性关系;线性外推得到的零流量角,即流量休止临界角随颗粒粒径与孔洞直径之比的减小而线性增加;在无穷大孔径极限下,此临界角在Bagnold角的误差范围内与样品的安息角一致.这些结果表明流量随倾角余弦线性变化的经验公式能揭示临界角的行为和特性,这是参数随倾角变化的Beverloo公式所不能描述的.
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关键词:
- 颗粒物质 /
- 倾斜孔洞流 /
- Beverloo公式
This work measured mass flux of a granular sample (glass beads) discharged from an inclined orifice for various inclination angles and orifice diameters. It is found that irrespective the orifice sizes, the fluxes all vary linearly with cosine of the inclination angle,and the linearly extrapolated angle of zero-flux,namely the critical angle of flow ceasing, increases linearly with ratio between grain and orifice diameter, tends to the angle of repose in the limit of infinite orifice diameter within an approximation of the Bagnold angle. The results show that the flux formula varying linearly with cosine of inclination angle is capable to reveal behaviors of the critical ceasing angle, a property that the Beverloo formula of which parameters vary with cosine of inclination angle can not describe.-
Keywords:
- granular matter /
- inclined orifice flow /
- Beverloo formula
[1] Nedderman R M 1992 Statics and Kinematics of Granular Materials (Cambridge: Cambridge University Press)
[2] Lu K Q, Liu J X 2004 Physics 33 713 (in Chinese) [陆坤权、刘寄星 2004 物理 33 713]
[3] Beverloo W A, Lenginer H A, van de Velde J 1961 Chem. Eng. Sci. 15 260
[4] Peng Z, Zheng H P, Jiang Y M 2009 arXiv: 0908.0258v3
[5] Sheldon H G, Durian D J 2010 Granular Matter 12 579
[6] Hou M, Chen W, Zhang T, Lu K, Chan C 2003 Phys. Rev. Lett. 91 204301
[7] Zhong J, Peng Z, Wu Y, Shi Q, Lu K, Hou M 2006 Acta Phys. Sin. 55 6691(in Chinese)[钟 杰、彭 政、吴耀宇、史庆藩、陆坤权、厚美瑛 2006 物理学报 55 6691]
[8] To K, Lai P K, Pak H K 2001 Phys. Rev. Lett. 86 71
[9] Kerner B S, Rehborn H 1997 Phys. Rev. Lett. 79 4030
[10] Appert-Rolland C, Chevoir F, Gondret P 2009 Traffic and Granular flow’07 (Heidelberg: Springer)
[11] Tang X, Zhang X, Lu K 2004 Traffic and Granular flow (Hangzhou:Zhejiang University Press)(in Chinese)[唐孝威、张训生、陆坤权 2004 交通流与颗粒流 (杭州:浙江大学出版社)]
[12] Nagel S R 1992 Rev. Mod. Phys.64 321
[13] Kong W, Hu L, Zhang X, Yue G 2010 Acta Phys. Sin. 59 411(in Chinese)[孔维姝、胡 林、张兴刚、 岳国联 2010 物理学报 59 411]
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[1] Nedderman R M 1992 Statics and Kinematics of Granular Materials (Cambridge: Cambridge University Press)
[2] Lu K Q, Liu J X 2004 Physics 33 713 (in Chinese) [陆坤权、刘寄星 2004 物理 33 713]
[3] Beverloo W A, Lenginer H A, van de Velde J 1961 Chem. Eng. Sci. 15 260
[4] Peng Z, Zheng H P, Jiang Y M 2009 arXiv: 0908.0258v3
[5] Sheldon H G, Durian D J 2010 Granular Matter 12 579
[6] Hou M, Chen W, Zhang T, Lu K, Chan C 2003 Phys. Rev. Lett. 91 204301
[7] Zhong J, Peng Z, Wu Y, Shi Q, Lu K, Hou M 2006 Acta Phys. Sin. 55 6691(in Chinese)[钟 杰、彭 政、吴耀宇、史庆藩、陆坤权、厚美瑛 2006 物理学报 55 6691]
[8] To K, Lai P K, Pak H K 2001 Phys. Rev. Lett. 86 71
[9] Kerner B S, Rehborn H 1997 Phys. Rev. Lett. 79 4030
[10] Appert-Rolland C, Chevoir F, Gondret P 2009 Traffic and Granular flow’07 (Heidelberg: Springer)
[11] Tang X, Zhang X, Lu K 2004 Traffic and Granular flow (Hangzhou:Zhejiang University Press)(in Chinese)[唐孝威、张训生、陆坤权 2004 交通流与颗粒流 (杭州:浙江大学出版社)]
[12] Nagel S R 1992 Rev. Mod. Phys.64 321
[13] Kong W, Hu L, Zhang X, Yue G 2010 Acta Phys. Sin. 59 411(in Chinese)[孔维姝、胡 林、张兴刚、 岳国联 2010 物理学报 59 411]
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