倾斜沙漏流与颗粒休止角研究

张昱; 韦艳芳; 彭政; 蒋亦民; 段文山; 厚美瑛

doi:10.7498/aps.65.084502

摘要

本文发现在测量误差内颗粒物质的下列三个临界角度相等: 1)从直径为D的倾斜孔洞流出的Beverloo颗粒流的流量开始停止的临界倾角c 向大孔径极限线性外推cc(D) 的补角s= 180-c;2) 从靠近堆顶的点源向光滑底板缓慢下落颗粒形成的圆锥形堆的休止角r; 3) 直接剪切矩形颗粒固体测得的库仑内摩擦角. 该结果倾向支持倾斜孔洞和颗粒堆自由表面的固-液转变与颗粒固体内部的库仑屈服均来自材料的同一临界性质. 由于三种情况样品的内部应力和变形等都是目前还远不能定量分析的复杂非均匀分布, 我们仅从定性角度对此给出一些讨论.

关键词:

Abstract

Systematic experimental study on inclined orifice flow and the measurement of the angle of repose are carried out in this work. The inclined orifice flow is formed by glass beads in an inclined channel. The flow is discharged near the bottom of the channel under gravity. The flow rates are measured at various inclination angles of the channel and opening sizes of the orifice. We then record the inclination angle when the rate becomes zero. We compare this zero-rate inclination angle with the repose angle of glass-beads, and the internal friction angle is determined by the yield stress obtained from a direct shear experiment. It is interesting to find that the experimental values at these three measured critical angles are equal within the experimental errors: 1) the supplementary angle of the extrapolating inclined angle at which the flow rate becomes zero and the inclined hole of diameter approaches infinitely large value (i. e. D), s= 180-c, where c is the critical angle for the inclined hole of diameter D and cc(D); 2) the repose angle r of a cone-shaped pile, which is formed when particles fall from the top point of the heap onto a smooth bottom plate; and 3) the internal friction angle that is measured by direct shear experiment. This result intends to support that the solid-liquid transitions occurring in the inclined orifice flow and free surface of granular heap, and the Coulomb yield occurring in the bulk of the granular solid all originate from the same critical property. Owing to the fact that the internal stresses and strains of samples in the three cases all have complicated and nonuniform distributions so that they cannot be analyzed quantitatively at present, Only some qualitative discussion on this issue is given in this paper.

Keywords:

作者及机构信息

1.
西北师范大学物理与电子工程学院, 兰州 730070;

2.
中国科学院物理研究所, 软物质物理重点实验室, 北京凝聚态国家重点实验室, 北京 100190;

3.
玉林师范学院物理科学与工程技术学院, 玉林 537000;

4.
上海大学, 上海市应用数学和力学研究所, 上海 200072;

5.
中南大学物理与电子学院, 长沙 410083

通信作者: 厚美瑛, mayhou@iphy.ac.cn

基金项目: 地震行业科研经费(批准号: 201208011)、国家自然科学基金(批准号: 11274354, 11047003)和中国科学院空间科学战略性先导科技专项(批准号: XDA04020200)资助的课题.

Authors and contacts

1.
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China;

2.
Key Laboratory of Soft Matter Physics, Beijing National Laboratory for Condense Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;

3.
College of Physical Science and Technology, Yulin Normal University, Yulin 537000, China;

4.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;

5.
School of Physical and Technology, Central South University, Changsha 410083, China

Corresponding author: Hou Mei-Ying, mayhou@iphy.ac.cn

Funds: Project supported by the Special Fund for Earthquake Research of China (Grant No. 201208011), the National Natural Science Foundation of China (Grant Nos. 11274354, 11047003), and the Strategic Priority Research Program-SJ-10 of the Chinese Academy of Sciences (Grant No. XDA04020200).

参考文献

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[2]	Sheldon H G, Durian D J 2010 Granular Matter 12 579
[3]	Thomas C C, Durian D J 2015 Phys. Rev. Lett. 114 178001
[4]	Thomas C C, Durian D J 2013 Phys. Rev. E 87 052201
[5]	Janda A, Zuriguel I, and Maza D 2012 Phys. Rev. Lett. 108 248001
[6]	Peng Z, Jiang Y M 2011 Acta Phys. Sin. 60 054501 [彭政, 蒋亦民 2011 60 054501]
[7]	Rubio-Largo S M, Janda A, Maza D, Zuriguel I, Hidalgo R C 2015 Phys. Rev. Lett. 114 238002
[8]	Ar'evaloab R, Garcimartnb A, Maza D 2007 Eur. Phys. J. E 23 191
[9]	Christian T V, Dimon P 2001 Granular Matter 3 151
[10]	Reydellet G, Rioual F E 2000 Europhys. Lett. 51 27
[11]	Pennec T L, Ammi M, Messager J C, Valancea A 1999 Eur. Phys. J. B 7 657
[12]	Narayanan M, Douglas J D 1997 Science 28 275
[13]	Baxter G W, Behringer R P 1989 Phys. Rev. Lett. 62 2825
[14]	Beverloo W A, Lengier H A 1961 Chem. Eng. Sci. 15 260
[15]	Jaeger H M, Liu C H, Nagel S R 1989 Phys. Rev. Lett. 62 40
[16]	Nagel S R 1992 Rev. Mod. Phys. 64 321
[17]	Bocquet L, Charlaix E, Ciliberto S, Crassous J 1998 Nature 396 24
[18]	Christian M D, Gerald H R, Jamie L M, Masami Nakagawa 1988 Phys. Rev. E 57 4991
[19]	Courrech du Pont S, Gondret P, Perrin B, Rabaud M 2003 Europhys. Lett. 61 492
[20]	Hornbaker D J, Albert R 1997 Nature 387 765
[21]	Tegzes P, Albert R, Paskvan M, Baraba'si A L, Vicsek T, Schiffer P 1999 Phys. Rev. E 60 5823
[22]	Boltenhagen P 1999 Eur. Phys. J. B 12 75
[23]	Jose M V, Antonio C, Antonio R 2000 Phys. Rev. E 62 6851
[24]	Aguirre M A, Nerone N, Calvo A, Ippolito I, Bideau D 2000 Phys. Rev. E 62 738
[25]	Albert R, Albert I, Hornbaker D, Schiffer P, Baraba'si A L 1997 Phys. Rev. E 56 6271
[26]	Azadeh S, Kudrolli A 2001 Phys. Rev. E 64 051301
[27]	Evesque P 1989 Phys. Rev. Lett. 62 44
[28]	Tennakoon S G K, Behringer R P 1998 Phys. Rev. Lett. 81 794
[29]	Grasselli Y, Herrmann H J 1997 Physica A 246 301
[30]	Liu C, Jeager H M, Nagel S R 1991 Phys. Rev. A 43 7091
[31]	Bagnold R A 1954 Proc. R. Soc. London A 49 225
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[33]	Liu Z C 2008 Measuring the Angle of Repose of Granular Systems Using Hollow Cylinders (New York: Academic Press) pp33-40
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[36]	Schwedes J 2003 Granular Matter 5 1

施引文献

[1]	Jaeger H M, Nagel S R, Behringer R P 1996 Rev. Mod. Phys. 68 1259
[2]	Sheldon H G, Durian D J 2010 Granular Matter 12 579
[3]	Thomas C C, Durian D J 2015 Phys. Rev. Lett. 114 178001
[4]	Thomas C C, Durian D J 2013 Phys. Rev. E 87 052201
[5]	Janda A, Zuriguel I, and Maza D 2012 Phys. Rev. Lett. 108 248001
[6]	Peng Z, Jiang Y M 2011 Acta Phys. Sin. 60 054501 [彭政, 蒋亦民 2011 60 054501]
[7]	Rubio-Largo S M, Janda A, Maza D, Zuriguel I, Hidalgo R C 2015 Phys. Rev. Lett. 114 238002
[8]	Ar'evaloab R, Garcimartnb A, Maza D 2007 Eur. Phys. J. E 23 191
[9]	Christian T V, Dimon P 2001 Granular Matter 3 151
[10]	Reydellet G, Rioual F E 2000 Europhys. Lett. 51 27
[11]	Pennec T L, Ammi M, Messager J C, Valancea A 1999 Eur. Phys. J. B 7 657
[12]	Narayanan M, Douglas J D 1997 Science 28 275
[13]	Baxter G W, Behringer R P 1989 Phys. Rev. Lett. 62 2825
[14]	Beverloo W A, Lengier H A 1961 Chem. Eng. Sci. 15 260
[15]	Jaeger H M, Liu C H, Nagel S R 1989 Phys. Rev. Lett. 62 40
[16]	Nagel S R 1992 Rev. Mod. Phys. 64 321
[17]	Bocquet L, Charlaix E, Ciliberto S, Crassous J 1998 Nature 396 24
[18]	Christian M D, Gerald H R, Jamie L M, Masami Nakagawa 1988 Phys. Rev. E 57 4991
[19]	Courrech du Pont S, Gondret P, Perrin B, Rabaud M 2003 Europhys. Lett. 61 492
[20]	Hornbaker D J, Albert R 1997 Nature 387 765
[21]	Tegzes P, Albert R, Paskvan M, Baraba'si A L, Vicsek T, Schiffer P 1999 Phys. Rev. E 60 5823
[22]	Boltenhagen P 1999 Eur. Phys. J. B 12 75
[23]	Jose M V, Antonio C, Antonio R 2000 Phys. Rev. E 62 6851
[24]	Aguirre M A, Nerone N, Calvo A, Ippolito I, Bideau D 2000 Phys. Rev. E 62 738
[25]	Albert R, Albert I, Hornbaker D, Schiffer P, Baraba'si A L 1997 Phys. Rev. E 56 6271
[26]	Azadeh S, Kudrolli A 2001 Phys. Rev. E 64 051301
[27]	Evesque P 1989 Phys. Rev. Lett. 62 44
[28]	Tennakoon S G K, Behringer R P 1998 Phys. Rev. Lett. 81 794
[29]	Grasselli Y, Herrmann H J 1997 Physica A 246 301
[30]	Liu C, Jeager H M, Nagel S R 1991 Phys. Rev. A 43 7091
[31]	Bagnold R A 1954 Proc. R. Soc. London A 49 225
[32]	Lajeunesse E, Mangeney-Castelnau A, Vilotte J P 2004 Phys. Fluids 16 2371
[33]	Liu Z C 2008 Measuring the Angle of Repose of Granular Systems Using Hollow Cylinders (New York: Academic Press) pp33-40
[34]	Zhang Q, Li Y C, Hou M Y, Jiang Y M, Liu M 2012 Phys. Rev. E 85 031306
[35]	Khidas Y, Jia X 2009 Sound Scattering in Dense Granular Media (Beijing: Science Press) pp4328-4336
[36]	Schwedes J 2003 Granular Matter 5 1

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