颗粒物质中空洞现象的实验研究
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摘要
本文用实验的方法研究了颗粒物质中存在空洞时对体系力链结构的影响。当在颗粒物质中竖直提拉圆棒时其下端将产生空洞，空洞的存在导致颗粒体系内部力链结构发生变化，变化的情况可通过测定棒受到的摩擦力来反映。在前人研究的基础上，我们结合自己的实验目的改进了实验装置，分别测量了不同颗粒填充高度(即空洞产生的深度)，颗粒直径，筒仓直径和探测棒直径条件时空洞对颗粒物质中应力变化的影响。实验结果表明，空洞对颗粒物质中应力变化的影响只与空洞产生的深度存在着一定的关系，而与颗粒直径，筒仓直径和探测棒直径无关。利用origin软件对实验数据拟合得到由于空洞的存在导致颗粒体系力链结构崩塌的时间t与空洞产生的深度h存在着如下关系：t=Aexp(h／λ)+B，公式中各拟合参数分别为：A=7.5+0.3，B=2.4±0.4，λ=70.0±0.7。因为t只与空洞产生深度h有关，因此，具有普适的意义，可以应用到与颗粒物质相关的体系中。我们还设计了二维的空洞实验，以便更好的理解和观察颗粒体系内部在空洞影响时颗粒力链的变化情况。
The change of force chain influenced by cavity effect in granular matter is studied experimentally. When pull out a rod from granular matter, that should exist a cavity under it and the force chain structure will be changed, the change should be studied by the friction of the rod. Based on former research, we improved our experimental set, measured the cavity effect of different depth of the filling granules(viz. the depth of the cavity), different diameter of the granules, different diameter of the container and different diameter of the rod. We found that the granular matter is influenced by the cavity's depth only, and this relationship is independent of the diameter of the granules, diameter of the container and diameter of the rod. By using origin soft, We found the relationship between the breakdown time t and thecavity's depth h is t= Aexp(h/λ.) +B and A=7.57±0.3 , B=2.45±0.4 ,λ=70.00±0.7. This expression could be used in the other granular system. We do an two-dimension experiment at the same time, to understand the inside situation of the granular matter clearly.
The change of force chain influenced by cavity effect in granular matter is studied experimentally. When pull out a rod from granular matter, that should exist a cavity under it and the force chain structure will be changed, the change should be studied by the friction of the rod. Based on former research, we improved our experimental set, measured the cavity effect of different depth of the filling granules(viz. the depth of the cavity), different diameter of the granules, different diameter of the container and different diameter of the rod. We found that the granular matter is influenced by the cavity's depth only, and this relationship is independent of the diameter of the granules, diameter of the container and diameter of the rod. By using origin soft, We found the relationship between the breakdown time t and thecavity's depth h is t= Aexp(h/λ.) +B and A=7.57±0.3 , B=2.45±0.4 ,λ=70.00±0.7. This expression could be used in the other granular system. We do an two-dimension experiment at the same time, to understand the inside situation of the granular matter clearly.
引文
[1] 陆坤权，刘寄星．颗粒物质(上)．物理．2004，33(09)．629～635．
[2] 陈唯，电场作用下颗粒流动的行为研究．博士论文．2002，1～35．
[3] 厚美瑛，陈唯等．物理．2004，33(7)：473～476．
[4] 周英，鲍德松等．边界条件对二维斜面颗粒流颗粒分布的影响．物理学报．2004．53(10)：3389～3394．
[5] 姜泽辉，李斌等．竖直震动颗粒物厚层中冲击力分叉现象．物理学报．2005．54(03)：1273～1278．
[6] 胡林 等．颗粒物质中圆棒受到的静摩擦力[J]．物理学报，2003，52(4)：879～882．
[7] 胡林 等．颗粒物质中压力随高度的变化规律[J]．物理实验，2002．22(11)：46～48．
[8] 肖文波，胡林．颗粒物质的两个典型效应及其研究现状的分析．物理实验，2004，24(3)：44～46．
[9] 厚美瑛，陆坤权．奇异的颗粒物质．新材料产业，2001，(2)：26～28．
[10] 谢向文．大堤洞穴隐患探测技术研究[J]．人民黄河，1996(12)：15～18．
[11] 徐光磊，胡国琦等．通道宽度和初始流量对颗粒稀疏流-密集流转变临界开口的影响．物理学报．2003，52(4)，875～878．
[12] 鲍德松，张训生等．平面颗粒流的瓶颈效应及其与速度的关系．物理学报，2003．52(2)：401～404．
[13] 鲍德松，周英等．通道宽度对二维粗糙边界斜面颗粒流的影响．物理学报。2005，54(2)：798～801．
[14] A. Mehta and S.F. Edwards. Statistical mechanics of powder mixtures. Physica A.,1989,157:1091～1100.
[15] A.P.J. Brea, H.M. Ensner, C.A. Kruelle and I. Rehberg. Reversing the Brazil-Nut Effect: Competition between Percolation and Condensation. Phys. Rev. Lett., 2003,90:014 302～014 310.
[16] C. A. Coulomb, Acad. Roy. Sci. Mem. Phys. Divers Savants. 1773.7, 343～382.
[17] Cates M E, Wittmer J P, Bouchaud J-P, Claudin P. Jamming, Force Chains, and Fragile Matter[J]. physical review letters, 1998,81:1841～1844.
[18] C.H.Liu, et al. Force Fluctuations in Bead Packs. Science, 1995, 269(28):513～515.
[19] D. C. Hong, V. Quinn, and S. Luding. Reverse Brazil nut problem: competition between percolation and condensation. Phys. Rev. Lett.2001, 86(15), 3423～3426.
[20] Geng J, Longhi E,Behringer RP. Memory in two—dimensional heap experiments[J]. Phy.Rev.E, 2001, 64: 060301-1～060301-4
[21] G. H. Ristow and H. J. Herrmann. Density patterns in two-dimensional hoppers. Phys. Rev. E.,1994, 50: R5～R8.
[22] G.Peng and H.J.Herrmann. Density waves of granular flow in a pipe using lattice-gas automata. Phys. Rev. E., 1994, 49:R1796～R1799.
[23] G. W. Baxter and R. P. Behringer. Cellular automata models of granular flow. Phys. Rev. A., 1990, 42:1017～1020.
[24] G. Oron, H. J. H errmann, Exact calculation of force networks in granular piles, physical review E. 1998, 58(2): 2079～2089
[25] Horvath V K, Janosi I M and Vella P J. Anomalous density dependence of static friction in sand. Phys. Rev. E. 1996, 54(2): 2005～2009.
[26] I. Roberts, Proc. Roy. Soc. 36,226 (1884)
[27] J. P. Hansen and I. R. McDonald. Theory of Simple Liquids. London: Academic Press Limited. 1986,26～58.
[28] J. Duran, Sand, Powder, and Grains:An introduction to the physics of Granular Materials. Springer-Verlag, New York, 2000.
[29] J. Duran, J. Rajchenbach and E.Clement. Arching Effect Model for Particle Size Segregation. Phys. Rev. Lett., 1993,70: 2431～2434.
[30] J. Knight, H. Jaeger and S. Nagel. Vibration-induced size separation in granular media: The convection connection. Phys. Rev. Lett., 1993, 70: 3728—3731.
[31] J. P. Wittmer, et al.An explanation for the contral s tress minimum in sand piles, nature. 1996, 382:336～338.
[32] J. H. Snoeijer,et al. Force Network Ensemble:A New Approach to static Granular Matter, Physical Review Letters. 2004, 92(5):054302-1～054302-4.
[33] J. E. S. Socolar. Discrete Models of Force chain Networks. 2003, 3(4): 601～618.
[34] Keiko M. Aoki, et al. Convective roll patterns in vertically vibrated beds of granules. Phys. Rev. E. 1996,54(1): 874～883.
[35] K. M. Hill, A. Caprihan and J. Kakalios. Bulk Segregation in Rotated Granular Material Measured by Magnetic Resonance Imaging. Phys. Rev. Lett. 1997, 78:50～53.
[36] K. Nagle and H. Herrmann. Deterministic modelf for traffic jams. Physica A. 1993. 199:254～269.
[37] K. To, P. Lai, and H. Pak. Jamming of Granular Flow in a Two-Dimensional Hopper. Phys. Rev. Lett., 2001,86:71～74.
[38] L Vanel, DW Howell, D. Clark, RP Behringer and E. Clement. Phys. Rev. E. 1999. 60, R5040.
[39] Loic Vanel et al. Memories in sand: Experimental tests of construction history on stress distributions under sandpiles. Phys. Rev. E. 1999,60: 5040～5043.
[40] M. Hou. et al. Global Nature of Dilute-to-Dense Transition of Granular flows in a 2D channel. Phys. Rev. Lett. 2003, 91 (20): 204301-1～204301-4.
[41] N. Burtally, et al. Spontaneous Air-Driven Separation in Vertically Vibrated Fine Granular Mixture. 2002,295:1877～1879.
[42] O. Reynold. On the dilatancy of media composed of rigid particles in contact. Phil. Mag. Fifth Series. 1885, 20(5):469～481.
[43] O. Moriyama, et al. 4/3 law of granular particles flowing through a vertical pipe. Phys. Rev. Lett. 1998. 80(13): 2833～2836.
[44] P. G. de Gennes. Granular Matter: A Tentative View. Reviews of Modern Physics. 1999. 71 (2):S374～S381.
[45] P.K. Haff. Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech., 1983, 134:401～430.
[46] P. V. Quinn and D. C. Hong. Liquid-solid transition of hard spheres under gravity. Phys. Rev. E. 2000, 62:8295～8298.
[47] Radjai F, Dietrich E Wolf, Jean M, Moreau J-J. Bimodal Character of Stress Transmission in Granular Packings[J]. physical review letters. 1998, 80(1): 61～64.
[48] R.M. Nedderman. Statics and kinematics of granular materials. Cambridge University Press. 1992.
[49] S. B. Savage. The mechanics of rapid granular flows. Adv. Appl. Mech.,1884, 24:289～366.
[50] S. F. Edwards and C. C. Mounfield. A theoretical model for the stress distribution in granular matter, physical A. 1996, 226:25～33.
[51] S.Luding, J. Duran, E. Cl' ement, and J. Rajchenbach. Segregation of Particulate Solids: Segregation via Convection. Pharmaceutical Technology., 1996, 20:42～52.
[52] S. N. Coppersmith, et al. Model for force fluctuations in bead packs. Phys. Rev. E, 1996,53:4673～4685.
[53] W. A. Beverloo, et al. The flow of granular material through orifices. J. Chem. Eng. Sci. 1961.15:260～269.
[54] W. Chen, et al. Intermittent granular flow in the presence of an electric field. Europhys. Lett. 2001, 56(4): 536～541.
[55] W. Chen, et al. Granular flows through vertical pipes controlled by an electric field. Phys. Rev. E. 2001. 64:061305～061311.
[56] W. Chen, et al. Retardation and transitions of dilute and dense granular flows in a vertical pipe induced by electric field. Appied Physics Letters 2002, 80(12):2213～2215.
[57] X. Wu and Maloy. Why hour glasses tick. Phys. Rev. Lett. 1993, 71:1363～1366.
[2] 陈唯，电场作用下颗粒流动的行为研究．博士论文．2002，1～35．
[3] 厚美瑛，陈唯等．物理．2004，33(7)：473～476．
[4] 周英，鲍德松等．边界条件对二维斜面颗粒流颗粒分布的影响．物理学报．2004．53(10)：3389～3394．
[5] 姜泽辉，李斌等．竖直震动颗粒物厚层中冲击力分叉现象．物理学报．2005．54(03)：1273～1278．
[6] 胡林 等．颗粒物质中圆棒受到的静摩擦力[J]．物理学报，2003，52(4)：879～882．
[7] 胡林 等．颗粒物质中压力随高度的变化规律[J]．物理实验，2002．22(11)：46～48．
[8] 肖文波，胡林．颗粒物质的两个典型效应及其研究现状的分析．物理实验，2004，24(3)：44～46．
[9] 厚美瑛，陆坤权．奇异的颗粒物质．新材料产业，2001，(2)：26～28．
[10] 谢向文．大堤洞穴隐患探测技术研究[J]．人民黄河，1996(12)：15～18．
[11] 徐光磊，胡国琦等．通道宽度和初始流量对颗粒稀疏流-密集流转变临界开口的影响．物理学报．2003，52(4)，875～878．
[12] 鲍德松，张训生等．平面颗粒流的瓶颈效应及其与速度的关系．物理学报，2003．52(2)：401～404．
[13] 鲍德松，周英等．通道宽度对二维粗糙边界斜面颗粒流的影响．物理学报。2005，54(2)：798～801．
[14] A. Mehta and S.F. Edwards. Statistical mechanics of powder mixtures. Physica A.,1989,157:1091～1100.
[15] A.P.J. Brea, H.M. Ensner, C.A. Kruelle and I. Rehberg. Reversing the Brazil-Nut Effect: Competition between Percolation and Condensation. Phys. Rev. Lett., 2003,90:014 302～014 310.
[16] C. A. Coulomb, Acad. Roy. Sci. Mem. Phys. Divers Savants. 1773.7, 343～382.
[17] Cates M E, Wittmer J P, Bouchaud J-P, Claudin P. Jamming, Force Chains, and Fragile Matter[J]. physical review letters, 1998,81:1841～1844.
[18] C.H.Liu, et al. Force Fluctuations in Bead Packs. Science, 1995, 269(28):513～515.
[19] D. C. Hong, V. Quinn, and S. Luding. Reverse Brazil nut problem: competition between percolation and condensation. Phys. Rev. Lett.2001, 86(15), 3423～3426.
[20] Geng J, Longhi E,Behringer RP. Memory in two—dimensional heap experiments[J]. Phy.Rev.E, 2001, 64: 060301-1～060301-4
[21] G. H. Ristow and H. J. Herrmann. Density patterns in two-dimensional hoppers. Phys. Rev. E.,1994, 50: R5～R8.
[22] G.Peng and H.J.Herrmann. Density waves of granular flow in a pipe using lattice-gas automata. Phys. Rev. E., 1994, 49:R1796～R1799.
[23] G. W. Baxter and R. P. Behringer. Cellular automata models of granular flow. Phys. Rev. A., 1990, 42:1017～1020.
[24] G. Oron, H. J. H errmann, Exact calculation of force networks in granular piles, physical review E. 1998, 58(2): 2079～2089
[25] Horvath V K, Janosi I M and Vella P J. Anomalous density dependence of static friction in sand. Phys. Rev. E. 1996, 54(2): 2005～2009.
[26] I. Roberts, Proc. Roy. Soc. 36,226 (1884)
[27] J. P. Hansen and I. R. McDonald. Theory of Simple Liquids. London: Academic Press Limited. 1986,26～58.
[28] J. Duran, Sand, Powder, and Grains:An introduction to the physics of Granular Materials. Springer-Verlag, New York, 2000.
[29] J. Duran, J. Rajchenbach and E.Clement. Arching Effect Model for Particle Size Segregation. Phys. Rev. Lett., 1993,70: 2431～2434.
[30] J. Knight, H. Jaeger and S. Nagel. Vibration-induced size separation in granular media: The convection connection. Phys. Rev. Lett., 1993, 70: 3728—3731.
[31] J. P. Wittmer, et al.An explanation for the contral s tress minimum in sand piles, nature. 1996, 382:336～338.
[32] J. H. Snoeijer,et al. Force Network Ensemble:A New Approach to static Granular Matter, Physical Review Letters. 2004, 92(5):054302-1～054302-4.
[33] J. E. S. Socolar. Discrete Models of Force chain Networks. 2003, 3(4): 601～618.
[34] Keiko M. Aoki, et al. Convective roll patterns in vertically vibrated beds of granules. Phys. Rev. E. 1996,54(1): 874～883.
[35] K. M. Hill, A. Caprihan and J. Kakalios. Bulk Segregation in Rotated Granular Material Measured by Magnetic Resonance Imaging. Phys. Rev. Lett. 1997, 78:50～53.
[36] K. Nagle and H. Herrmann. Deterministic modelf for traffic jams. Physica A. 1993. 199:254～269.
[37] K. To, P. Lai, and H. Pak. Jamming of Granular Flow in a Two-Dimensional Hopper. Phys. Rev. Lett., 2001,86:71～74.
[38] L Vanel, DW Howell, D. Clark, RP Behringer and E. Clement. Phys. Rev. E. 1999. 60, R5040.
[39] Loic Vanel et al. Memories in sand: Experimental tests of construction history on stress distributions under sandpiles. Phys. Rev. E. 1999,60: 5040～5043.
[40] M. Hou. et al. Global Nature of Dilute-to-Dense Transition of Granular flows in a 2D channel. Phys. Rev. Lett. 2003, 91 (20): 204301-1～204301-4.
[41] N. Burtally, et al. Spontaneous Air-Driven Separation in Vertically Vibrated Fine Granular Mixture. 2002,295:1877～1879.
[42] O. Reynold. On the dilatancy of media composed of rigid particles in contact. Phil. Mag. Fifth Series. 1885, 20(5):469～481.
[43] O. Moriyama, et al. 4/3 law of granular particles flowing through a vertical pipe. Phys. Rev. Lett. 1998. 80(13): 2833～2836.
[44] P. G. de Gennes. Granular Matter: A Tentative View. Reviews of Modern Physics. 1999. 71 (2):S374～S381.
[45] P.K. Haff. Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech., 1983, 134:401～430.
[46] P. V. Quinn and D. C. Hong. Liquid-solid transition of hard spheres under gravity. Phys. Rev. E. 2000, 62:8295～8298.
[47] Radjai F, Dietrich E Wolf, Jean M, Moreau J-J. Bimodal Character of Stress Transmission in Granular Packings[J]. physical review letters. 1998, 80(1): 61～64.
[48] R.M. Nedderman. Statics and kinematics of granular materials. Cambridge University Press. 1992.
[49] S. B. Savage. The mechanics of rapid granular flows. Adv. Appl. Mech.,1884, 24:289～366.
[50] S. F. Edwards and C. C. Mounfield. A theoretical model for the stress distribution in granular matter, physical A. 1996, 226:25～33.
[51] S.Luding, J. Duran, E. Cl' ement, and J. Rajchenbach. Segregation of Particulate Solids: Segregation via Convection. Pharmaceutical Technology., 1996, 20:42～52.
[52] S. N. Coppersmith, et al. Model for force fluctuations in bead packs. Phys. Rev. E, 1996,53:4673～4685.
[53] W. A. Beverloo, et al. The flow of granular material through orifices. J. Chem. Eng. Sci. 1961.15:260～269.
[54] W. Chen, et al. Intermittent granular flow in the presence of an electric field. Europhys. Lett. 2001, 56(4): 536～541.
[55] W. Chen, et al. Granular flows through vertical pipes controlled by an electric field. Phys. Rev. E. 2001. 64:061305～061311.
[56] W. Chen, et al. Retardation and transitions of dilute and dense granular flows in a vertical pipe induced by electric field. Appied Physics Letters 2002, 80(12):2213～2215.
[57] X. Wu and Maloy. Why hour glasses tick. Phys. Rev. Lett. 1993, 71:1363～1366.