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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.
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Keywords:
- inclined orifice flow /
- repose angle /
- internal friction angle /
- Beverloo formula
[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 物理学报 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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[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 物理学报 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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