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The distribution of average velocities, fluctuation of velocities, regional definition, and granular self-diffusion characters in dense granular flows between sheared parallel plates are discussed. In order to study the above problems, we use computer-established discrete element model with an average solid fraction of 0.80. Theoretical results show that the average velocities decrease with increasing height, and are larger for the case of lower plate with greater velocity; the average velocities in y direction are close to 0 because there is no bulk motion in y direction. Flows of the lower plate with a greater velocity induce relatively greater fluctuation of velocities in the x and y directions, the fluctuation of velocities increases with the height and is larger in the area close to the upper plate. The flows consist of a “solid-like” area in the lower test region, but a “fluid-like” region in the upper, and an “oscillating” region in the middle of the channel. By tracking the movements of granules continually, variations of the mean-square self-diffusion relative displacements with square time are plotted, and the mean self-diffusion relative coefficients are determined. As the fluctuation and self-diffusion analysis directly reflect the macroscopic properties of granules and provide bases and references for researching the flow mechanisms of “dense granular sheared flows”.
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Keywords:
- dense granular flow /
- discrete element /
- rheology /
- self diffusion
[1] Hsiau S S, Shieh Y M 1999 J. Rheol. 43 1049
[2] Majmudar T S, Behringer R P 2005 Nature 43 1079
[3] Ji S Y, Li P F, and Chen X D 2012 Acta Phys. Sin. 61 184703 (in Chinese)[季顺迎, 李鹏飞, 陈晓东 2012 物理学报 61 184703]
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[26] Utter B, Behringer R P 2004 Phys. Rev. E 69 031308
[27] Meng F J, Liu K, Wang W 2013 Applied Mathematics and Mechanics 34 7 14 (in Chinese). [孟凡净, 刘焜, 王伟 2013 应用数学和力学 347 14]
[28] Han X M, Gao F, Fu R, Song B W, Nong W H 2009 Materials China 28 8 ( in Chinese) [韩晓明, 高飞, 符蓉, 宋宝韫, 农万华 2009 中国材料进展 28 8]
[29] Zhang B P 2011 MS Thesis (Hefei: Hefei University of Technology) (in Chinese) [张柏平 2011 硕士学位论文(合肥: 合肥工业大学)]
[30] Chun C L, Shu S H, Wen J Y 2012 Inter. J. Multi. Flow 46 22
[31] Giulio B 2007 Nature Physics 3 222
[32] Zhang Y, Campbell C S 1992 J. Fluid Mech. 237 541
[33] Wang W, Liu X J, Jiao M H, Liu K 2009 J. Mech. Eng. 45 101 (in Chinese) [王伟, 刘小君, 焦明华, 刘焜 2009 机械工程学报 45 101]
[34] Campbell C S 1990 Annu. Rev. Fluid Mech. 22 57
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[1] Hsiau S S, Shieh Y M 1999 J. Rheol. 43 1049
[2] Majmudar T S, Behringer R P 2005 Nature 43 1079
[3] Ji S Y, Li P F, and Chen X D 2012 Acta Phys. Sin. 61 184703 (in Chinese)[季顺迎, 李鹏飞, 陈晓东 2012 物理学报 61 184703]
[4] Peng Z, Li X Q, Jiang L, Fu L P, Jiang Y M 2009 Acta Phys. Sin. 58 2090 (in Chinese) [彭政, 李湘群, 蒋礼, 符力平, 蒋亦民 2009 物理学报 58 2090]
[5] Peng Y J, Zhang Z, Wang Y, Liu X S 2012 Acta Phys. Sin. 61 134501 (in Chinese)[[彭亚晶, 张卓, 王勇, 刘小嵩 2012 物理学报 61 134501]
[6] Leonard A, Daraio C 2012 Phys. Rev. Lett. 108 214301
[7] Eugenio H, Franco T, Francisco M 2011 Phys. Rev. E 84 041304
[8] Seguin A, Bertho Y, Martinez F, Crassous J 2013 Phys. Rev. E 87 012201
[9] Lehane B M, Liu Q B 2013 Geotech. Geol. Eng. 31 329
[10] Wang W, Liu X J, Liu K 2012 Tribol. Lett. 48 229
[11] Yi C H, Liu Y, Miao T D, Mu Q S, Qi Y L 2007 Granular Matter 9 195
[12] Shojaaee Z, Roux J N, Chevoir F, Wolf D E 2012 Phys. Rev. E 86 011301
[13] Azèma E, Estrada N, Radjaï F 2012 Phys. Rev. E 86 041301
[14] Zhen H P, Jiang Y M, Peng Z 2013 Chin. Phys. B 22 040511
[15] Elkholy K N, Khonsari M M 2008 J. Eng. Tribo. 222 741
[16] Bose M, Kumaran V 2004 Phys. Rev. E 69 061301
[17] Bocquet L, Losert W, Schalk D, Lubensky T C, Gollub J P 2001 Phys. Rev. E 65 011307
[18] Johnson P C, Jackson R 1987 J. Fluid Mech. 176 67
[19] Kondic L, Fang X, Losert W, O'Hern C S, BehringerR P 2012 Phys. Rev. E 85 011305
[20] Tordesillas A, Walker D M, Lin Q 2010 Phys. Rev. E 81 011302
[21] Cai Q D, Chen S Y, Shen X W 2011 Chin. Phys. B 20 024502
[22] Zhou G G D and Sun Q C 2013 Powder Technology 239 115
[23] Bei Z W, Sun Q C, Liu J G, Jin F, Zhang C H 2011 Acta Phys. Sin. 60 034502 (in Chinese) [毕忠伟, 孙其诚, 刘建国, 金峰, 张楚汉 2011 物理学报 60 034502]
[24] Ragione L L, Magnanimo V 2012 Phys. Rev. E 85 031304
[25] Lu L S, Hsiau S S 2008 Particuology 6 445
[26] Utter B, Behringer R P 2004 Phys. Rev. E 69 031308
[27] Meng F J, Liu K, Wang W 2013 Applied Mathematics and Mechanics 34 7 14 (in Chinese). [孟凡净, 刘焜, 王伟 2013 应用数学和力学 347 14]
[28] Han X M, Gao F, Fu R, Song B W, Nong W H 2009 Materials China 28 8 ( in Chinese) [韩晓明, 高飞, 符蓉, 宋宝韫, 农万华 2009 中国材料进展 28 8]
[29] Zhang B P 2011 MS Thesis (Hefei: Hefei University of Technology) (in Chinese) [张柏平 2011 硕士学位论文(合肥: 合肥工业大学)]
[30] Chun C L, Shu S H, Wen J Y 2012 Inter. J. Multi. Flow 46 22
[31] Giulio B 2007 Nature Physics 3 222
[32] Zhang Y, Campbell C S 1992 J. Fluid Mech. 237 541
[33] Wang W, Liu X J, Jiao M H, Liu K 2009 J. Mech. Eng. 45 101 (in Chinese) [王伟, 刘小君, 焦明华, 刘焜 2009 机械工程学报 45 101]
[34] Campbell C S 1990 Annu. Rev. Fluid Mech. 22 57
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