颗粒物质内自旋小球运动行为的数值模拟研究
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摘要
针对大耳沙蜥在沙子中的运动行为,以球形物体为研究对象,利用3维离散元数值模拟程序LIGGGHTS模拟了旋转运动模式对颗粒物质中球形物体平动和上升/下降行为的影响,定量分析了旋转速度以及颗粒间摩擦系数等因素的具体影响.研究结果表明:球形物体与颗粒物质基底颗粒间的摩擦系数以及球形物体的自转角速度对球形物体的运动有明显影响,摩擦系数越大物体运动越明显,自转角速度越大物体运动越明显.该结果比较好地解释了沙漠生物外表具有鳞片的原因.
Recently, how the desert lizards run, hide or swim in the sand has attracted much attention of many scientists in granular matter field, and many valuable results have been published, except for the Phrynocephalus mystaceus, a type of the desert lizard, which can embeds itself into the sand through a motion mode which is completely different from other types of desert lizards. To illuminate the roles played by the spinning-mode in the Phrynocephalus mystaceus' motion in the sand, the three-dimentional(3 D) numerical simulation using the Hertz model on the system, in which one sphere is spinning in the granular matter, is carried out with the open-source code LIGGGHTS released by the Sandia National Laboratory in USA. In the numerical simulations for all the cases, the initial conditions are the same and the sphere spins around X-axis while the X-Y plane is the horizontal plan and the Z axis is the vertical direction. According to the numerical results and analyses, for the spinning sphere deeply embedded in the granular matter we can draw some conclusions. 1) The X-axis spinning motion can cause the sphere embedded in the granular to notably displace along the Z-axis and Y-axis, but the displacement along the spinning direction is smaller than the sphere diameter. 2) The friction coefficient μ between the sphere and the granular matter has a notable influence on the motion of the sphere in granular matter, the spinning sphere can move vertically and horizontally only when the friction coefficient μ between the sphere and the granular matter is larger than that of the granular matter; and the bigger the μ, the more violent the movement of the sphere is. This can be used to explain why most of the desert creatures each have a coarse skin. 3) On the premise that the friction coefficient μbetween the sphere and the granular matter is larger than that of the granular matter, the spinning velocity of the sphere also has a great influence on the movement of the sphere in the granular matter. In a spinning velocity range between 10 rad/s and 640 rad/s, the larger the ω, the more obvious the movement of the sphere is. When the spinning velocity reaches 1280 rad/s, the movement of the sphere slightly decreases compared with when the spinning velocity is 640 rad/s. 4) For the spining sphere in granular matter, the sphere always moves upward in the Z direction, but in the Y direction the sphere may move in a positive or negative direction depending on the ω and μ. The sphere moves in the positive direction of Y axis if the ω and μ are relatively small, while it moves in the negative direction if the ω and μ are larger.
Recently, how the desert lizards run, hide or swim in the sand has attracted much attention of many scientists in granular matter field, and many valuable results have been published, except for the Phrynocephalus mystaceus, a type of the desert lizard, which can embeds itself into the sand through a motion mode which is completely different from other types of desert lizards. To illuminate the roles played by the spinning-mode in the Phrynocephalus mystaceus' motion in the sand, the three-dimentional(3 D) numerical simulation using the Hertz model on the system, in which one sphere is spinning in the granular matter, is carried out with the open-source code LIGGGHTS released by the Sandia National Laboratory in USA. In the numerical simulations for all the cases, the initial conditions are the same and the sphere spins around X-axis while the X-Y plane is the horizontal plan and the Z axis is the vertical direction. According to the numerical results and analyses, for the spinning sphere deeply embedded in the granular matter we can draw some conclusions. 1) The X-axis spinning motion can cause the sphere embedded in the granular to notably displace along the Z-axis and Y-axis, but the displacement along the spinning direction is smaller than the sphere diameter. 2) The friction coefficient μ between the sphere and the granular matter has a notable influence on the motion of the sphere in granular matter, the spinning sphere can move vertically and horizontally only when the friction coefficient μ between the sphere and the granular matter is larger than that of the granular matter; and the bigger the μ, the more violent the movement of the sphere is. This can be used to explain why most of the desert creatures each have a coarse skin. 3) On the premise that the friction coefficient μbetween the sphere and the granular matter is larger than that of the granular matter, the spinning velocity of the sphere also has a great influence on the movement of the sphere in the granular matter. In a spinning velocity range between 10 rad/s and 640 rad/s, the larger the ω, the more obvious the movement of the sphere is. When the spinning velocity reaches 1280 rad/s, the movement of the sphere slightly decreases compared with when the spinning velocity is 640 rad/s. 4) For the spining sphere in granular matter, the sphere always moves upward in the Z direction, but in the Y direction the sphere may move in a positive or negative direction depending on the ω and μ. The sphere moves in the positive direction of Y axis if the ω and μ are relatively small, while it moves in the negative direction if the ω and μ are larger.
引文
[1]Soller R,Koehler S A 2006 Phys.Rev.E.Stat.Nonlin.Soft Matter Phys.74 021305
[2]Guillard F,Forterre Y,Pouliquen O 2013 Phys.Rev.Lett.110 138303
[3]Guillard F,Forterre Y,Pouliquen O 2014 Phys.Fluids26 043301
[4]Guillard F,Forterre Y,Pouliquen O 2015 Phys.Rev.E:Stat.Nonlin.Soft Matter Phys.91 022201
[5]Knight J B,Ehrichs E E,Kuperman V Y,Flint J K,Jaeger H M,Nagel S R 1996 Phys.Rev.E 54 5726
[6]Eshuis P,van der Meer D,Alam M,van Gerner H J,van der Weele K,Lohse D 2010 Phys.Rev.Lett.104 038001
[7]Shinbrot T,Muzzio F J 1998 Phys.Rev.Lett.81 4365
[8]M?bius M E,Lauderdale B E,Nagel S R,Jaeger H M2001 Nature 414 270
[9]Shinbrot T 2004 Nature 429 352
[10]Cheuk C Y,White D J,Bolton M D 2008 J.Geotech.Geoenviron.Eng.134 154
[11]Metcalfe G,Shattuck M 1996 Physica A:Stat.Mech.Appl.233 709
[12]Wood R J K,Wheeler D W 1998 Wear 220 95
[13]Lohse D,Rauhe R,Bergmann R,van der Meer D 2004Nature 432 689
[14]Lohse D,Bergmann R,Mikkelsen R,Zeilstra C,van der Meer D,Versluis M,van der Weele K,van der Hoef M,Kuipers H 2004 Phys.Rev.Lett.93 198003
[15]Katsuragi H,Durian D J 2007 Nat.Phys.3 420
[16]Clark A H,Petersen A J,Kondic L,Behringer R P 2015Phys.Rev.Lett.114 144502
[17]Dowling K J 1996 Ph.D.Dissertation(Pittsburgh:Carnegie Mellon University)
[18]Maladen R D,Ding Y,Li C,Goldman D I 2009 Science325 314
[19]Maladen R D,Ding Y,Umbanhowar P B,Kamor A,Goldman D I 2011 J.R.Soc.Interface 8 1332
[20]Costantino D J,Bartell J,Scheidler K,Schiffer P 2011Phys.Rev.E:Stat.Nonlin.Soft Matter Phys.83 011305
[21]Percier B,Manneville S,Mcelwaine J N,Morris S W,Taberlet N 2011 Phys.Rev.E:Stat.Nonlin.Soft Matter Phys.84 051302
[22]Wassgren C R,Cordova J A,Zenit R,Karion A 2003Phys.Fluids 15 3318
[23]Chehata D,Zenit R,Wassgren C R 2003 Phys.Fluids15 1622
[24]Ding Y,Gravish N,Goldman D I 2011 Phys.Rev.Lett.106 028001
[25]Maladen R D,Umbanhowar P B,Ding Y,Masse A,Doldman D I 2011 Robotics and Automation(ICRA),2011 IEEE International Conference on.IEEE Shanghai,China,May 9–13,2011 p1398
[26]Potiguar F Q,Ding Y 2013 Phys.Rev.E 88 012204
[27]Huang L,Ran X,Blumenfeld R 2016 Phys.Rev.E 94062906
[28]Kloss C,Goniva C,Hager A,Amberger S,Pirker S 2012Prog.Comput.Fluid Dyn.12 140
[29]Gran model hertz model,Christoph K http://www cfdem com/media/DEM/docu/gran_model_hertz html[2017-04-03]
[30]Sun Q C,Wang G Q 2009 Introduction to Mechanics of Granular Materials(Beijing:Science Press)p31(in Chinese)[孙其诚,王光谦2009颗粒物质力学导论(北京:科学出版社)第31页]
[31]Huang D C,Feng Y D,Xie W M,Lu M,Wu H P,Hu F L,Deng K M 2012 Acta Phys.Sin.61 124501(in Chinese)[黄德财,冯耀东,解为梅,陆明,吴海平,胡凤兰,邓开明2012物理学报61 124501]
[2]Guillard F,Forterre Y,Pouliquen O 2013 Phys.Rev.Lett.110 138303
[3]Guillard F,Forterre Y,Pouliquen O 2014 Phys.Fluids26 043301
[4]Guillard F,Forterre Y,Pouliquen O 2015 Phys.Rev.E:Stat.Nonlin.Soft Matter Phys.91 022201
[5]Knight J B,Ehrichs E E,Kuperman V Y,Flint J K,Jaeger H M,Nagel S R 1996 Phys.Rev.E 54 5726
[6]Eshuis P,van der Meer D,Alam M,van Gerner H J,van der Weele K,Lohse D 2010 Phys.Rev.Lett.104 038001
[7]Shinbrot T,Muzzio F J 1998 Phys.Rev.Lett.81 4365
[8]M?bius M E,Lauderdale B E,Nagel S R,Jaeger H M2001 Nature 414 270
[9]Shinbrot T 2004 Nature 429 352
[10]Cheuk C Y,White D J,Bolton M D 2008 J.Geotech.Geoenviron.Eng.134 154
[11]Metcalfe G,Shattuck M 1996 Physica A:Stat.Mech.Appl.233 709
[12]Wood R J K,Wheeler D W 1998 Wear 220 95
[13]Lohse D,Rauhe R,Bergmann R,van der Meer D 2004Nature 432 689
[14]Lohse D,Bergmann R,Mikkelsen R,Zeilstra C,van der Meer D,Versluis M,van der Weele K,van der Hoef M,Kuipers H 2004 Phys.Rev.Lett.93 198003
[15]Katsuragi H,Durian D J 2007 Nat.Phys.3 420
[16]Clark A H,Petersen A J,Kondic L,Behringer R P 2015Phys.Rev.Lett.114 144502
[17]Dowling K J 1996 Ph.D.Dissertation(Pittsburgh:Carnegie Mellon University)
[18]Maladen R D,Ding Y,Li C,Goldman D I 2009 Science325 314
[19]Maladen R D,Ding Y,Umbanhowar P B,Kamor A,Goldman D I 2011 J.R.Soc.Interface 8 1332
[20]Costantino D J,Bartell J,Scheidler K,Schiffer P 2011Phys.Rev.E:Stat.Nonlin.Soft Matter Phys.83 011305
[21]Percier B,Manneville S,Mcelwaine J N,Morris S W,Taberlet N 2011 Phys.Rev.E:Stat.Nonlin.Soft Matter Phys.84 051302
[22]Wassgren C R,Cordova J A,Zenit R,Karion A 2003Phys.Fluids 15 3318
[23]Chehata D,Zenit R,Wassgren C R 2003 Phys.Fluids15 1622
[24]Ding Y,Gravish N,Goldman D I 2011 Phys.Rev.Lett.106 028001
[25]Maladen R D,Umbanhowar P B,Ding Y,Masse A,Doldman D I 2011 Robotics and Automation(ICRA),2011 IEEE International Conference on.IEEE Shanghai,China,May 9–13,2011 p1398
[26]Potiguar F Q,Ding Y 2013 Phys.Rev.E 88 012204
[27]Huang L,Ran X,Blumenfeld R 2016 Phys.Rev.E 94062906
[28]Kloss C,Goniva C,Hager A,Amberger S,Pirker S 2012Prog.Comput.Fluid Dyn.12 140
[29]Gran model hertz model,Christoph K http://www cfdem com/media/DEM/docu/gran_model_hertz html[2017-04-03]
[30]Sun Q C,Wang G Q 2009 Introduction to Mechanics of Granular Materials(Beijing:Science Press)p31(in Chinese)[孙其诚,王光谦2009颗粒物质力学导论(北京:科学出版社)第31页]
[31]Huang D C,Feng Y D,Xie W M,Lu M,Wu H P,Hu F L,Deng K M 2012 Acta Phys.Sin.61 124501(in Chinese)[黄德财,冯耀东,解为梅,陆明,吴海平,胡凤兰,邓开明2012物理学报61 124501]