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准静态颗粒流流动规律的热力学分析

刘中淼 孙其诚 宋世雄 史庆藩

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准静态颗粒流流动规律的热力学分析

刘中淼, 孙其诚, 宋世雄, 史庆藩

Non-equilibrium thermodynamic analysis of quasi-static granular flows

Liu Zhong-Miao, Sun Qi-Cheng, Song Shi-Xiong, Shi Qing-Fan
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  • 本文分析了颗粒流的介观结构及其特征,提出了颗粒流的双颗粒温度概念Tkin 和Tconf,表征颗粒无序运动和构型无序演化的程度;进而作为非平衡变量,与经典非平衡热力学(classical irreversible thermodynamics,CIT)变量共同构成颗粒流的热力学状态变量集,确定了颗粒流的能量转换规律和熵产生率等,发展了颗粒流双颗粒温度(two granular temperate,TGT)模型. 以体积恒定的简单剪切准静态颗粒流为例,结合离散元模拟(discrete element method,DEM),确定了双颗粒温度模型所需的材料参数,分析了颗粒流发展段的规律和稳恒段的有效摩擦系数.
    Granular flow is usually divided into three kinds of flow pattern, namely quasi static flow, slow flow, and rapid flow. The core issue of the research is the constitutive relation. A series of constitutive relations of application value have been received up to now, however, the study on principal theory is insufficient. Granular flow has an emergent mesoscopic structure, such as force chain network and vortex, involving complex irreversible processes. This paper studies its mesoscopic structure and principal characters, introduces the concept of two granular temperatures Tconf and Tkin of the granular flow to characterize the degree of chaotic motion and disordered configuration evolution, sets them as the non-equilibrium variables to constitute the thermodynamic state variables set for granular flow with the classical irreversible thermodynamic (CIT) variables, also determines the granular flow law of energy conversion and the entropy production rate, etc., and develops the two granular temperatures (TGT) model. Taking the simple shear quasi-static granular flow in a constant volume as example, and combining it with the discrete element method (DEM), this work confirms the material parameters needed for the TGT model, and analyzes the law of developing period and the effective coefficient of friction of steady period of granular flow.
    • 基金项目: 国家重点基础研究发展计划项目(批准号:2010CB731504)、国家自然科学基金重点项目(批准号:11034010,51239006)和欧盟Marie Curie国际合作项目(批准号:IRSES-294976)资助的课题.
    • Funds: Project supported by the National Key Basic Research Program of China (Grant No. 2010CB731504), the National Natural Science Foundation of China (Grant Nos. 11034010, 51239006), and the European Commission Marie Curie Actions (IRSES-294976).
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    Tordesillas A, Muthuswamy M, Walsh S 2009 J. Eng. Mech. 134 1095

    [3]

    Sun Q C, Song S X, Liu J G, Fei M L, Jin F 2013 Theor. Appl. Mech. Lett. 3 021008

    [4]

    Jou D, Lebon G, Casas-Vázquez J 2010 Extended Irreversible Thermodynamics (New York:Springer)

    [5]

    Jiang Y M, Liu M 2012 arXiv:1207.1284v1 [cond-mat.soft]

    [6]

    Landau L, Lifshitz E 1987 Fluid Mechanics (2nd edition) (Oxford:Butterworth-Heinemann)

    [7]

    Khalatnikov I 1965 Introduction to the Theory of Superfluidity (New York:Benjamin)

    [8]

    de Gennes P, Prost J 1993 The Physics of Liquid Crystals (Oxford: Clarendon Press)

    [9]

    Sun Q C, Jin F, Liu J G, Zhang G 2010 Modern Phys. B 24 5743

    [10]

    Ichimaru S 1973 Basic Principles of Plasma Physics (New York: Benjamin-Cummings)

    [11]

    Bobylev A V, Potapenko I F, Sakanaka P H 1997 Phys. Rev. E 56 2081

    [12]

    Rat V, Andre P, Aubreton J, Elchinger M F, Fauchais P, Lefort A 2001 Phys. Rev. E 64 026409

    [13]

    Casas-Vázquez J, Jou D 2003 Rep. Prog. Phys. 66 1937

    [14]

    Butler B D, Ayton G, Jepps O G, Evans D J 1998 J. Chem. Phys. 109 6519

    [15]

    Einstein A 1956 Investigations on the theory of the Brownian movement (Dover, NY)

    [16]

    Ogawa S, Umemura A, Oshima N 1980 ZAMP 31 483

    [17]

    Goldhirsch I 2008 Powder Technol. 182 130

    [18]

    Rugh H H 1997 Phys. Rev. Lett. 78 772

    [19]

    Rugh H H 1998 J. Phys. A: Math. Gen. 31 7761

    [20]

    Sun Q C, Wang G Q 2008 Acta Phys. Sin. 57 4667 (in Chinese) [孙其诚, 王光谦 2008 物理学报 57 4667]

    [21]

    Bi 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]

    [22]

    Song S X, Sun Q C, Fei M L, Jin F, Zhang C H 2013 Sci. China 43 81 (in Chinese) [宋世雄, 孙其诚, 费明龙, 金峰, 张楚汉 2013 中国科学 43 81]

    [23]

    Ji S Y, Sun Q C, Yan Y 2011 Sci. China 41 1 (in Chinese) [季顺迎, 孙其诚, 严颖 2011 中国科学 41 1]

    [24]

    Sun Q, Jin F, Zhou G D 2013 Granular Matter 15 119

    [25]

    Zheng H P, Jiang Y M, Fu L P 2012 Acta Phys. Sin 61 214502 (in Chinese) [郑鹤鹏, 蒋亦民, 彭政, 符力平 2012 物理学报 61 214502]

    [26]

    Hatano T 2010 J Physics: Conf Series 258 012006

    [27]

    Edwards S F, Oakeshott R B S 1989 Physica A 157 1080

    [28]

    Pica Ciamarra M, Richard P, Schröter M, Tighe B P 2012 Soft Matter 8 9731

  • [1]

    Forterre Y, Pouliquen O 2008 Annu. Rev. Fluid Mech. 40 1

    [2]

    Tordesillas A, Muthuswamy M, Walsh S 2009 J. Eng. Mech. 134 1095

    [3]

    Sun Q C, Song S X, Liu J G, Fei M L, Jin F 2013 Theor. Appl. Mech. Lett. 3 021008

    [4]

    Jou D, Lebon G, Casas-Vázquez J 2010 Extended Irreversible Thermodynamics (New York:Springer)

    [5]

    Jiang Y M, Liu M 2012 arXiv:1207.1284v1 [cond-mat.soft]

    [6]

    Landau L, Lifshitz E 1987 Fluid Mechanics (2nd edition) (Oxford:Butterworth-Heinemann)

    [7]

    Khalatnikov I 1965 Introduction to the Theory of Superfluidity (New York:Benjamin)

    [8]

    de Gennes P, Prost J 1993 The Physics of Liquid Crystals (Oxford: Clarendon Press)

    [9]

    Sun Q C, Jin F, Liu J G, Zhang G 2010 Modern Phys. B 24 5743

    [10]

    Ichimaru S 1973 Basic Principles of Plasma Physics (New York: Benjamin-Cummings)

    [11]

    Bobylev A V, Potapenko I F, Sakanaka P H 1997 Phys. Rev. E 56 2081

    [12]

    Rat V, Andre P, Aubreton J, Elchinger M F, Fauchais P, Lefort A 2001 Phys. Rev. E 64 026409

    [13]

    Casas-Vázquez J, Jou D 2003 Rep. Prog. Phys. 66 1937

    [14]

    Butler B D, Ayton G, Jepps O G, Evans D J 1998 J. Chem. Phys. 109 6519

    [15]

    Einstein A 1956 Investigations on the theory of the Brownian movement (Dover, NY)

    [16]

    Ogawa S, Umemura A, Oshima N 1980 ZAMP 31 483

    [17]

    Goldhirsch I 2008 Powder Technol. 182 130

    [18]

    Rugh H H 1997 Phys. Rev. Lett. 78 772

    [19]

    Rugh H H 1998 J. Phys. A: Math. Gen. 31 7761

    [20]

    Sun Q C, Wang G Q 2008 Acta Phys. Sin. 57 4667 (in Chinese) [孙其诚, 王光谦 2008 物理学报 57 4667]

    [21]

    Bi 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]

    [22]

    Song S X, Sun Q C, Fei M L, Jin F, Zhang C H 2013 Sci. China 43 81 (in Chinese) [宋世雄, 孙其诚, 费明龙, 金峰, 张楚汉 2013 中国科学 43 81]

    [23]

    Ji S Y, Sun Q C, Yan Y 2011 Sci. China 41 1 (in Chinese) [季顺迎, 孙其诚, 严颖 2011 中国科学 41 1]

    [24]

    Sun Q, Jin F, Zhou G D 2013 Granular Matter 15 119

    [25]

    Zheng H P, Jiang Y M, Fu L P 2012 Acta Phys. Sin 61 214502 (in Chinese) [郑鹤鹏, 蒋亦民, 彭政, 符力平 2012 物理学报 61 214502]

    [26]

    Hatano T 2010 J Physics: Conf Series 258 012006

    [27]

    Edwards S F, Oakeshott R B S 1989 Physica A 157 1080

    [28]

    Pica Ciamarra M, Richard P, Schröter M, Tighe B P 2012 Soft Matter 8 9731

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出版历程
  • 收稿日期:  2013-08-20
  • 修回日期:  2013-11-05
  • 刊出日期:  2014-02-05

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