纳米尺度低速流动的速度计算新方法
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摘要
随着纳米科技的日益发展,迫切需要了解纳米尺度流动特性。由于实验和理论研究的困难,分子动力学模拟方法成为探索纳米尺度流动问题的有力工具。在研究流动特性过程中,如何分离出真实的流速成为众多难点之一。传统的分子动力学方法是把流速与,分子热运动速度之和在一个长时间段上取平均值,这种方法只在流速相当大的情况下适用。对于低速流动问题,由于较低的流动速度和较高的分子热运动速度的非线性耦合,流体的流速被大大地高估,失去其真实性。低速纳米尺度流动速度的求解是解决纳米尺度流动问题的基础,所以对这个问题的成功解决具有十分重要的意义。
本文首先对两种纳米尺度流速求解方法进行系统的阐述和比较,然后采用流体力学中的牛顿内摩擦定律公式和分子动力学相结合的新方法,通过模拟液氩在圆截面纳米通道内的三维Poiseuile流动,研究流体的流动特性。通过改变流动模型的径向尺寸、壁面与流体之间的作用力和载荷加速度的大小,建立了多个模拟模型。模拟高速流动,将应用新方法求得的流速分布与传统的分子动力学方法得到的流速分布进行比较,观察是否具有一致性。模拟低速流动,观察得到的流速分布是否稳定。研究结果表明:在流体高速流动时,新方法求得的流速与传统的分子动力学方法求出的流速十分接近;在低速流动时,新方法也能得到稳定的流速。通过模拟研究了模型的径向尺寸、壁面与流体之间的作用力和载荷加速度对流动的影响,考察的主要信息包括流体的密度分布、粘度分布、剪切应力分布和速度分布,通过比较得到了许多重要的结论。
With the development of modern science and nanotechnology, the behavior of nanoscale fluid has been attracting more and more attention. As the difficulties of experimental and theoretical studies, molecular dynamics simulations has been a powerful tool to explore nanoflow problems. In the process of studying flow characteristics, how to extract the true flow velocity is a major difficulty. The flow velocity got by traditional molecular dynamics method is the average value of bulk flow velocity and the molecules’thermal motion over time. This method only can apply in the case of high speed flow problems. For low speed flow problems, because of the highly nonlinear coupling of the low bulk flow velocity and the high velocity of molecules’thermal motion, and usually over-estimate the true flow velocity in such cases and lose its authenticity. Calculation of flow velocity in low speed nanoflow problems is the basis for nanoflow problems, so the successful resolution of this issue has great significance.
In the paper, firstly, two kinds of solution method of flow velocity in nanoflow system were described and compared, and combine Newton’s law of internal friction and molecular dynamics method, Three-dimensional liquid argon Poiseuille flows in circular cross sectional nanochannels are simulated and the flow characteristics are studyed with this new method. By changing the radial size of flow model and external force and wall-fluid interaction, established a number of simulated examples. Simulation results show that: high-speed flows, the flow velocities obtained by the new method are close to conventional results, for low speed flows, the flow velocities calculated by the new method are still stable. By simulation, focused on the effect of the radial size of flow model and external force and wall-fluid interaction, We mainly pay attention to density and viscosity and shear stress and flow velocity distribution, and get a number of important conclusions by comparing.
本文首先对两种纳米尺度流速求解方法进行系统的阐述和比较,然后采用流体力学中的牛顿内摩擦定律公式和分子动力学相结合的新方法,通过模拟液氩在圆截面纳米通道内的三维Poiseuile流动,研究流体的流动特性。通过改变流动模型的径向尺寸、壁面与流体之间的作用力和载荷加速度的大小,建立了多个模拟模型。模拟高速流动,将应用新方法求得的流速分布与传统的分子动力学方法得到的流速分布进行比较,观察是否具有一致性。模拟低速流动,观察得到的流速分布是否稳定。研究结果表明:在流体高速流动时,新方法求得的流速与传统的分子动力学方法求出的流速十分接近;在低速流动时,新方法也能得到稳定的流速。通过模拟研究了模型的径向尺寸、壁面与流体之间的作用力和载荷加速度对流动的影响,考察的主要信息包括流体的密度分布、粘度分布、剪切应力分布和速度分布,通过比较得到了许多重要的结论。
With the development of modern science and nanotechnology, the behavior of nanoscale fluid has been attracting more and more attention. As the difficulties of experimental and theoretical studies, molecular dynamics simulations has been a powerful tool to explore nanoflow problems. In the process of studying flow characteristics, how to extract the true flow velocity is a major difficulty. The flow velocity got by traditional molecular dynamics method is the average value of bulk flow velocity and the molecules’thermal motion over time. This method only can apply in the case of high speed flow problems. For low speed flow problems, because of the highly nonlinear coupling of the low bulk flow velocity and the high velocity of molecules’thermal motion, and usually over-estimate the true flow velocity in such cases and lose its authenticity. Calculation of flow velocity in low speed nanoflow problems is the basis for nanoflow problems, so the successful resolution of this issue has great significance.
In the paper, firstly, two kinds of solution method of flow velocity in nanoflow system were described and compared, and combine Newton’s law of internal friction and molecular dynamics method, Three-dimensional liquid argon Poiseuille flows in circular cross sectional nanochannels are simulated and the flow characteristics are studyed with this new method. By changing the radial size of flow model and external force and wall-fluid interaction, established a number of simulated examples. Simulation results show that: high-speed flows, the flow velocities obtained by the new method are close to conventional results, for low speed flows, the flow velocities calculated by the new method are still stable. By simulation, focused on the effect of the radial size of flow model and external force and wall-fluid interaction, We mainly pay attention to density and viscosity and shear stress and flow velocity distribution, and get a number of important conclusions by comparing.
引文
1 C. Jan.T.Eijel, Albert van den berg. Nanofluidics: What Is It and What Can We Expect from It? Microfluid Nanofluid, 2005, 1(4): 249–267
2贾宝贤,李文卓.微纳米科学技术导论.北京:化学工业出版社, 2007
3 R. P. Feynman. There’s Plenty of Room at the Bottom. 1961
4李旭辉. MEMS发展应用现状.传感器与微系统, 2006, 25(5): 7-9
5张栋.对微机电系统发展趋势和面临挑战的思考.科技情报开发与经济, 2006, 16(24): 180-181
6房振乾.微电子机械系统(MEMS)中介孔硅材料的热学、力学及电学特性研究. [天津大学博士论文]. 2007: 1-29
7李昕欣,夏晓媛,张志祥.从MEMS到NEMS进程中的技术思考.微纳电子技术, 2008, 45(1): 1-5
8刘锦.微机电系统技术的发展趋势研究.机电产品开发与创新, 2008, 21(4): 42-44
9 K. Gabriel, J.Javris, W. Trimmer. Small Machines, Large Opportunities. Technical report. NSF,1988: 10-30
10白春礼.纳米科技及其发展前景.微纳电子技术, 2002, 38(1): 2-5
11 M. Gad-El-Hak. The Fluid Mechanics of Microdevices. J Fluids Engineering, 1999, 12(1): 5-33
12 C. Ho, Y. Tai. Micro-electro-mechanical Systems(MEMS) and Fluid Flows. Ann.Rev. Fluid Mech, 1998, 30(1): 579-612
13 J. Evans, D. Liepmann, A. Pisano. Planar Laminar Mixer. In MEMS-97,The Tenth Annual International Workshop on MEMS,1997: 26-30
14庄礼贤,尹协远,马晖阳.流体力学.合肥:中国科学技术大学出版社, 1997
15 (美)卡尼亚达克斯,帕斯考克. (译)中国科学院过程工程研究所多相反应重点实验室多想复杂系统与多尺度方法课题组.微流动——基础与模拟.北京:化学工业出版社, 2006: 201-243
16 M. P. Allen, D. J. Tildesley. Computer Simulation of Liquids. New York, Oxford University Press, 1989: 71-110
17 D. C. Rapaport. The Art of Molecular Dynamics Simulation. Cambridge, United Kingdom. Cambridge University Press, 2004: 83-153
18 Frenkel and Smit.分子模拟——从算法到应用.北京:化学工业出版社, 2002: 51-95
19徐超等.流体静态和动态平衡性质的分子动力学模拟.工程热物理学报,2004, 25(5): 725-728
20刘娟芳.流体输运特性和物态转变的分子动力学研究. [重庆大学博士论文]. 2005: 27-51
21 P. A. Thompson, M. O. Robbins. Simulations of Contact-Line Motion:Slip and the Dynamic Contact Angle. Physical Review Letters, 1989, 63(7): 766-769
22 T. Z. Qian, X. P. Wang, P. Sheng. Molecular Scale Contact Line Hydrodynamics of Immiscible Flow.Physical Review E, 2003, 68(12): 1630601-1630615
23 T. Z. Qian, X. P. Wang, P. Sheng. Power-Law Slip Profile of the Moving Contact Line in Tow-Phase Immiscible Flow.Phsical Review Letters, 2004, 93(9): 945011-945014
24 M. Cieplak, J. Koplik, J. R. Banavar. Boundary Conditions at a Fluid-Solid interface Physical Review Letters, 2001, 86(5): 803-806
25 G. Nagayama, P. Cheng. Effects of Interface Wettability on Microscale Flow by Molecular Dynamics Simulation. International Journal of Heat and Mass Transfer, 2004, 47(3): 501-513
26 A. S. Ziarani, A. A. Mohamad. A molecular Dynamics Study of Perturbed Poiseuille Flow in a Nanochannel. Microfluid Nanofluid, 2006, 2(1): 12-20
27 H. Zhang, et al. Shear Viscosity of Simple Fluids in Porous Media: Molecular Dynamic Simulations and Correlation Models. Chemical Physics Lerrers, 2001, 350(3-4): 247-252
28 H. Zhang, et al. Molecular Dynamics Simulations on the Adsorption and Surface Phenomena of Simple Fluid inPorous Media. Chemical Physics Lerrers, 2002, 366(1-2): 24-27
29 J. Bear.多孔介质流体动力学.北京:中国建筑工业出版社, 1982
30孔祥言.高等渗流力学.合肥:中国科学技术大学出版社, 1999
31 X. B. Mi, A. T. Chwang. Molecular Dynamics Simulations of Nanochannel Flows at Low Reynolds Numbers. Molecules, 2003, 8(1): 193-206
32 J. Eggers.Dynamics of Liquid Nanojets. Phys Rev Lett, 2002, 89(8): 845021-845024
33 M. Moseler, U. Landman. Formation, Stability and Breakup of Nanojets. Science, 2000, 289(5482): 1165-1169
34 W. F. Zhang, D. Q. Li. Simulation of Low Speed 3D Nanochannel Flow. Microfluid Nanofluid, 2007, 3(4): 417-425
35 K. P. Travis, B. D. Todd, D. J. Evans. Departure from Navier-Stokes Hydrodynamics in Confined Liquids. Phys. Rev. E, 1997, 55(4): 4288-4295
36 K. P. Travis,K. E. Gubbins. Poiseuille Flow of Lennard-Jones Fluids in Narrow Slit Pores. J. Chem. Phys, 2000, 112(4): 1984-1994
37 B. D. Todd, D. J. Evans, P. J. Daivis.Pressure Tensor for Inhomogeneous Fluids. Phys Rev E, 1995, 52(4): 1627-1638
38 B. J. Alder, T. E. Wainwright. Studies in Molecular Dynamics. The Journal of Chemical Physics, 1957, (27): 1208-1209
39 A. Rahman. Correlations in the Motion of Atoms in Liquid Argon. Physical Review, 1964, 136(2): 405-410
40 L. Verlet. Computer "Experiments" On Classical Fluids. I. Thermo dynamical Properties of Lennard-Jones Molecules. Physical Review, 1967, 159(1): 98-106
41 H. C. Andersen. Molecular Dynamics Simulations at Constant Pressure and/or Temperature. The Journal of Chemical Physics, 1980, 72(4): 2384-2393
42 M. Parrinello, A. Rahman. Polymorphic Transitions in Single Crystals: a New Molecular Dynamics Method. Journal of Applied Physics, 1981, (52): 7182-7191
43 S. Nosé. A Molecular Dynamics Method for Simulations in the Canonical Ensemble. Molecular Physics, 1984, 52(2): 255-268
44 R.Car, M. Parrinello. Unified Approach for Molecular Dynamics and Density-Functional Theory. Physical Review Letters, 1985, 55(22): 2471-2474
45 A. M. Polubotko, A. Hatta, Y. Suzuki, M. Ciofalo, M. W. Collins, Hennessy. T. R. Modeling Nanoscale Fluid Dynamics and Transport in Physiological Flows. Med Eng Phys,1996, 18(6): 437-451
46 N. Giordano, J. T. Cheng. Microfluid Mechanics: Progress and Opportunities. J Phys Condens Matter, 2001, 13(15): 271-295
47陈煜,陈硕,巨永林,等.超临界L-J流体粘度的分子动力学模拟.低温工程, 2008, 22(4): 32-37
48向恒,姜培学,刘其鑫,毛志方.平直纳米通道内液体流动规律的分子动力学研究.自然科学进展, 2008, 18(11): 1346-1350
49秦丰华,微尺度气体流动特性研究. [中国科学技术大学博士论文]. 2005: 1-35
50陈正隆,徐为人,汤立达.分子模拟的理论与实践.北京:化学工业出版社, 2007: 67-88
51马文淦.计算物理学.合肥:中国科技技术大学出版社, 2001: 91-97
52 R. M. J. Cotterill, M. Doyama. Emergier and Atom Configuration of Line Defects and Plane Defects. Gordon and Breach Science Publishers, 1967: 301-305
53 M. S. Daw, M. I. Baskes. Embedded Atom Mehtod Derivation and Application to Impurities, Surfaces, and Other Defects in Metals. Physical Review, 1984, 29(12): 8486-8495
54 M. P. Allen, ,D. J. Tildesley. Computer Simulation of Liquids.Oxford: Oxford University Press, 1989: 22-23
55文玉华,朱如曾,匾直周,等.分子动力学模拟的主要技术.力学进展, 2003, 33(1): 65-76
56 Berendsen, H. J. C. Postma, J. P. M. Van Gunsteren, W. F. DiNola, A. Haak, J. R. Molecular Dynamics with Coupling to an External Bath. The Journal of Chemical Physics, 1984, (81): 3684-3690
57 W. G. Hoover. Computational Statistical Mechanics.Elsevier Science Pub,1991
58 Nose S. A Unified Formulation of the Constant Temperature Molecular Dynamics Methods. The Journal of Chemical Physics, 1984, (81): 511-520
59 W. G. Hoover. Canonical Dynamics: Equilibrium Phase-space Distribution. Physical.Review, 1985, (31): 1695-1697
60曹炳阳.速度滑移及其对微纳尺度流动影响的分子动力学研究. [清华大学博士论文]. 2005: 1-22
61 U. Heinbuch, J. Fischer. Liquid Flow in Pores: Slip, No-slip, or Multilayer Sticking. Physical Review A, 1989, 40(2): 1144-1146
62过增元.国际传热研究前沿——微细尺度传热.力学进展, 2000. 30(1): 1-7
63刘静,微米/纳米尺度传热学.北京:科学出版社, 2001
64 X. J. Fan, et al. Molecular Dynamics Simulation of a Liquid In a Complex Nano Channel Flow. Physics of Fluids, 2002, 14(3): 1146-1153
65 N. V. Priezjev, A. A. Darhuber, S. M. Troian. Slip Behavior in Liquid Films on Surfaces of Patterend Wettability: Comparison Between Contimuum and Molecular Dynamics Simulation. Physical Review E, 2005, 71(4): 4160801-4160811
66 N. V. Priezjev. Effect of Surface Roughness on Rate-Dependent Slip in Simple Fluids. J. Chem. Phys, 2007, 127(14): 144708-144712
67曹炳阳,陈民,过增元,纳米通道内液体流动的滑移现象.物理学报, 2006. 55(10): 5305-5310
68 N. V. Priezjev, S. M. Troian. Influence of Periodic Wall Roughness on the Slip Behavior at Liquid/Soild Interfaces: Molecular-Scale Simulations Versus Continuum Predictions. J. Fluid Mech, 2006, 554(1): 25-46
2贾宝贤,李文卓.微纳米科学技术导论.北京:化学工业出版社, 2007
3 R. P. Feynman. There’s Plenty of Room at the Bottom. 1961
4李旭辉. MEMS发展应用现状.传感器与微系统, 2006, 25(5): 7-9
5张栋.对微机电系统发展趋势和面临挑战的思考.科技情报开发与经济, 2006, 16(24): 180-181
6房振乾.微电子机械系统(MEMS)中介孔硅材料的热学、力学及电学特性研究. [天津大学博士论文]. 2007: 1-29
7李昕欣,夏晓媛,张志祥.从MEMS到NEMS进程中的技术思考.微纳电子技术, 2008, 45(1): 1-5
8刘锦.微机电系统技术的发展趋势研究.机电产品开发与创新, 2008, 21(4): 42-44
9 K. Gabriel, J.Javris, W. Trimmer. Small Machines, Large Opportunities. Technical report. NSF,1988: 10-30
10白春礼.纳米科技及其发展前景.微纳电子技术, 2002, 38(1): 2-5
11 M. Gad-El-Hak. The Fluid Mechanics of Microdevices. J Fluids Engineering, 1999, 12(1): 5-33
12 C. Ho, Y. Tai. Micro-electro-mechanical Systems(MEMS) and Fluid Flows. Ann.Rev. Fluid Mech, 1998, 30(1): 579-612
13 J. Evans, D. Liepmann, A. Pisano. Planar Laminar Mixer. In MEMS-97,The Tenth Annual International Workshop on MEMS,1997: 26-30
14庄礼贤,尹协远,马晖阳.流体力学.合肥:中国科学技术大学出版社, 1997
15 (美)卡尼亚达克斯,帕斯考克. (译)中国科学院过程工程研究所多相反应重点实验室多想复杂系统与多尺度方法课题组.微流动——基础与模拟.北京:化学工业出版社, 2006: 201-243
16 M. P. Allen, D. J. Tildesley. Computer Simulation of Liquids. New York, Oxford University Press, 1989: 71-110
17 D. C. Rapaport. The Art of Molecular Dynamics Simulation. Cambridge, United Kingdom. Cambridge University Press, 2004: 83-153
18 Frenkel and Smit.分子模拟——从算法到应用.北京:化学工业出版社, 2002: 51-95
19徐超等.流体静态和动态平衡性质的分子动力学模拟.工程热物理学报,2004, 25(5): 725-728
20刘娟芳.流体输运特性和物态转变的分子动力学研究. [重庆大学博士论文]. 2005: 27-51
21 P. A. Thompson, M. O. Robbins. Simulations of Contact-Line Motion:Slip and the Dynamic Contact Angle. Physical Review Letters, 1989, 63(7): 766-769
22 T. Z. Qian, X. P. Wang, P. Sheng. Molecular Scale Contact Line Hydrodynamics of Immiscible Flow.Physical Review E, 2003, 68(12): 1630601-1630615
23 T. Z. Qian, X. P. Wang, P. Sheng. Power-Law Slip Profile of the Moving Contact Line in Tow-Phase Immiscible Flow.Phsical Review Letters, 2004, 93(9): 945011-945014
24 M. Cieplak, J. Koplik, J. R. Banavar. Boundary Conditions at a Fluid-Solid interface Physical Review Letters, 2001, 86(5): 803-806
25 G. Nagayama, P. Cheng. Effects of Interface Wettability on Microscale Flow by Molecular Dynamics Simulation. International Journal of Heat and Mass Transfer, 2004, 47(3): 501-513
26 A. S. Ziarani, A. A. Mohamad. A molecular Dynamics Study of Perturbed Poiseuille Flow in a Nanochannel. Microfluid Nanofluid, 2006, 2(1): 12-20
27 H. Zhang, et al. Shear Viscosity of Simple Fluids in Porous Media: Molecular Dynamic Simulations and Correlation Models. Chemical Physics Lerrers, 2001, 350(3-4): 247-252
28 H. Zhang, et al. Molecular Dynamics Simulations on the Adsorption and Surface Phenomena of Simple Fluid inPorous Media. Chemical Physics Lerrers, 2002, 366(1-2): 24-27
29 J. Bear.多孔介质流体动力学.北京:中国建筑工业出版社, 1982
30孔祥言.高等渗流力学.合肥:中国科学技术大学出版社, 1999
31 X. B. Mi, A. T. Chwang. Molecular Dynamics Simulations of Nanochannel Flows at Low Reynolds Numbers. Molecules, 2003, 8(1): 193-206
32 J. Eggers.Dynamics of Liquid Nanojets. Phys Rev Lett, 2002, 89(8): 845021-845024
33 M. Moseler, U. Landman. Formation, Stability and Breakup of Nanojets. Science, 2000, 289(5482): 1165-1169
34 W. F. Zhang, D. Q. Li. Simulation of Low Speed 3D Nanochannel Flow. Microfluid Nanofluid, 2007, 3(4): 417-425
35 K. P. Travis, B. D. Todd, D. J. Evans. Departure from Navier-Stokes Hydrodynamics in Confined Liquids. Phys. Rev. E, 1997, 55(4): 4288-4295
36 K. P. Travis,K. E. Gubbins. Poiseuille Flow of Lennard-Jones Fluids in Narrow Slit Pores. J. Chem. Phys, 2000, 112(4): 1984-1994
37 B. D. Todd, D. J. Evans, P. J. Daivis.Pressure Tensor for Inhomogeneous Fluids. Phys Rev E, 1995, 52(4): 1627-1638
38 B. J. Alder, T. E. Wainwright. Studies in Molecular Dynamics. The Journal of Chemical Physics, 1957, (27): 1208-1209
39 A. Rahman. Correlations in the Motion of Atoms in Liquid Argon. Physical Review, 1964, 136(2): 405-410
40 L. Verlet. Computer "Experiments" On Classical Fluids. I. Thermo dynamical Properties of Lennard-Jones Molecules. Physical Review, 1967, 159(1): 98-106
41 H. C. Andersen. Molecular Dynamics Simulations at Constant Pressure and/or Temperature. The Journal of Chemical Physics, 1980, 72(4): 2384-2393
42 M. Parrinello, A. Rahman. Polymorphic Transitions in Single Crystals: a New Molecular Dynamics Method. Journal of Applied Physics, 1981, (52): 7182-7191
43 S. Nosé. A Molecular Dynamics Method for Simulations in the Canonical Ensemble. Molecular Physics, 1984, 52(2): 255-268
44 R.Car, M. Parrinello. Unified Approach for Molecular Dynamics and Density-Functional Theory. Physical Review Letters, 1985, 55(22): 2471-2474
45 A. M. Polubotko, A. Hatta, Y. Suzuki, M. Ciofalo, M. W. Collins, Hennessy. T. R. Modeling Nanoscale Fluid Dynamics and Transport in Physiological Flows. Med Eng Phys,1996, 18(6): 437-451
46 N. Giordano, J. T. Cheng. Microfluid Mechanics: Progress and Opportunities. J Phys Condens Matter, 2001, 13(15): 271-295
47陈煜,陈硕,巨永林,等.超临界L-J流体粘度的分子动力学模拟.低温工程, 2008, 22(4): 32-37
48向恒,姜培学,刘其鑫,毛志方.平直纳米通道内液体流动规律的分子动力学研究.自然科学进展, 2008, 18(11): 1346-1350
49秦丰华,微尺度气体流动特性研究. [中国科学技术大学博士论文]. 2005: 1-35
50陈正隆,徐为人,汤立达.分子模拟的理论与实践.北京:化学工业出版社, 2007: 67-88
51马文淦.计算物理学.合肥:中国科技技术大学出版社, 2001: 91-97
52 R. M. J. Cotterill, M. Doyama. Emergier and Atom Configuration of Line Defects and Plane Defects. Gordon and Breach Science Publishers, 1967: 301-305
53 M. S. Daw, M. I. Baskes. Embedded Atom Mehtod Derivation and Application to Impurities, Surfaces, and Other Defects in Metals. Physical Review, 1984, 29(12): 8486-8495
54 M. P. Allen, ,D. J. Tildesley. Computer Simulation of Liquids.Oxford: Oxford University Press, 1989: 22-23
55文玉华,朱如曾,匾直周,等.分子动力学模拟的主要技术.力学进展, 2003, 33(1): 65-76
56 Berendsen, H. J. C. Postma, J. P. M. Van Gunsteren, W. F. DiNola, A. Haak, J. R. Molecular Dynamics with Coupling to an External Bath. The Journal of Chemical Physics, 1984, (81): 3684-3690
57 W. G. Hoover. Computational Statistical Mechanics.Elsevier Science Pub,1991
58 Nose S. A Unified Formulation of the Constant Temperature Molecular Dynamics Methods. The Journal of Chemical Physics, 1984, (81): 511-520
59 W. G. Hoover. Canonical Dynamics: Equilibrium Phase-space Distribution. Physical.Review, 1985, (31): 1695-1697
60曹炳阳.速度滑移及其对微纳尺度流动影响的分子动力学研究. [清华大学博士论文]. 2005: 1-22
61 U. Heinbuch, J. Fischer. Liquid Flow in Pores: Slip, No-slip, or Multilayer Sticking. Physical Review A, 1989, 40(2): 1144-1146
62过增元.国际传热研究前沿——微细尺度传热.力学进展, 2000. 30(1): 1-7
63刘静,微米/纳米尺度传热学.北京:科学出版社, 2001
64 X. J. Fan, et al. Molecular Dynamics Simulation of a Liquid In a Complex Nano Channel Flow. Physics of Fluids, 2002, 14(3): 1146-1153
65 N. V. Priezjev, A. A. Darhuber, S. M. Troian. Slip Behavior in Liquid Films on Surfaces of Patterend Wettability: Comparison Between Contimuum and Molecular Dynamics Simulation. Physical Review E, 2005, 71(4): 4160801-4160811
66 N. V. Priezjev. Effect of Surface Roughness on Rate-Dependent Slip in Simple Fluids. J. Chem. Phys, 2007, 127(14): 144708-144712
67曹炳阳,陈民,过增元,纳米通道内液体流动的滑移现象.物理学报, 2006. 55(10): 5305-5310
68 N. V. Priezjev, S. M. Troian. Influence of Periodic Wall Roughness on the Slip Behavior at Liquid/Soild Interfaces: Molecular-Scale Simulations Versus Continuum Predictions. J. Fluid Mech, 2006, 554(1): 25-46