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密集颗粒体系的颗粒运动及结构测量技术

杨晖 张国华 王宇杰 孙其诚

杨晖, 张国华, 王宇杰, 孙其诚. 密集颗粒体系的颗粒运动及结构测量技术[J]. 力学进展, 2018, 48(1): 1812. doi: 10.6052/1000-0992-17-010
引用本文: 杨晖, 张国华, 王宇杰, 孙其诚. 密集颗粒体系的颗粒运动及结构测量技术[J]. 力学进展, 2018, 48(1): 1812. doi: 10.6052/1000-0992-17-010
YANG Hui, ZHANG Guohua, WANG Yujie, SUN Qicheng. Measurement techniques of grain motion and inter-grain structures in dense granular materials[J]. Advances in Mechanics, 2018, 48(1): 1812. doi: 10.6052/1000-0992-17-010
Citation: YANG Hui, ZHANG Guohua, WANG Yujie, SUN Qicheng. Measurement techniques of grain motion and inter-grain structures in dense granular materials[J]. Advances in Mechanics, 2018, 48(1): 1812. doi: 10.6052/1000-0992-17-010

密集颗粒体系的颗粒运动及结构测量技术

doi: 10.6052/1000-0992-17-010
基金项目: 致谢:国家自然科学基金项目(11572201, 11572178, 11675110, 91634202) 资助.
详细信息
    作者简介:

    null

    作者简介:
    杨晖, 上海理工大学光电信息与计算机工程学院教授, 博士生导师. 从事颗粒介质力学和颗粒/流体两相流的基础研究, 相应的测试技术和仪器的研发, 并应用于流化床颗粒流动特性分析、核反应堆球床颗粒流测量以及碎屑流起动和流动规律分析等工程项目.近5年承担包括国家自然科学基金重大研究计划项目、面上项目和青年项目、上海市科委和教委专项基金, 以及中国石化、西门子中国有限公司、上海电缆研究所等十多项课题.发表论文50多篇, 其中SCI检索20多篇, 授权发明专利10多项.

    通讯作者:

    孙其诚

  • 中图分类号: ;

Measurement techniques of grain motion and inter-grain structures in dense granular materials

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    Author Bio:

    ɛ E-mail:qcsun@tsinghua.edu.cn

    Corresponding author: SUN Qicheng
  • 摘要: 颗粒材料由大量粗颗粒堆积形成, 是复杂的多体相互作用体系, 呈现出颗粒尺度的结构不均匀和动力学不均匀性的基本特征, 这决定了颗粒材料具有很多独特的宏观性质. 借鉴学科历史的发展途径, 基于统计力学, 从颗粒结构和动力学开始建立颗粒材料体系的宏观连续介质力学理论框架是必然途径.但是, 颗粒材料的基本特征决定了从基本理论到实验手段上, 表征与建立颗粒材料结构与性能的相关性都极其困难.这是由于现有测试分析手段所描述的颗粒系统组织结构过于简单化, 缺乏对颗粒结构和动力学的真正认识, 从而制约了颗粒物质研究的发展.因此, 开展颗粒体系结构和动力学性质的测量, 是理解和认识颗粒材料重要物理和力学问题的基础和依据.笔者来自不同的科研院所, 近十年来开展了颗粒体系结构和动力学性质的测量研究, 主要集中于以下两个方向: (1)数字图像测速法、散斑能见度光谱法和X射线- CT等非侵入式测量技术在颗粒运动方面的应用; (2)体积响应谱、力学谱(有效质量和内耗等)和声速测量技术等直接或间接测量颗粒接触力和颗粒结构技术.本文综述了这些实验手段的基本原理及其特点、取得的主要成果, 以及国际最新进展和困难. 最后是对全文的总结, 结合笔者开展测量的经验和教训, 提出了自己的看法, 并试图展望颗粒材料测量技术研究的前景.

     

  • [1] 费明龙, 徐小蓉, 孙其诚, 周公旦, 金峰. 2016. 颗粒介质固---流态转变的理论分析及实验研究. 力学学报, 48: 48-55

    (Fei M L, Xu X R, Sun Q C, Zhou G D, Jin F.2016. Studies on the transition between solid- and fluid-like states of granular materials. Chinese Journal of Theoretical and Applied Mechanics, 48: 48-55).
    [2] 马文波, 赵雪丹, 张国华, 孙其诚, 侯志坚,董军军. 颗粒密度对氧化锆颗粒系统的动力学体积响应的影响. 2015. 科学技术与工程, 15: 5-11

    (Ma W B, Zhao X D, Zhang G H, Sun Q C, Hou Z J, Dong J J. The effect of the particle density on the spectrum of dynamical responses on packing volume of the granular system composed of spherical zirconium oxide.2015. Science Technology and Engineering,15: 5-11 ).
    [3] 彭政, 蒋亦民, 刘锐, 厚美瑛. 垂直振动激发下颗粒物质的能量耗散. 2013. 物理学报, 62: 24502

    (Peng Z, Jiang Y M, Liu R, Hou M Y.2013. Energy dissipation of a granular system under vertical vibration. Acta Physica Sinica, 62: 24502).
    [4] 孙其诚, 王光谦. 2009. 颗粒介质力学导论. 北京: 科学出版社

    (Sun Q C, Wang G Q.2009. An Introduction to the Mechanics of Granular Materials. Beijing: Science Press).
    [5] 吴学邦, 刘长松, 朱震刚. 内耗技术在软物质研究中的一些应用. 2016. 物理, 45: 720-728

    (Wu X B, Liu C S, Zhu Z G.2016. Applications of internal friction technology in the study of soft matter. Physics, 45: 720-728).
    [6] 余田, 张国华, 孙其诚, 赵雪丹, 马文波. 2015. 垂直振动激励下颗粒材料有效质量和耗散功率的研究. 物理学报, 64: 044501

    (Yu T, Zhang G, Sun Q, Zhao X, Ma W. Dynamic effective mass and power dissipation of the granular material under vertical vibration.2015. Acta Phys.Sin.,64: 044501).
    [7] 张进修, 熊小敏. 内耗频谱仪的应用及内耗频率峰机理的探讨. 2003. 金属学报, 39: 1127-1132

    (Zhang J X, Xiong X M.2003. Applications of apparatus of internal friction frequency spectroscopy and interstation of mechanism of frequency internal friction peak. Acta Metallurgica Sinica,39: 1127-1132).
    [8] 张攀, 赵雪丹, 张国华, 张祺, 孙其诚, 侯志坚,董军军. 垂直载荷下颗粒物质的声波探测和非线性响应. 2016. 物理学报, 65: 024501

    (Zhang P, Zhao X D, Zhang G H, Zhang Q, Sun Q C, Hou Z J, Dong J J.2016. Acoustic detection and nonlinear response of granular materials under vertical vibrations. Acta Phys. Sin., 65: 024501).
    [9] Adrian R.2005. Twenty years of particle image velocimetry. Experiments in Fluids, 39: 159-169
    [10] Aizu Y, Asakura T.1987. Principles and development of spatial filtering velocimetry. Applied Physics B, 43: 209-224.
    [11] Bandyopadhyay R, Gittings A S, Suh S S, Dixon P K, Durian D J.2005. Speckle-visibility spectroscopy: A tool to study time-varying dynamics. Review of Scientific Instruments, 76: 093110.
    [12] Basu A, Xu Y, Still T, Arratia P E, Zhang Z, Nordstrom K N, Rieser J M, Gollub J P, Durian D J, Yodh A G.2014. Rheology of soft colloids across the onset of rigidity: Scaling behavior, thermal, and non-thermal responses. Soft Matter, 10: 3027-3035.
    [13] Beetstra R, Hoef M A V D, Kuipers J A M.2007. Drag force of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres. Aiche Journal, 53: 489-501.
    [14] Bendicks C, Tarlet D, Roloff C, Bord'{a}s R, Wunderlich B, Michaelis B, Th'{e}venin D.2011. Improved 3-D particle tracking velocimetry with colored particles. 2011. Journal of Signal & Information Processing, 2: 59-71.
    [15] Bergeler S, Krambeer H.2004. Novel optical spatial filtering methods based on two-dimensional photodetector arrays. Measurement Science and Technology, 15: 1309-1315.
    [16] Bokkers G A, Annaland M V S, Kuipers J A M.2004. Mixing and segregation in a bidisperse gas--solid fluidised bed: a numerical and experimental study. Powder Technology, 140: 176-186.
    [17] Brunet T, Jia X, Johnson P A.2008. Transitional nonlinear elastic behaviour in dense granular media. Geophysical Research Letters, 35: L19308.
    [18] Capart H, Young D L, Zech Y.2002. Vorono"{i} imaging methods for the measurement of granular flows. Experiments in Fluids, 32: 121-135.
    [19] Cao Y, Zhang X, Kou B, Li X T, Xiao X H, Fezzaa K, Wang Y J.2014. A dynamic synchrotron X射线 imaging study of effective temperature in a vibrated granular medium. Soft Matter, 10: 5398-5404.
    [20] Chung Y C, Hsiau S S, Liao H H, Ooi J.2010. An improved PTV technique to evaluate the velocity field of non-spherical particles. Powder Technology, 202: 151-161.
    [21] Clark A H, Petersen A J, Kondic L, Behringer R P.2015. Nonlinear force propagation during granular impact. Physical Review Letters, 114: 144502.
    [22] Coniglio A, de Candia A, Fierro A, Nicodemi M, Pica Ciamarra M, Tarzia M.2004. On Edwards' theory of powders. Physica A, 339: 1-6.
    [23] Dixon P K, Durian D J.2002. Speckle visibility spectroscopy and variable granular fluidization. Physical Review Letters, 90: 184302.
    [24] Dijksman J A, van Hecke M.2009. The role of tap duration for the steady-state density of vibrated granular media. EPL( Europhysics Letters), 88: 44001.
    [25] Druckrey A M, Alshibli K A. 3D Behavior of sand particles using X-ray synchrotron micro-tomography.2014. Geotechnical Special Publication, 234: 2814-2821.
    [26] Dub'{e} O, Alizadeh E, Chaouki J, Bertrand F.2013. Dynamics of non-spherical particles in a rotating drum. emph{Chemical Engineering Science}, 101: 486-502.
    [27] Edwards S.1998. The equations of stress in a granular material. Physica A, 249: 226-231.
    [28] Ellenbroek W, Somfai E, van Hecke M, van Saarloos W.2006. Critical scaling in linear response of frictionless granular packings near jamming. Physical Review Letters, 97: 258001.
    [29] Ellenbroek W, van Hecke M, van Saarloos W.2009. Jammed frictionless disks: Connecting local and global response.2009. Physical Review E, 80: 061307.
    [30] Felice R D.1994. The voidage function for fluid-particle interaction systems. International Journal of Multiphase Flow, 20: 153-159.
    [31] Flenner E, Szamel G. Dynamic heterogeneity in a glass forming fluid: Susceptibility, structure factor,correlation length.2010. Physical Review Letters, 105: 217801.
    [32] Fiedler O, Werther J, Labahn N, Christofori K.1997. Measurement of local particle velocities and velocity distributions in gas-solid flows by means of the spatial filter method. Powder Technology, 94: 51-57.
    [33] Gao Q, Wang H P, Shen G X.2013. Review on development of volumetric particle image velocimetry. Science Bulletin, 58: 4541-4556.
    [34] Gao Q, Ortizdue~{n}as C, Longmire E K.2011. Analysis of vortex populations in turbulent wall-bounded flows. Journal of Fluid Mechanics, 678: 87-123.
    [35] GDR Midi. On dense granular flows.2003. European Physical Journal E, 14: 341-365.
    [36] Gittings A S, Durian D J. Statistics of bubble rearrangement dynamics in a coarsening foam.2008. Physical Review E, 78: 066313.
    [37] Gong J M, Yang H, Lin S H, Li R, Zivkovic V.2018. Spatial filtering velocimetry for surface velocity measurement of granular flow. Powder Technology, 324: 76-84.
    [38] Goodrich C P, Liu A J, Nagel S R.2014. Solids between the mechanical extremes of order and disorder. Nature Physics, 10: 578-581.
    [39] Haacke E M, Brown R W, Thompson M R, Venkatesan R.1999. Magnetic Resonance Imaging: Physical Principles and Sequence Design. New York: JohnWiley and Sons.
    [40] Hagemeier T, B"{o}rner M, Bück A, Tsotsas E.2015. A comparative study on optical techniques for the estimation of granular flow velocities. Chemical Engineering Science, 131: 63-75.
    [41] Hagemeier T, B"{o}rner M, Bück A, Tsotsas E.2015. Estimation of particle dynamics in 2-D fluidized beds using particle tracking velocimetry. Particuology, 22: 39-51.
    [42] Hawkesworth M R, Parker D J.1991. Nonmedical applications of a positron camera. Nuclear Instruments and Methods in Physics Research, 310: 423-434.
    [43] Hsiau S S, Jang H W.1998. Measurements of velocity fluctuations of granular materials in a shear cell. Experimental Thermal & Fluid Science, 17: 202-209.
    [44] Hosokawa S, Matsumoto T, Tomiyama A.2013. Measurement of bubble velocity using spatial filter velocimetry. Experiments in Fluids, 54: 1-12.
    [45] Hsu C J, Johnson D L, Ingale R A, Valenza J J, Gland N, Makse H A.2009. Dynamic effective mass of granular media. Physical Review Letters, 102: 058001.
    [46] Ianni F, Lasne D, Sarcia R, H'{e}braud P.2006. Relaxation of jammed colloidal suspensions after shear cessation. Physical Review E, 74: 011401.
    [47] Itakura Y, Sugimura A, Tsutsumi S.1981. Amplitude-modulated reticle constructed by a liquid crystal cell array. Applied Optics, 20: 2819-2826.
    [48] Jesuthasan N, Baliga B R, Savage S B.2006. Use of particle tracking velocimetry for measurements of granular flows: Review and application particle tracking velocimetry for granular flow measurements. Powder & Particle, 24: 15-26.
    [49] Katsuragi H, Abate A R, Durian D J.2010. Jamming and growth of dynamical heterogeneities versus depth for granular heap flow. Soft Matter, 6: 3023-3029.
    [50] Khidas Y, Jia X.2010. Anisotropic nonlinear elasticity in a spherical-bead pack: Influence of the fabric anisotropy. Physical Review E, 81: 021303.
    [51] Kitagawa Y, Hayashi A, Minami S.1991. Particle velocity measurements using an optical fiber array spatial filter. Transactions of the Society of Instrument and Control Engineers, 27: 1041-1043.
    [52] Kou B, Cao Y, Li J, Xia C, Li Z, Dong H, Zhang A, Zhang J, Kob W, Wang Y.2017. Granular materials flow like complex fluids. Nature, 551: 360-363.
    [53] Laufer M B.2013. Granular dynamics in pebble bed reactor cores. [PhD Thesis]. UC Berkeley
    [54] Le M M, Cohenaddad S, H"{o}hler R.2012. Bubble rearrangement duration in foams near the jamming point. Physical Review Letters, 108: 188301.
    [55] Li J, Cao Y, Xia C, Kou B, Xiao X H, Fezzaa K, Wang Y J.2014. Similarity of wet granular packing to gels. Nature Communications, 5: 5014.
    [56] Liebling T M, Tsukahara M.2009. Jamming in granular media. EPFL.
    [57] Liu R, Yin X, Li H, Shao Q, York P, He Y, Xiao T, Zhang J.2013. Visualization and quantitative profiling of mixing and segregation of granules using synchrotron radiation X射线 microtomography and three dimensional reconstruction. International Journal of Pharmaceutics, 445: 125-133.
    [58] Li R, Yang H, Zheng G, Zhang B F, Fei M L, Sun Q C.2016. Double speckle visibility spectroscopy for the dynamics of a passive layer in a rotating drum. Powder Technology, 295: 167-174.
    [59] Liu J, Sun Q, Jin F.2011. The influence of flow rate on the decrease in pressure beneath a conical pile. Powder Technology, 212: 296-298.
    [60] Li J, Xu C, Wang S.2014. Spatial filtering characteristics of electrostatic sensor matrix for local velocity measurement of pneumatically conveyed particles. Measurement, 53: 194-205.
    [61] Lim E W C, Wong Y S, Wang C H.2007. Particle image velocimetry experiment and discrete-element simulation of voidage wave instability in a vibrated liquid-fluidized bed. Industrial & Engineering Chemistry Research, 46: 1375-1389.
    [62] Liu G Q, Li S Q, Zhao X L, Yao Q.2008. Experimental studies of particle flow dynamics in a two-dimensional spouted bed. Chemical Engineering Science, 63: 1131-1141.
    [63] Lueptow R M, Akonur A, Shinbrot T.2000. PIV for granular flows. Experiments in Fluids, 28: 183-186.
    [64] Ludewig F, Dorbolo S, Gilet T, Vandewalle N.2008. Energetic approach for the characterization of taps in granular compaction. EPL( Europhysics Letters), 84: 44001.
    [65] Manning M, Liu A.2011. Vibrational modes identify soft spots in a sheared disordered packing. Physical Review Letters, 107: 108302.
    [66] Müller C R, Holland D J, Sederman A J, Mantle M D, Gladden L F, Davidson J F.2008. Magnetic resonance imaging of fluidized beds. Theoretical Foundations of Chemical Engineering, 42: 469-478.
    [67] Müller C R, Holland D J, Sederman A J, Mantle M D, Gladden L F, Davidson J F.2008. Granular temperature: Comparison of magnetic resonance measurements with discrete element model simulations.Powder Technology, 184: 241-253.
    [68] Natarajan V V R, Hunt M L, Taylor E D.1995. Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow. Journal of Fluid Mechanics, 304: 1-25.
    [69] Nowak E R, Knight J B, Ben-Naim E, Jaeger H M, Nagel S R.1998. Density fluctuations in vibrated granular materials. Physical Review E, 57: 1971-1982.
    [70] Orpe A V, Khakhar D V.2007. Rheology of surface granular flows. Journal of Fluid Mechanics, 571: 1-32.
    [71] Percin M, Hu Y, Oudheusden B W V, Remes B, Scarano F.2011. Wing flexibility effects in clap-and-fling. Delft University of Technology, 3: 217-227.
    [72] Petrak D.2002. Simultaneous measurement of particle size and particle velocity by the spatial filtering technique. Particle & Particle Systems Characterization, 19: 391-400.
    [73] Pine D J, Weitz D A, Chaikin P M, Herbolzheimer E.1988. Diffusing wave spectroscopy. Physical Review Letters, 60: 1134-1137.
    [74] Karimi K, Maloney C E.2011. Local anisotropy in globally isotropic granular packings. Physical Review Letters, 107: 268001.
    [75] Parker D J, Broadbent C J, Fowles P, Hawkesworth M R, McNeil P.1993. Positron emission particle tracking: A technique for studying flow within engineering equipment. Nuclear Instruments and Methods in Physics Research, 326: 592-607.
    [76] Parker D J, Forster R N, Fowles P, Takhar P S.2002. Positron emission particle tracking using the new Birmingham positron camera. Nuclear Instruments and Methods in Physics Research Section A, 477: 540-546.
    [77] Parker D J, Dijkstra A E, Martin T W, Seville J P K.1997. Positron emission particle tracking studies of spherical particle motion in rotating drums. Chemical Engineering Science, 52: 2011-2022.
    [78] Parker D, Fan X F.2008. Positron emission particle tracking---Application and labelling techniques. Particuology, 6: 16-23.
    [79] Qian M, Liu J, Yan M S, Shen Z H, Lu J, Ni X W, Li Q, Xuan Y M.2006. Investigation on utilizing laser speckle velocimetry to measure the velocities of nanoparticles in nanofluids. Optics Express, 14: 7559-7566.
    [80] Rix S J L, Glass D H, Greated C A.1996. Preliminary studies of elutriation from gas-fluidised beds using particle image velocimetry. Chemical Engineering Science, 51: 3479-3489.
    [81] Sinha S K.1988. Improving the accuracy and resolution of particle image or laser speckle velocimetry. Experiments in Fluids, 6: 67-68.
    [82] Sederman A J, Gladden L F, Mantle M D.2007. Application of magnetic resonance imaging techniques to particulate systems. Advanced Powder Technology, 18: 23-38.
    [83] Shirsath S S, Padding J T, Clercx H J H, Kuipers J A M.2015. Cross-validation of 3D particle tracking velocimetry for the study of granular flows down rotating chutes. Chemical Engineering Science, 134: 312-323.
    [84] Tang Z Q, Jiang N, Schroder A.2012. Tomographic PIV investigation of coherent structures in a turbulent boundary layer flow. Acta Mechanica Sinica, 28: 572-582.
    [85] Tighe B.2011. Relaxations and rheology near jamming. Physical Review Letters, 107: 158303.
    [86] Uddin M S, Inaba H, Itakura Y, Kasahara M.1998. Estimation of the surface velocity of debris flow with computer-based spatial filtering. Applied Optics, 37: 6234-6239.
    [87] Valenza J J, Hsu C J, Johnson D L. Effect of granular media on the vibrational response of a resonant structure: Theory and experiment.2010. The Journal of the Acoustical Society of America, 128: 2768-2781.
    [88] Valenza J, Hsu C J, Ingale R, et al.2009.Dynamic effective mass of granular media and the attenuation of structure-borne sound. Physical Review E, 80: 051304.
    [89] Valenza J, Johnson D L.2012. Normal-mode spectrum of finite-sized granular systems: The effects of fluid viscosity at the grain contacts. Physical Review E, 85: 041302.
    [90] Vitelli V.2010. Attenuation of shear sound waves in jammed solids. Soft Matter, 6: 3007-3012.
    [91] Villarruel F X, Lauderdale B E, Mueth D M, Jaeger H M.2000. Compaction of rods: Relaxation and ordering in vibrated, anisotropic granular material. Physical Review E, 61: 6914-6921.
    [92] Wang W J, Kong X Z, Zhu Z G.2007. Friction and relative energy dissipation in sheared granular materials. Physical Review E, 75: 041302.
    [93] Wang Y.2016. Granular packing as model glass formers. Chinese Physics B, 1: 1-9.
    [94] Wang Y, Liu X, Im K S, Lee W-K, Wang J, Fezzaa K, Hung DLS, Winkelman J R.2008. Ultrafast X射线 study of dense-liquid-jet flow dynamics using structure-tracking velocimetry. Nature Physics, 4: 305-309.
    [95] Wang Z, Zhang J.2015. Fluctuations of particle motion in granular avalanches - from the microscopic to the macroscopic scales. Soft Matter, 11: 5408.
    [96] Wyart M, Silbert L E, Nagel S R, Witten T A.2005. Effects of compression on the vibrational modes of marginally jammed solids. Physical Review E, 72: 051306.
    [97] Xia C, Li J, Cao Y, Kou B, Xiao X, Fezzaa K, Xiao T, Wang Y.2015. The structural origin of the hard-sphere glass transition in granular packing. Nature Communications, 6: 1-9.
    [98] Xu C, Tang G, Zhou B, Wang S M.2009. The spatial filtering method for solid particle velocity measurement based on an electrostatic sensor. Measurement Science and Technology, 20: 045404.
    [99] Xu X, Sun Q, Jin F, Chen Y P.2016. Measurements of velocity and pressure of a collapsing granular pile. Powder Technology, 303: 147-155.
    [100] Yang H, Jiang G L, Sawe H Y, Davies C, Biggs M J, Zivkovic V.2016. Granular dynamics of cohesive powders in a rotating drum as revealed by speckle visibility spectroscopy and synchronous measurement of forces due to avalanching. Chemical Engineering Science, 149: 1-9.
    [101] Yang H, Zhang B F, Li R, Zheng G, Zivkovic V.2017. Particle dynamics in avalanche flow of irregular sand particles in the slumping regime of a rotating drum. Powder Technology, 311: 439-448.
    [102] Yang H, Li R, Kong P, Sun Q C, Biggs M J, Zivkovic V.2015. Avalanche dynamics of granular materials under the slumping regime in a rotating drum as revealed by speckle visibility spectroscopy. Physical Review E, 91: 042206.
    [103] Zhang W, Wang Y, Sang J L.2008. Simultaneous PIV and PTV measurements of wind and sand particle velocities. Experiments in Fluids, 45: 241-256.
    [104] Zhang X D, Xia C J, Xiao X H, Wang Y J.2014. Fast synchrotron X-ray tomography study of the packing structures of rods with different aspect ratios. Chinese Physics B, 23: 373-376.
    [105] Zou L N.2010. Spectral responses in granular compaction. Physical Review E, 81: 031302.
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