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气体-表面相互作用中动量和能量分量间转化机制的分子动力学研究

于航 张冉 杨帆 李桦

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气体-表面相互作用中动量和能量分量间转化机制的分子动力学研究

于航, 张冉, 杨帆, 李桦

Molecular dynamics study on the conversion mechanism between momentum and energy components in gas-surface interaction

Yu Hang, Zhang Ran, Yang Fan, Li Hua
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  • 气体分子与壁面之间的相互作用是影响稀薄气体流动状态的主要因素, 但是由于其物理上的复杂性和微观性, 这一过程的机理并没有得到充分揭示. 本文利用分子束法对Ar分子在金属Pt表面的碰撞过程进行了分子动力学模拟, 并探究了入射速度、角度和壁面粗糙度对动量、能量转化机制的影响. 结果表明, 当气体分子以$ 5^{\circ}$的极角入射时, 分子的法向速度分量占主导因素, 在与壁面发生碰撞之后, 分子的切向和法向动量都会损失, 法向动能会向切向转移, 并且当分子速度不低于2.0时, 切向和法向动能的比值会稳定在一个很小的区间, 而粗糙度对动量和能量转化的影响不明显. 与小角度入射时不同, 当气体分子以$ 75^{\circ} $的极角与金属表面碰撞时, 粗糙度的影响就不能再被忽略了. 大极角入射的气体分子在光滑壁面散射之后, 其运动规律基本符合Maxwell所假设的镜面反射, 动量和能量分量的变化都不明显. 而粗糙度的引入则会促进气体分子切向动量和能量向法向转移, 并且会使分子总能量的损失更加显著.
    With the rapid development of micro-nano technology and aerospace technology, researches related to rarefied gas flows have received more and more attention. For micro-/nanoscale systems and spacecraft in a rarefied environment, the reduction in the frequency of intermolecular collisions in the flow field makes the interaction between gas molecules and the solid surface develop into a major factor affecting the flow state. However, the mechanism of gas-surface interaction in rarefied flow has not been fully revealed due to its microscopic nature and physical complexity, and the existing simulation methods cannot accurately reflect the effect of this process on the flow state. In this paper, molecular beam method is adopted to simulate the scattering process of argon molecules on platinum surface, and the impacts of incident velocity, angle and wall roughness on the momentum and energy conversion mechanism are explored. By simulating the molecular scattering process under the two incident angles of $ 5^{\circ} $ and $ 75^{\circ}$, the following conclusions are obtained. When colliding with the wall at an angle close to vertical, both components of the momentum of the gas molecules are lost. The normal energy transfers to the tangential direction, and when the molecular velocity is not less than 2.0, the transfer rate is not significantly affected by the incident energy of the molecule and the surface roughness. The total energy loss of gas molecules after scattering becomes significant with the increase of incident velocity, and it is not sensitive to changes of surface roughness. When the gas molecules are incident at $ 75^{\circ} $, the roughness of the surface has a significant impact on the conversion mechanism of molecular momentum and energy. After colliding with a smooth wall, the momentum and energy values of the gas molecules remain basically unchanged, only the direction of the momentum is reversed. The motion state of molecules is close to the mirror reflection, and the conversion between momentum and energy components is not obvious. The introduction of roughness enhances the degree of accommodation between gas molecules and metal surface, and promotes the transfer of molecular tangential momentum and kinetic energy to the normal direction. When incident at a large polar angle, as opposed to the small-angle cases, the total energy loss of molecules is not sensitive to changes of incident velocity, it goes up significantly with the surface roughness increasing. The research in this article not only explores the gas-surface interaction mechanism, but also provides a useful reference for the high-fidelity simulation of rare gas flow and the development of appropriate gas-surface interaction models.
      通信作者: 张冉, zr07024221@126.com
    • 基金项目: 国家自然科学基金(批准号: 11472004)资助课题
      Corresponding author: Zhang Ran, zr07024221@126.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11472004)
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    Liang T, Li Q, Ye W 2017 J. Comput. Phys. 352 105Google Scholar

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    曹炳阳, 陈民, 过增元 2006 物理学报 55 5305Google Scholar

    Cao B Y, Chen M, Guo Z Y 2006 Acta Phys. Sin. 55 5305Google Scholar

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    Sharipov F, Kalempa D 2005 Phys. Fluids 10 16Google Scholar

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    Burnett D 1935 Proc. Lond. Math. Soc. 1 1Google Scholar

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    Shavaliyev M S 1993 J. Appl. Math. Mech. 57 573Google Scholar

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    Bird G A 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford: Oxford University Press) p199

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    Yuan Y D, Rahman S 2016 Phys. A 463 25Google Scholar

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    Lockerby D A, Reese J M, Emerson D R, Barber R W 2004 Phys. Rev. E 70 017303Google Scholar

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    Barber R W, Emerson D R 2006 Heat Transfer Eng. 27 3Google Scholar

    [10]

    Lockerby D A, Reese J M, Gallis M A 2005 AIAA J. 43 1391Google Scholar

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    Reese J M, Zheng Y, Lockerby D A 2007 J. Comput. Theor. Nanosci. 4 807Google Scholar

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    Bruno D, Cacciatore M, Longo S, Rutigliano M 2000 Chem. Phys. Lett. 320 245Google Scholar

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    Padilla, J F, Bo yd, Iain D 2009 J. Thermophys. Heat Transfer 23 96Google Scholar

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    Liang T, Li Q, Ye W 2013 Phys. Rev. E 88 013009Google Scholar

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    Woronowicz M S, Rault D F 1994 J. Spacecraft Rockets 31 532Google Scholar

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    Myong R S 2004 J. Comput. Phys. 195 655Google Scholar

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    Alder B J, Wainwright T E 1957 J. Chem. Phys. 27 1208Google Scholar

    [18]

    Kovalev V, Yakunchikov A, Li F 2011 Acta Astronaut. 69 744Google Scholar

    [19]

    张忠强, 刘汉伦, 范晋伟, 丁建宁, 程广贵 2019 物理学报 68 170202Google Scholar

    Zhang Z Q, Liu H L, Fan J W, Ding J N, Cheng G G 2019 Acta Phys. Sin. 68 170202Google Scholar

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    Chirita V, Pailthorpe B A, Collins R E 1997 Nucl. Instrum. Meth. B 129 465Google Scholar

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    Yamanishi N, Matsumoto Y, Shobatake K 1999 Phys. Fluids 11 3540Google Scholar

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    曹炳阳 2005 博士学位论文 (北京: 清华大学)

    Cao B Y 2005 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese)

    [23]

    Finger G W, Kapat J S, Bhattacharya A 2007 J. Fluids Eng-Trans. ASME 129 31Google Scholar

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    Ozhgibesov M S, Leu T, Cheng C 2012 J. Mol. Graph. Model. 38 375Google Scholar

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    Ozhgibesov M S, Leu T, Cheng C 2013 J. Mol. Graph. Model. 45 45Google Scholar

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    Leu T, Cheng C, Ozhgibesov M S 2011 J. Mol. Graph. Model. 31 35Google Scholar

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    Bao F, Mao Z, Qiu L 2014 Int. J. Numer. Methods Heat Fluid Flow 24 1338Google Scholar

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    宋诚谦 2014 博士学位论文 (合肥: 中国科技大学)

    Song C Q 2014 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)

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    Cao B Y, Sun J, Chen M, Guo Z Y 2009 Int. J. Mol. Sci. 10 11Google Scholar

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    Sun J, Li Z 2008 Mol. Phys. 106 2325Google Scholar

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    Sun J, Li Z 2009 Mol. Simul. 35 228Google Scholar

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    张冉, 常青, 李桦 2018 物理学报 67 223401Google Scholar

    Zhang R, Chang Q, Li H 2018 Acta Phys. Sin. 67 223401Google Scholar

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    Maruyama S 2000 Adv. Numer. Heat Transfer 2 189Google Scholar

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    Wu L, Bogy D B 2002 J. Tribol.-Trans. ASME 124 562Google Scholar

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    Swope W C, Andersen H C, Berens P H, Wilson K R 1982 J. Chem. Phys. 76 637Google Scholar

    [36]

    Dongari N, Zhang Y H, Reese J M 2012 AIP Conf. Proc. 1501 895Google Scholar

    [37]

    张烨, 张冉, 赖剑奇, 李桦 2019 物理学报 68 124702Google Scholar

    Zhang Y, Zhang R, Lai J Q, Li H 2019 Acta Phys. Sin. 68 124702Google Scholar

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    Chirita V, Pailthorpe B A, Collins R E 1993 J. Phys. D: Appl. Phys. 26 133Google Scholar

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    Maxwell J C 1878 Proc. R. Soc. London 27 304Google Scholar

  • 图 1  三种表面粗糙度构型

    Fig. 1.  Three surface roughness structures.

    图 2  气体分子的入射极角$ \theta$和反射速度的分解在笛卡尔坐标系下的示意图

    Fig. 2.  Schematic diagram of the incident polar angle $ \theta $ and the decompositions of molecular scattering velocity in Cartesian coordinate.

    图 3  入射角为$ 5^{\circ}$时, 气体分子与光滑表面碰撞中速度和能量随时间的变化 (a)速度随时间的变化; (b)能量随时间的变化

    Fig. 3.  When the incident angle is $ 5^{\circ} $, the variations of molecular velocity and energy in the collision with a smooth surface: (a) Variation of molecular velocity; (b) variation of molecular energy.

    图 4  $ 5^{\circ}$极角入射时, 气体分子在不同粗糙表面的法向动量适应系数(NMAC)

    Fig. 4.  Normal momentum accommodation coefficient (NMAC) of gas molecules on different rough surfaces when the incident polar angle is $ 5^{\circ} $.

    图 5  $ 5^{\circ} $极角入射时, 气体分子在不同粗糙表面的能量损失率

    Fig. 5.  Energy loss rate of gas molecules on different rough surfaces when the incident polar angle is $ 5^{\circ} $.

    图 6  入射角为$ 75^{\circ} $时, 气体分子与光滑表面碰撞中速度和能量随时间的变化 (a)速度随时间的变化; (b)能量随时间的变化

    Fig. 6.  When the incident angle is $ 75^{\circ}$, the variations of molecular velocity and energy in the collision with a smooth surface: (a) Variation of molecular velocity; (b) variation of molecular energy.

    图 7  入射角为$ 75^{\circ} $时, 气体分子与粗糙表面碰撞中速度和能量随时间的变化 (a)速度随时间的变化; (b)能量随时间的变化

    Fig. 7.  When the incident angle is $ 75^{\circ}$, the variations of molecular velocity and energy in the collision with a rough surface: (a) Variation of molecular velocity; (b) variation of molecular energy.

    图 8  $ 75^{\circ}$极角入射时, 气体分子在不同粗糙表面的的切向动量适应系数(TMAC)

    Fig. 8.  Tangential momentum accommodation coefficient (TMAC) of gas molecules on different rough surfaces when the incident polar angle is $ 75^{\circ}$.

    图 9  $ 75^{\circ} $极角入射时, 气体分子在不同粗糙表面的能量损失率

    Fig. 9.  Energy loss rate of gas molecules on different rough surfaces when the incident polar angle is $ 75^{\circ} $.

    表 1  入射极角为$ 5^{\circ}$时, 不同速度的气体分子在不同表面上散射后的平均速度和能量

    Table 1.  When the incident polar angle is $ 5^{\circ}$, the mean velocity and energy of gas molecules that with different velocities after scattering on different surfaces.

    ${V_{\rm{i}}}$/$\sqrt {2{k_{\rm{B}}}T} $States${V_{\rm{t}}}$/($\sigma \cdot {\tau^{-1}}$)${V_{\rm{n}}}$/($\sigma \cdot {\tau^{-1}}$)${E_{{\rm{t}}}}$/$\varepsilon $${E_{{\rm{n}}}}$/$\varepsilon $E/$\varepsilon $
    1.0 Incident 3.0566 –0.8191 4.6720 0.3355 5.0083
    Re-R = 0 Å 2.1165 1.8812 3.1534 2.0912 5.2478
    Re-R = 0.5 Å 0.2948 1.8122 2.2248 1.9670 4.1892
    Re-R = 1.0 Å 0.1625 1.7772 1.9206 1.9334 3.8632
    2.0 Incident 6.1133 –1.6382 18.692 1.3420 20.034
    Re-R = 0 Å 5.6211 2.2725 16.724 3.1156 19.829
    Re-R = 0.5 Å 2.0090 2.9777 9.8840 5.6781 15.547
    Re-R = 1.0 Å 0.2579 3.3517 7.4644 6.7519 14.216
    4.0 Incident 12.226 –3.2766 74.766 5.3679 80.135
    Re-R = 0.0 Å 11.937 3.0014 72.802 5.1488 78.079
    Re-R = 0.5 Å 5.7585 5.6367 34.796 18.909 62.501
    Re-R = 1.0 Å 1.0305 6.6301 26.878 25.619 52.504
    8.0 Incident 24.452 –6.5532 299.06 21.472 320.54
    Re-R = 0 Å 24.021 6.0509 293.14 19.210 312.38
    Re-R = 0.5 Å 16.386 9.6325 209.77 49.747 259.52
    Re-R = 1.0 Å 2.0656 12.770 117.64 95.714 213.20
    16.0 Incident 48.906 –13.106 1196.3 85.880 1282.1
    Re-R = 0 Å 47.378 12.256 1143.2 79.050 1220.8
    Re-R = 0.5 Å 32.525 16.818 832.86 177.59 1009.5
    Re-R = 1.0 Å 2.9900 23.156 474.64 318.22 790.68
    下载: 导出CSV

    表 2  入射极角为$ 75^{\circ}$时, 不同速度的气体分子在不同表面上散射后的平均速度和能量

    Table 2.  When the incident polar angle is $ 75^{\circ} $, the mean velocity and energy of gas molecules that with different velocities after scattering on different surfaces.

    ${V_{\rm{i}}}$/$\sqrt {2{k_{\rm{B}}}T} $States${V_{\rm{t}}}$/($\sigma \cdot {\tau^{-1} }$)${V_{\rm{n}}}$/($\sigma \cdot {\tau^{-1}}$)${E_{{\rm{t}}}}$/$\varepsilon$${E_{{\rm{n}}}}$/$\varepsilon $E/$\varepsilon $
    1.0Incident3.0566–0.81914.67200.33555.0083
    Re-R = 0 Å2.11651.88123.15342.09125.2478
    Re-R = 0.5 Å0.29481.81222.22481.96704.1892
    Re-R = 1.0 Å0.16251.77721.92061.93343.8632
    2.0Incident6.1133–1.638218.6921.342020.034
    Re-R = 0 Å5.62112.272516.7243.115619.829
    Re-R = 0.5 Å2.00902.97779.88405.678115.547
    Re-R = 1.0 Å0.25793.35177.46446.751914.216
    4.0Incident12.226–3.276674.7665.367980.135
    Re-R = 0.0 Å11.9373.001472.8025.148878.079
    Re-R = 0.5 Å5.75855.636734.79618.90962.501
    Re-R = 1.0 Å1.03056.630126.87825.61952.504
    8.0Incident24.452–6.5532299.0621.472320.54
    Re-R = 0 Å24.0216.0509293.1419.210312.38
    Re-R = 0.5 Å16.3869.6325209.7749.747259.52
    Re-R = 1.0 Å2.065612.770117.6495.714213.20
    16.0Incident48.906–13.1061196.385.8801282.1
    Re-R = 0 Å47.37812.2561143.279.0501220.8
    Re-R = 0.5 Å32.52516.818832.86177.591009.5
    Re-R = 1.0 Å2.990023.156474.64318.22790.68
    下载: 导出CSV
  • [1]

    Liang T, Li Q, Ye W 2017 J. Comput. Phys. 352 105Google Scholar

    [2]

    曹炳阳, 陈民, 过增元 2006 物理学报 55 5305Google Scholar

    Cao B Y, Chen M, Guo Z Y 2006 Acta Phys. Sin. 55 5305Google Scholar

    [3]

    Sharipov F, Kalempa D 2005 Phys. Fluids 10 16Google Scholar

    [4]

    Burnett D 1935 Proc. Lond. Math. Soc. 1 1Google Scholar

    [5]

    Shavaliyev M S 1993 J. Appl. Math. Mech. 57 573Google Scholar

    [6]

    Bird G A 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford: Oxford University Press) p199

    [7]

    Yuan Y D, Rahman S 2016 Phys. A 463 25Google Scholar

    [8]

    Lockerby D A, Reese J M, Emerson D R, Barber R W 2004 Phys. Rev. E 70 017303Google Scholar

    [9]

    Barber R W, Emerson D R 2006 Heat Transfer Eng. 27 3Google Scholar

    [10]

    Lockerby D A, Reese J M, Gallis M A 2005 AIAA J. 43 1391Google Scholar

    [11]

    Reese J M, Zheng Y, Lockerby D A 2007 J. Comput. Theor. Nanosci. 4 807Google Scholar

    [12]

    Bruno D, Cacciatore M, Longo S, Rutigliano M 2000 Chem. Phys. Lett. 320 245Google Scholar

    [13]

    Padilla, J F, Bo yd, Iain D 2009 J. Thermophys. Heat Transfer 23 96Google Scholar

    [14]

    Liang T, Li Q, Ye W 2013 Phys. Rev. E 88 013009Google Scholar

    [15]

    Woronowicz M S, Rault D F 1994 J. Spacecraft Rockets 31 532Google Scholar

    [16]

    Myong R S 2004 J. Comput. Phys. 195 655Google Scholar

    [17]

    Alder B J, Wainwright T E 1957 J. Chem. Phys. 27 1208Google Scholar

    [18]

    Kovalev V, Yakunchikov A, Li F 2011 Acta Astronaut. 69 744Google Scholar

    [19]

    张忠强, 刘汉伦, 范晋伟, 丁建宁, 程广贵 2019 物理学报 68 170202Google Scholar

    Zhang Z Q, Liu H L, Fan J W, Ding J N, Cheng G G 2019 Acta Phys. Sin. 68 170202Google Scholar

    [20]

    Chirita V, Pailthorpe B A, Collins R E 1997 Nucl. Instrum. Meth. B 129 465Google Scholar

    [21]

    Yamanishi N, Matsumoto Y, Shobatake K 1999 Phys. Fluids 11 3540Google Scholar

    [22]

    曹炳阳 2005 博士学位论文 (北京: 清华大学)

    Cao B Y 2005 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese)

    [23]

    Finger G W, Kapat J S, Bhattacharya A 2007 J. Fluids Eng-Trans. ASME 129 31Google Scholar

    [24]

    Ozhgibesov M S, Leu T, Cheng C 2012 J. Mol. Graph. Model. 38 375Google Scholar

    [25]

    Ozhgibesov M S, Leu T, Cheng C 2013 J. Mol. Graph. Model. 45 45Google Scholar

    [26]

    Leu T, Cheng C, Ozhgibesov M S 2011 J. Mol. Graph. Model. 31 35Google Scholar

    [27]

    Bao F, Mao Z, Qiu L 2014 Int. J. Numer. Methods Heat Fluid Flow 24 1338Google Scholar

    [28]

    宋诚谦 2014 博士学位论文 (合肥: 中国科技大学)

    Song C Q 2014 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)

    [29]

    Cao B Y, Sun J, Chen M, Guo Z Y 2009 Int. J. Mol. Sci. 10 11Google Scholar

    [30]

    Sun J, Li Z 2008 Mol. Phys. 106 2325Google Scholar

    [31]

    Sun J, Li Z 2009 Mol. Simul. 35 228Google Scholar

    [32]

    张冉, 常青, 李桦 2018 物理学报 67 223401Google Scholar

    Zhang R, Chang Q, Li H 2018 Acta Phys. Sin. 67 223401Google Scholar

    [33]

    Maruyama S 2000 Adv. Numer. Heat Transfer 2 189Google Scholar

    [34]

    Wu L, Bogy D B 2002 J. Tribol.-Trans. ASME 124 562Google Scholar

    [35]

    Swope W C, Andersen H C, Berens P H, Wilson K R 1982 J. Chem. Phys. 76 637Google Scholar

    [36]

    Dongari N, Zhang Y H, Reese J M 2012 AIP Conf. Proc. 1501 895Google Scholar

    [37]

    张烨, 张冉, 赖剑奇, 李桦 2019 物理学报 68 124702Google Scholar

    Zhang Y, Zhang R, Lai J Q, Li H 2019 Acta Phys. Sin. 68 124702Google Scholar

    [38]

    Chirita V, Pailthorpe B A, Collins R E 1993 J. Phys. D: Appl. Phys. 26 133Google Scholar

    [39]

    Maxwell J C 1878 Proc. R. Soc. London 27 304Google Scholar

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出版历程
  • 收稿日期:  2020-07-24
  • 修回日期:  2020-08-31
  • 上网日期:  2021-01-13
  • 刊出日期:  2021-01-20

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