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

Yu Hang; Zhang Ran; Yang Fan; Li Hua

doi:10.7498/aps.70.20201192

Abstract

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.

Keywords:

Authors and contacts

1.
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
2.
State Key Laboratory of Laser Interaction with Matter, Northwest Institute of Nuclear Technology, Xi’an 710024, China

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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References

[1]	Liang T, Li Q, Ye W 2017 J. Comput. Phys. 352 105 Google Scholar
[2]	曹炳阳, 陈民, 过增元 2006 物理学报 55 5305 Google Scholar Cao B Y, Chen M, Guo Z Y 2006 Acta Phys. Sin. 55 5305 Google Scholar
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Cited By

图 1 三种表面粗糙度构型

Figure 1. Three surface roughness structures.

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 4 以$ 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)

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

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 8 以$ 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)

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

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

DownLoad: 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 $
1.0	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

DownLoad: CSV

[1]	Liang T, Li Q, Ye W 2017 J. Comput. Phys. 352 105 Google Scholar
[2]	曹炳阳, 陈民, 过增元 2006 物理学报 55 5305 Google Scholar Cao B Y, Chen M, Guo Z Y 2006 Acta Phys. Sin. 55 5305 Google Scholar
[3]	Sharipov F, Kalempa D 2005 Phys. Fluids 10 16 Google Scholar
[4]	Burnett D 1935 Proc. Lond. Math. Soc. 1 1 Google Scholar
[5]	Shavaliyev M S 1993 J. Appl. Math. Mech. 57 573 Google 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 25 Google Scholar
[8]	Lockerby D A, Reese J M, Emerson D R, Barber R W 2004 Phys. Rev. E 70 017303 Google Scholar
[9]	Barber R W, Emerson D R 2006 Heat Transfer Eng. 27 3 Google Scholar
[10]	Lockerby D A, Reese J M, Gallis M A 2005 AIAA J. 43 1391 Google Scholar
[11]	Reese J M, Zheng Y, Lockerby D A 2007 J. Comput. Theor. Nanosci. 4 807 Google Scholar
[12]	Bruno D, Cacciatore M, Longo S, Rutigliano M 2000 Chem. Phys. Lett. 320 245 Google Scholar
[13]	Padilla, J F, Bo yd, Iain D 2009 J. Thermophys. Heat Transfer 23 96 Google Scholar
[14]	Liang T, Li Q, Ye W 2013 Phys. Rev. E 88 013009 Google Scholar
[15]	Woronowicz M S, Rault D F 1994 J. Spacecraft Rockets 31 532 Google Scholar
[16]	Myong R S 2004 J. Comput. Phys. 195 655 Google Scholar
[17]	Alder B J, Wainwright T E 1957 J. Chem. Phys. 27 1208 Google Scholar
[18]	Kovalev V, Yakunchikov A, Li F 2011 Acta Astronaut. 69 744 Google Scholar
[19]	张忠强, 刘汉伦, 范晋伟, 丁建宁, 程广贵 2019 物理学报 68 170202 Google Scholar Zhang Z Q, Liu H L, Fan J W, Ding J N, Cheng G G 2019 Acta Phys. Sin. 68 170202 Google Scholar
[20]	Chirita V, Pailthorpe B A, Collins R E 1997 Nucl. Instrum. Meth. B 129 465 Google Scholar
[21]	Yamanishi N, Matsumoto Y, Shobatake K 1999 Phys. Fluids 11 3540 Google 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 31 Google Scholar
[24]	Ozhgibesov M S, Leu T, Cheng C 2012 J. Mol. Graph. Model. 38 375 Google Scholar
[25]	Ozhgibesov M S, Leu T, Cheng C 2013 J. Mol. Graph. Model. 45 45 Google Scholar
[26]	Leu T, Cheng C, Ozhgibesov M S 2011 J. Mol. Graph. Model. 31 35 Google Scholar
[27]	Bao F, Mao Z, Qiu L 2014 Int. J. Numer. Methods Heat Fluid Flow 24 1338 Google 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 11 Google Scholar
[30]	Sun J, Li Z 2008 Mol. Phys. 106 2325 Google Scholar
[31]	Sun J, Li Z 2009 Mol. Simul. 35 228 Google Scholar
[32]	张冉, 常青, 李桦 2018 物理学报 67 223401 Google Scholar Zhang R, Chang Q, Li H 2018 Acta Phys. Sin. 67 223401 Google Scholar
[33]	Maruyama S 2000 Adv. Numer. Heat Transfer 2 189 Google Scholar
[34]	Wu L, Bogy D B 2002 J. Tribol.-Trans. ASME 124 562 Google Scholar
[35]	Swope W C, Andersen H C, Berens P H, Wilson K R 1982 J. Chem. Phys. 76 637 Google Scholar
[36]	Dongari N, Zhang Y H, Reese J M 2012 AIP Conf. Proc. 1501 895 Google Scholar
[37]	张烨, 张冉, 赖剑奇, 李桦 2019 物理学报 68 124702 Google Scholar Zhang Y, Zhang R, Lai J Q, Li H 2019 Acta Phys. Sin. 68 124702 Google Scholar
[38]	Chirita V, Pailthorpe B A, Collins R E 1993 J. Phys. D: Appl. Phys. 26 133 Google Scholar
[39]	Maxwell J C 1878 Proc. R. Soc. London 27 304 Google Scholar

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