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Molecular dynamics simulation of particle trajectory for the evaluation of surface accommodation coefficients

  • Sai Abhishek Peddakotla
  • Kishore K. Kammara
  • Rakesh KumarEmail author
Research Paper
  • 129 Downloads

Abstract

Molecular dynamics approach has been employed in this work to model experiments for the interaction of a single particle with a surface. Some important modifications are implemented in the present approach as compared to the previous works. Investigations have been performed to compute the reflected distribution of molecules and calculate accommodation coefficients for interaction of noble gases with platinum and graphite surfaces. Through a few numerical tests, it is verified that the results obtained using the present approach are in good agreement with some established data in the literature. The method is then utilized to predict the surface accommodation coefficients, which are required as boundary conditions in the gas–surface interaction models, such as the Cercignani–Lampis–Lord (CLL) model, for mesoscopic simulations using the direct simulation Monte Carlo approach. Interestingly, it is shown that the CLL model shows some disagreement with the molecular dynamics simulation data for the distribution of reflected molecules. However, the CLL model can still be utilized in practical applications, as it is shown to predict the average macroscopic properties to a very high degree of accuracy. The behavior of accommodation coefficients with a change in the incident flow properties, such as bulk velocity, gas temperature, and gas-to-surface molecule mass ratio, is also investigated in detail.

Nomenclature

\(\lambda\)

Mean free path

L

Characteristic length

Kn

Knudsen number

\(\Phi\)

Flux of a physical property

M

Mass of the molecule

T

Temperature

\(k_\text {B}\)

Boltzmann constant

\(\sigma _\text {t}\)

Tangential momentum accommodation coefficient

\(\alpha\)

Energy accommodation coefficient

\(\sigma\)

Size parameter for LJ potential

\(\varepsilon\)

Depth of the potential well

a

Lattice constant

\(r_{0,\text {cc}}\)

Equilibrium bond length

\(\theta _{0,\text {cc}}\)

Equilibrium angle for graphite

k

Harmonic style parameter

\(\phi\)

Azimuthal angle

\(\theta\)

Elevation angle

c

Speed of the molecule

Subscripts

n

Normal to the surface (z-direction)

i

Incident

r

Reflected

s

Surface

mp

Most probable speed

t1, t2

Tangential direction to the surface; x- and y-directions respectively

g

Gas

gs

Gas–surface parameter

bond

Bond parameters

angle

Angle parameters

dih

Dihedral angle parameters

Notes

Acknowledgements

The authors acknowledge the use of high-performance computing facilities available at the Indian Institute of Technology Kanpur, without which this research work would not have been possible.

References

  1. Allen MP, Tildesley DJ (2017) Computer simulation of liquids. Oxford University Press, OxfordCrossRefGoogle Scholar
  2. Arkilic EB, Breuer KS, Schmidt MA (2001) Mass flow and tangential momentum accommodation in silicon micromachined channels. J Fluid Mech 437:29–43CrossRefGoogle Scholar
  3. Arya G, Chang H-C, Maginn EJ (2003) Molecular simulations of Knudsen wall-slip: effect of wall morphology. Mol Simul 29(10–11):697–709CrossRefGoogle Scholar
  4. Berendsen HJC, Postma JPM, van Gunsteren WF, DiNola A, Haak JR (1984) J Chem Phys 81:3684CrossRefGoogle Scholar
  5. Bird G (1994) Molecular gas dynamics and the direct simulation of gas flows. The Oxford engineering science series. Clarendon Press, ClarendonGoogle Scholar
  6. Cao B-Y, Sun J, Chen M, Guo Z-Y (2009) Molecular momentum transport at fluid–solid interfaces in MEMS/NEMS: a review. Int J Mol Sci 10(11):4638–4706CrossRefGoogle Scholar
  7. Cercignani C (2000) Rarefied gas dynamics: from basic concepts to actual calculations, vol 21. Cambridge University Press, CambridgezbMATHGoogle Scholar
  8. Cercignani C, Lampis M (1971) Kinetic models for gas–surface interactions. Transp Theory Stat Phys 1(2):101–114MathSciNetCrossRefGoogle Scholar
  9. Chirita V, Pailthorpe B, Collins R (1993) Molecular dynamics study of low-energy Ar scattering by the Ni (001) surface. J Phys D Appl Phys 26(1):133CrossRefGoogle Scholar
  10. Cohen LK (1993) A lower bound on the loss of graphite by atomic oxygen attack at asymptotic energy. J Chem Phys 99(12):9652–9663CrossRefGoogle Scholar
  11. Crowell A (1958) Potential energy functions for graphite. J Chem Phys 29(2):446–447CrossRefGoogle Scholar
  12. Daun K, Liu F, Smallwood G (2008) Molecular dynamics simulations of translational thermal accommodation coefficients for time-resolved LII. In: ASME 2008 heat transfer summer conference collocated with the fluids engineering, energy sustainability, and 3rd energy nanotechnology conferences, American Society of Mechanical Engineers, pp 333–342Google Scholar
  13. Foiles S, Baskes M, Daw MS (1986) Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys Rev B 33(12):7983CrossRefGoogle Scholar
  14. Gabis DH, Loyalka SK, Storvick TS (1996) Measurements of the tangential momentum accommodation coefficient in the transition flow regime with a spinning rotor gauge. J Vacuum Sci Technol A Vacuum Surf Films 14(4):2592–2598CrossRefGoogle Scholar
  15. Harley JC, Huang Y, Bau HH, Zemel JN (1995) Gas flow in micro-channels. J Fluid Mech 284:257–274CrossRefGoogle Scholar
  16. Kuhlthau A (1949) Air friction on rapidly moving surfaces. J Appl Phys 20(2):217–223CrossRefGoogle Scholar
  17. Liu S-M, Sharma P, Knuth E (1979) Satellite drag coefficients calculated from measured distributions of reflected helium atoms. AIAA J 17(12):1314–1319CrossRefGoogle Scholar
  18. Lord R (1976) Tangential momentum accommodation coefficients of rare gases on polycrystalline metal surface. In: Proceedings of 10th international symposium on rarefied gas dynamics, pp 49:531–538Google Scholar
  19. Lord R (1990) Application of the Cercignani–Lampis scattering kernel to direct simulation Monte Carlo calculations. In: Proceedings of 17th international symposium on rarefied gas dynamics, vol 49, pp 1427–1433Google Scholar
  20. Lord R (1991) Some extensions to the Cercignani–Lampis gas–surface scattering kernel. Phys Fluids A Fluid Dyn 3(4):706–710CrossRefGoogle Scholar
  21. Lord R (1995) Some further extensions of the Cercignani–Lampis gas–surface interaction model. Phys Fluids 7(5):1159–1161CrossRefGoogle Scholar
  22. Maxwell JC (1878) III. On stresses in rarefied gases arising from inequalities of temperature. Proc R Soc Lond 27(185–189):304–308zbMATHGoogle Scholar
  23. Mehta NA, Levin DA (2017) Molecular-dynamics-derived gas-surface models for use in direct-simulation Monte Carlo. J Thermophys Heat Transf 31(4):757–771CrossRefGoogle Scholar
  24. Padilla JF, Boyd ID (2009) Assessment of gas–surface interaction models for computation of rarefied hypersonic flow. J Thermophys Heat Transf 23(1):96–105CrossRefGoogle Scholar
  25. Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117(1):1–19CrossRefGoogle Scholar
  26. Rettner CT (1998) Thermal and tangential–momentum accommodation coefficients for N/sub 2/colliding with surfaces of relevance to disk-drive air bearings derived from molecular beam scattering. IEEE Trans Magn 34(4):2387–2395CrossRefGoogle Scholar
  27. Rettner C, Auerbach D, Tully J, Kleyn A (1996) Chemical dynamics at the gas–surface interface. J Phys Chem 100(31):13021–13033CrossRefGoogle Scholar
  28. Sone Y (1972) Flow induced by thermal stress in rarefied gas. Phys Fluids 15(8):1418–1423CrossRefGoogle Scholar
  29. Spijker P, Markvoort AJ, Nedea SV, Hilbers PA (2010) Computation of accommodation coefficients and the use of velocity correlation profiles in molecular dynamics simulations. Phys Rev E 81(1):011203CrossRefGoogle Scholar
  30. Suetsugu Y (1996) Application of the Monte Carlo method to pressure calculation. J Vacuum Sci Technol A Vacuum Surf Films 14(1):245–250CrossRefGoogle Scholar
  31. Trott WM, Castañeda JN, Torczynski JR, Gallis MA, Rader DJ (2011) An experimental assembly for precise measurement of thermal accommodation coefficients. Rev Sci Instrum 82(3):035120CrossRefGoogle Scholar
  32. Yamaguchi H, Ho M, Matsuda Y, Niimi T, Graur I (2017) Conductive heat transfer in a gas confined between two concentric spheres: from free-molecular to continuum flow regime. Int J Heat Mass Transf 108:1527–1534CrossRefGoogle Scholar
  33. Yamamoto K, Takeuchi H, Hyakutake T (2006) Characteristics of reflected gas molecules at a solid surface. Phys Fluids 18(4):046103CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Sai Abhishek Peddakotla
    • 1
  • Kishore K. Kammara
    • 1
  • Rakesh Kumar
    • 1
    Email author
  1. 1.Department of Aerospace EngineeringIndian Institute of Technology KanpurKanpurIndia

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