Abstract
In this work, we have studied the effects of macroscopic (temperature of gas and wall atoms; velocity of gas near the wall) and microscopic properties (energy well-depth parameter, \(\epsilon\), used in Lennard–Jones potential to describe gas–surface interaction strength) on both energy accommodation coefficients (EAC) and tangential momentum accommodation coefficient (TMAC) using molecular dynamics approach. The effect of aforementioned properties is studied through classical force-driven nano-Poiseuille flow using argon gas and platinum walls. Parameters like temperature of wall, external force acting on gas atoms, and energy well depth (\(\epsilon\)) between gas and surface are varied systematically to study the effects of these parameters on accommodation coefficients. Empirical relationship between the accommodation coefficients (TMAC and EAC) and the above-mentioned properties is obtained by performing non-linear regression analysis.
Similar content being viewed by others
References
Agrawal A, Prabhu SV (2008) Survey on measurement of tangential momentum accommodation coefficient. J Vac Sci Technol A Vac Surf Films 26(4):634–645
Arkilic EB, Breuer KS, Schmodt MA (2001) J Fluid Mech. Mass flow and tangential momentum accommodation in silicon micromachined channels 437:29–43
Arya G, Chang H-C, Maginn EJ (2003) Molecular simulations of Knudsen wall-slip: effect of wall morphology. Mol Simul 29(10–11):697–709
Barisik M, Beskok A (2012) Surface-gas interaction effects on nanoscale gas flows. Microfluid Nanofluid 13(5):789–798
Bird G (1994) Molecular gas dynamics and the direct simulation of gas flows, The Oxford engineering science series. Clarendon Press, Oxford
Birkhoff GD (1931) Proof of the Ergodic Theorem. Proc Natl Acad Sci 17(12):656–660
Cahill DG, Ford WK, Goodson KE, Mahan GD, Majumdar A, Humphrey J, Merlin R, Phillpot SR, Ford WK, Maris HJ (2003) Nanoscale thermal transport. J Appl Phys 93:2
Cao B-Y, Chen M, Guo Z-Y (2005) Temperature dependence of the tangential momentum accommodation coefficient for gases. Appl Phys Lett 86:1–4
Cao BY, Sun J, Chen M, Guo ZY (2009) Molecular momentum transport at fluid-solid interfaces in MEMS/NEMS: a review. Int J Mol Sci 10(11):4638–4706
Cercignani C, Lampis M (1971) Kinetic models for gas-surface interactions. Transp Theory Stat Phys 1(2):101–114
Cercignani C, Lampis M, Lentati A (1995) A new scattering kernel in kinetic theory of gases. Transp Theory Stat Phys 24(9):1319–1336
Chirita V, Pailthorpe B, Collins R (1997) Non-equilibrium energy and momentum accommodation coefficients of Ar atoms scattered from Ni (001) in the thermal regime: a molecular dynamics study. Nucl Instrum Methods Phys Res B 129:465–473
Christoper D (2016) Introduction to econometrics. Oxford University Press, Oxford
Dadzie SK, Méolans JG (2004) Anisotropic scattering kernel: Generalized and modified Maxwell boundary conditions. J Math Phys 45(5):1804–1819
Ewart T, Perrier P, Graur IA, Meolans JG (2007) Mass flow rate measurements in a microchannel, from hydrodynamic to near free molecular regimes. J Fluid Mech 584:337–356
Foiles S, Baskes M, Daw M (1986) Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys Rev B 33(12):7983–7991
Frezzotti A, Nedea SV, Markvoort AJ, Spijker P, Gibelli L (2008) Comparison of molecular dynamics and kinetic modeling of gas-surface interaction. In: 26th International Symposium on Rarefied Gas Dynamics (RGD26), Kyoto, Japan, 20-25 July 2008
Goodman FO (1980) Thermal accommodation coefficients. J Phys Chem 84(12):1431–1445
Gu K, Watkins CB, Koplik J (2010) Atomistic hybrid DSMC/NEMD method for nonequilibrium multiscale simulations. J Comput Phys 229(5):1381–1400
Honig CDF, Ducker WA (2010) Effect of molecularly thin films on lubrication forces and accommodation coefficients in air. J Phys Chem C 114(47):20114–20119
Hoover W (1985) Canonical dynamics: equilibrium phase-space distributions. Phys Rev A 31:1695–1697
Kammara KK, Malaikannan G, Kumar R (2016) Molecular dynamics study of gas-surface interactions in a force-driven flow of argon through a rectangular nanochannel. Nanoscale Microscale Thermophys Eng 20(2):121–136
Kammara KK, Kumar R, Singh AK, Chinnappan AK (2019) Systematic direct simulation Monte Carlo approach to characterize the effects of surface roughness on accommodation coefficients. Phys Rev Fluids 4:123401
Ketsdever AD, Wadsworth DC, Muntz EP (2001) Gas-surface interaction model influence on predicted performance of microelectromechanical system resistojet. J Thermophys Heat Transfer 15(3):302–307
Koplik J, Banavar JR, Willemsen JF (1989) Molecular dynamics of fluid flow at solid surfaces. Phys Fluids A Fluid Dyn 781(1):781–794
Léonard C, Brites V, Pham TT, To QD, Lauriat G (2013) Influence of the pairwise potential on the tangential momentum accommodation coefficient: A multi-scale study applied to the argon on Pt(111) system. Euro Phys J B 86(4):164
Leung R, Cheung H, Gang H, Ye W (2010) A Monte Carlo simulation approach for the modeling of free-molecule squeeze-film damping of flexible microresonators. Microfluid Nanofluid 9(4):809–818
Lord RG (1977) Gas-surface interaction: Tangential momentum accommodation coefficients of rare gases on polycrystalline metal surfaces. Rarefied Gas Dynamics, Parts I and II, Progress in Astronautics and Aeronautics, American Institute of Aeronautics and Astronautics, pp 531–538
Lord RG (1995) Some further extensions of the Cercignani-Lampis gas-surface interaction model. Phys Fluids 7(5):1159–1161
Maxwell JC (1879) On stresses in rarified gases aArising from inequalities of temperature. Philos Transact R Soc London 170:231–256
Maxwell JC (2011) The scientific papers of James Clerk Maxwell (Cambridge Library Collection—Physical Sciences). Cambridge University Press, Cambridge
Mehta NA, Levin DA (2017) Molecular dynamics derived gas-surface models for use in direct simulation Monte Carlo. J Thermophys Heat Transfer 31(4):757–771
Nedea SV, Frijns AJH, Van Steenhoven AA, Markvoort AJ, Hilbers PAJ (2005) Hybrid method coupling molecular dynamics and Monte Carlo simulations to study the properties of gases in microchannels and nanochannels. Phys Rev E 72(1):16705
Nose S (1984) A unified formulation of the constant temperature molecular dynamics methods. J Chem Phys 81:511–519
Ohwada T (1996) Heat flow and temperature and density distributions in a rarefied gas between parallel plates with different temperatures. Finite-difference analysis of the nonlinear Boltzmann equation for hard-sphere molecules. Phys Fluids 8(8):2153–2160
Peddakotla SA, Kammara KK, Rakesh K (2019) Molecular dynamics simulation of particle trajectory for the evaluation of surface accommodation coefficients. Microfluid Nanofluid 23(6):1–17
Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117(1995):1–19
Prabha SK, Sathian SP (2013) Calculation of thermo-physical properties of Poiseuille flow in a nano-channel. Int J Heat Mass Transf 58(1–2):217–223
Rader DJ, Trott WM, Torczynski JR, Castañeda JN, Grasser TW (2005) Measurements of Thermal Accomodation Coefficients. Sandia Technical Report: SAND2005-6084
Santos WFN (2007) Gas-surface interaction effect on round leading edge aerothermodynamics. Brazilian Journal of Physics 37(2a):337–348
Seidl M, Steinheil E (1974) Measurement of momentum accommodation coefficients on surfaces characterized by Auger spectroscopy. In: SIMS and LEED Proccedings International Symposium on Rarefied Gas Dynamics, No. 47, pp 20114–20119
Spijker P, Markvoort AJ, Nedea SV, Hilbers PAJ (2010) Computation of accommodation coefficients and the use of velocity correlation profiles in molecular dynamics simulations. Phys Rev E 81(1):11203
Struchtrup H (2013) Maxwell boundary condition and velocity dependent accommodation coefficient. Phys Fluids 25:11
Sun J, Li Z-X (2008) Effect of gas adsorption on momentum accommodation coefficients in microgas flows using molecular dynamic simulations. Mol Phys 106(19):2325–2332
Sun J, Li Z-X (2011) Three-dimensional molecular dynamic study on accommodation coefficients in rough nanochannels. Heat Transf Eng 32:658–666
Toxvaerd S (1998) The structure and thermodynamics of a solid—fluid interface. J Chem Phys 74:1998–2005
Travis KP, Todd BD, Evans DJ (1997) Departure from Navier-Stokes hydrodynamics in confined liquids. Phys Rev E 55(4):4288–4295
Trott W, Rader D, Castaneda J, Torczynski J, Gallis M (2007) Experimental measurements of thermal accommodation coefficients for microscale gas-phase heat transfer. In: 39th AIAA Thermophysics Conference, pp 1–31
Verlet L (1967) Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys Rev 159:98–103
Wachman HY (1962) The thermal accommodation coefficient: a critical survey. ARS J 32(1):2–12
Yamamoto K (2001) Slightly rarefied gas flow over a smooth platinum surface. AIP Conf Proc 585(1):339–346
Yamamoto K (2002) Slip flow over a smooth platinum surface. JSME Int J Ser B Fluids Therm Eng 45(4):788–795
Yamamoto K, Takeuchi H, Hyakutake T (2006) Characteristics of reflected gas molecules at a solid surface. Phys Fluids 18(4):046103–1–046103–11
Yamamoto K, Takeuchi H, Hyakutake T (2007) Scattering properties and scattering kernel based on the molecular dynamics analysis of gas-wall interaction. Phys Fluids 19(8):087102
Yamanishi N, Matsumoto Y, Shobatake K (1999) Multistage gas-surface interaction model for the direct simulation Monte Carlo method. Phys Fluids 11(11):3540–3552
Acknowledgements
We acknowledge the use of computing facilities available at the High-Performance Computing Facility at the Computer Center, IIT Kanpur, for carrying out the work presented in the article.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kammara, K.K., Kumar, R. Development of empirical relationships for surface accommodation coefficients through investigation of nano-poiseuille flows using molecular dynamics method. Microfluid Nanofluid 24, 70 (2020). https://doi.org/10.1007/s10404-020-02375-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10404-020-02375-x