Skip to main content
SpringerLink
Log in

Rarefied gas flow through a rough channel into a vacuum

  • Research Paper
  • Published:
Microfluidics and Nanofluidics Aims and scope Submit manuscript

A Correction to this article was published on 20 April 2020

This article has been updated

Abstract

Rarefied gas flow through a rough channel of finite length into a vacuum was investigated using the direct simulation Monte Carlo method. The non-equilibrium effects at the input and output of the channel were considered by including certain pre-and post-channel regions into the geometry under consideration. The mass flow rate through a short and long channel was computed in a wide range of gas rarefaction from the free molecular regime to the hydrodynamic near. It is shown that the noticeable effect of surface roughness on flow rate is manifested in the free molecular and transition regimes. The analysis is provided for the flow field inside the channel as well as in the upstream and downstream regions. The results obtained are consistent with the theoretical, numerical, and experimental data available in the open literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Change history

  • 20 April 2020

    There is a mistype in one cell [first row, fifth column].

References

  • Barantsev RG (1975) Interaction between rarefied gases and streamlined surfaces. Moscow Izdatel Nauka (in Russian)

  • Barisik M, Beskok A (2016) Law of the nano-wall in nano-channel gas flows. Microfluid Nanofluid 20(3):46

    Google Scholar 

  • Beeby S, Ensel G, Kraft M White N (2004) MEMS mechanical sensors. Artech House

  • Berman AS (1965) Free molecule transmission probabilities. J Appl Phys 36(10):3356

    Google Scholar 

  • Berman AS (1966) Erratum: free molecule transmission probabilities. J Appl Phys 37(7):2930

    Google Scholar 

  • Bird GA (1994) Molecular gas dynamics and the direct simulation of gas flow. Oxford University Press, Oxford

    Google Scholar 

  • Cao B-Y, Chen M, Guo Z-Y (2006) Effect of surface roughness on gas flow in microchannels by molecular dynamics simulation. Int J Eng Sci 44(13-14):927–937

    Google Scholar 

  • Chai Z, Guo Z, Zheng L, Shi B (2008) Lattice Boltzmann simulation of surface roughness effect on gaseous flow in a microchannel. J Appl Phys 104(1):014902

    Google Scholar 

  • Davis DH, Levenson LL, Milleron N (1964) Effect of «rougher-than-rough» surface on molecular flow through short duct. J Appl Phys 35:529–532

    Google Scholar 

  • Deng Z, Chen Y, Shao C (2016) Gas flow through rough microchannels in the transition flow regime. Phys Rev E 93(1):013128

    Google Scholar 

  • Gad-el-Hak M (2001) The MEMS handbook. CRC Press, USA

    MATH  Google Scholar 

  • Guo L, Huijin Xu, Gong L (2015) Influence of wall roughness models on fluid flow and heat transfer in microchannels. Appl Therm Eng 84:399–408

    Google Scholar 

  • He X, Luo L-S (1997) Lattice Boltzmann model for the incompressible Navier–Stokes equation. J Stat Phys 88(3-4):927–944

    MathSciNet  MATH  Google Scholar 

  • Ivanov MS, Rogasinsky SV (1988) Analysis of numerical techniques of the direct simulation Monte Carlo method in the rarefied gas dynamics. Russ J Numer Anal Math Model 3:453–466

    MathSciNet  MATH  Google Scholar 

  • Ji Y, Yuan K, Chung JN (2006) Numerical simulation of wall roughness on gaseous flow and heat transfer in a microchannel. Int J Heat Mass Transf 49(7–8):1329–1339

    MATH  Google Scholar 

  • Li D (ed) (2008) Encyclopedia of microfluidics and nanofluidics. Springer Science & Business Media, New York

    Google Scholar 

  • Li WL, Lin JW, Lee SC, Chen MD (2002) Effects of roughness on rarefied gas flow in long microtubes. J Micromech Microeng 12(2):149

    Google Scholar 

  • Lilly TC, Duncan JA, Nothnagel SL, Gimelshein SF, Gimelshein NE, Ketsdever AD, Wysong IJ (2007) Numerical and experimental investigation of microchannel flows with rough surfaces. Phys Fluids 19(10):106101

    MATH  Google Scholar 

  • Liu CF, Ni YS (2009) The fractal roughness effect of micro Poiseuille flows using the lattice Boltzmann method. Int J Eng Sci 47(5-6):660–668

    MathSciNet  MATH  Google Scholar 

  • Rovenskaya OI (2017) Numerical analysis of surface roughness effects on the Poiseuille flow caused by a small pressure drop. Int J Heat Mass Transf 110:817–826

    Google Scholar 

  • Sazhin O (2008) Gas flow through a slit into a vacuum in a wide range of rarefaction. J Exp Theor Phys 107(1):162–169

    MathSciNet  Google Scholar 

  • Sazhin O (2009a) Gas molecule–molecule interaction and the gas–surface scattering effect on the rarefied gas flow through a slit into a vacuum. J Exp Theor Phys 108(5):874–879

    Google Scholar 

  • Sazhin O (2009b) Rarefied gas flow through a channel of finite length into a vacuum. J Exp Theor Phys 109(4):700–706

    Google Scholar 

  • Sazhin O (2010) Impact of the gas–surface scattering and gas molecule–molecule interaction on the mass flow rate of the rarefied gas through a short channel into a vacuum. J Vac Sci Technol A Vac Surf Films 28(6):1393–1398

    Google Scholar 

  • Sazhin O (2012) Pressure-driven flow of rarefied gas through a slit at a various pressure ratios. J Vac Sci Technol A Vac Surf Films 30(2):021603

    Google Scholar 

  • Sazhin O (2015a) Comment on “Data on Internal Rarefied Gas Flows” [J. Phys. Chem. Ref. Data 27, 657 (1998)]. J Phys Chem Ref Data 44(3):036101

    Google Scholar 

  • Sazhin O (2015b) Rarefied gas flow through a slit and channel of finite length due to a large pressure difference. A benchmark problem. Vacuum 115:75–79

    Google Scholar 

  • Sazhin O (2018) Regarding a benchmark problem: rarefied gas flow through a rough-surfaced channel. Comput Math Math Phys 58(10):1640–1646

    MathSciNet  MATH  Google Scholar 

  • Sazhin O (2019) The effect of surface roughness on internal free molecular gas flow. Vacuum 159:287–292

    Google Scholar 

  • Schaaf SA, Chambre PL (1961) Flow of rarefied gases. Princeton University Press, USA

    MATH  Google Scholar 

  • Sharipov F (2004) Numerical simulation of rarefied gas flow through a thin orifice. J Fluid Mech 518:35–60

    MATH  Google Scholar 

  • Sharipov F (2012) Transient flow of rarefied gas through an orifice. J Vac Sci Technol A Vac Surf Films 30(2):021602

    Google Scholar 

  • Sharipov F (2013) Transient flow of rarefied gas through a short tube. Vacuum 90:25–30

    Google Scholar 

  • Sharipov F (2017) Ab initio simulation of gaseous mixture flow through an orifice. Vacuum 143:106–118

    Google Scholar 

  • Sharipov F, Barreto YB (2015) Influence of gas–surface interaction on gaseous transmission probability through conical and spherical ducts. Vacuum 121:22–25

    Google Scholar 

  • Sharipov F, Kozak DV (2009) Rarefied gas flow through a thin slit into vacuum simulated by the Monte Carlo method over the whole range of the Knudsen number. J Vac Sci Technol A Vac Surf Films 27(3):479–484

    Google Scholar 

  • Sharipov F, Kozak DV (2011) Rarefied gas flow through a thin slit at an arbitrary pressure ratio. Eur J Mech-B/Fluids 30(5):543–549

    MATH  Google Scholar 

  • Sharipov F, Seleznev V (1998) Data on internal rarefied gas flows. J Phys Chem Ref Data 27(3):657–706

    Google Scholar 

  • Su W, Liu H, Zhang Y, Wu L (2017) Rarefaction cloaking: influence of the fractal rough surface in gas slider bearings. Phys Fluids 29(10):102003

    Google Scholar 

  • Sugiyama W, Sawada T, Nakamori K (1996) Rarefied gas flow between two flat plates with two dimensional surface roughness. Vacuum 47(6-8):791–794

    Google Scholar 

  • Sugiyama W, Sawada T, Yabuki M, Chiba Y (2001) Effects of surface roughness on gas flow conductance in channels estimated by conical roughness model. Appl Surf Sci 169:787–791

    Google Scholar 

  • Sukop Jr. MC, Thorne DT (2006) Lattice Boltzmann Modeling. Springer, Heidelberg, Berlin, New York

    Google Scholar 

  • Sun H, Faghri M (2003) Effect of surface roughness on nitrogen flow in a microchannel using the direct simulation Monte Carlo method. Numer Heat Transf Part A Appl 43(1):1–8

    Google Scholar 

  • Turner SE, Lam LC, Faghri M, Gregory OJ (2004) Experimental investigation of gas flow in microchannels. J Heat Transfer 126(5):753–763

    Google Scholar 

  • Usami M, Fujimoto T, Kato S (1989) Monte Carlo simulation on mass flow reduction due to roughness of a slit surface. Prog Astronaut Aeronaut 116:283–297

    Google Scholar 

  • Varoutis S, Valougeorgis D, Sazhin O, Sharipov F (2008) Rarefied gas flow through short tubes into vacuum. J Vac Sci Technol A Vac Surf Films 26(2):228–238

    Google Scholar 

  • Varoutis S, Valougeorgis D, Sharipov F (2009) Simulation of gas flow through tubes of finite length over the whole range of rarefaction for various pressure drop ratios. J Vac Sci Technol A Vac Surf Films 27(6):1377–1391

    Google Scholar 

  • Varoutis S, Day C, Sharipov F (2012) Rarefied gas flow through channels of finite length at various pressure ratios. Vacuum 86(12):1952–1959

    Google Scholar 

  • Wang X-Q, Yap C, Mujumdar AS (2005) Effects of two-dimensional roughness in flow in microchannels. J Electron Packag 127(3):357–361

    Google Scholar 

  • Xing Y, Zhi T, Haiwang Li, Yitu T (2016) Experimental investigation of surface roughness effects on flow behavior and heat transfer characteristics for circular microchannels. Chin J Aeronaut 29(6):1575–1581

    Google Scholar 

  • Yan H, Zhang WM, Peng ZK, Meng G (2015) Effect of random surface topography on the gaseous flow in microtubes with an extended slip model. Microfluid Nanofluid 18(5-6):897–910

    Google Scholar 

  • Yoshida H, Shiro M, Arai K, Hirata M, Akimichi H (2010) Effect of surface material and roughness on conductance of channel between parallel disks at molecular flow. J Vac Sci Technol A Vac Surf Films 28(4):937–941

    Google Scholar 

  • Zhang C, Chen Y, Deng Z, Shi M (2012) Role of rough surface topography on gas slip flow in microchannels. Phys Rev E 86(1):016319

    Google Scholar 

Download references

Acknowledgements

The support by the Ministry of Education and Science of the Russian Federation through the State task for high educational institutions (the research project # FEUZ-2020-0057) is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Ural Federal University, Lenin av. 51, Ekaterinburg, 620000, Russia

    O. Sazhin

Authors
  1. O. Sazhin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. Sazhin.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sazhin, O. Rarefied gas flow through a rough channel into a vacuum. Microfluid Nanofluid 24, 27 (2020). https://doi.org/10.1007/s10404-020-2330-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10404-020-2330-y

Keywords

Search

Navigation