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The effect of Knudsen layers on rarefied cylindrical Couette gas flows

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An Erratum to this article was published on 14 March 2013

Abstract

We investigate a power-law probability distribution function to describe the mean free path of rarefied gas molecules in non-planar geometries. A new curvature-dependent model is derived by taking into account the boundary-limiting effects on the molecular mean free path for surfaces with both convex and concave curvatures. The Navier–Stokes constitutive relations and the velocity-slip boundary conditions are then modified based on this power-law scaling through the transport property expressions in terms of the mean free path. Velocity profiles for isothermal cylindrical Couette flow are obtained using this power-law model and compared with direct simulation Monte Carlo (DSMC) data. We demonstrate that our model is more accurate than the classical slip solution, and we are able to capture important non-linear trends associated with the non-equilibrium physics of the Knudsen layer. In addition, we establish a new criterion for the critical accommodation coefficient that leads to the non-intuitive phenomenon of velocity inversion. The power-law model predicts that the critical accommodation coefficient is significantly lower than that calculated using the classical slip solution, and is in good agreement with available DSMC data. Our proposed constitutive scaling for non-planar surfaces is based on simple physical arguments and can be readily implemented in conventional fluid dynamics codes for arbitrary geometric configurations of microfluidic systems.

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Acknowledgments

The research leading to these results has received funding from the European Community’s Seventh Framework Programme FP7/2007-2013 under grant agreement ITN GASMEMS no. 215504. Additional support was provided by the UK Engineering and Physical Sciences Research Council (EPSRC) under the auspices of Collaborative Computational Project 12 (CCP12).

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow, G1 1XJ, UK

    Nishanth Dongari, Yonghao Zhang & Jason M. Reese

  2. STFC Daresbury Laboratory, Centre for Microfluidics and Microsystems Modelling, Warrington, WA4 4AD, UK

    Nishanth Dongari, Robert W. Barber & David R. Emerson

  3. Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113, Sofia, Bulgaria

    Stefan K. Stefanov

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  1. Nishanth Dongari
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  2. Robert W. Barber
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  3. David R. Emerson
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  4. Stefan K. Stefanov
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  5. Yonghao Zhang
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  6. Jason M. Reese
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Correspondence to Nishanth Dongari.

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Dongari, N., Barber, R.W., Emerson, D.R. et al. The effect of Knudsen layers on rarefied cylindrical Couette gas flows. Microfluid Nanofluid 14, 31–43 (2013). https://doi.org/10.1007/s10404-012-1019-2

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  • DOI: https://doi.org/10.1007/s10404-012-1019-2

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