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Slow rotation of a sphere in a confined volume of a dilute gas

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Abstract

The axially symmetric motion of a gas in a volume confined between an external immobile surface of rotation and a coaxial surface of a rotating sphere is considered. A solution is obtained by the moment method based on the Boltzmann equation with a collision integral of Maxwellian molecules. The gas-velocity distribution and an expression for the friction torque exerted on the sphere are obtained for arbitrary Knudsen numbers and for an arbitrary shape of the outer surface. The proportionality of the gas slip velocity over the surface of the sphere to the friction strain is shown. The friction torque is investigated for specific shapes of the outer surface. The motion of a gas filling the space between concentric spheres, each of which rotates about an arbitrary axis, is treated. In the limiting case of small Knudsen numbers the expressions obtained are compared with the corresponding results for a continuous medium.

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Literature cited

  1. M. N. Kogan, Rarefied Gasdynamics [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  2. L. Lees and L. Chung-yen, “Kinetic theory description of conductive heat transfer from a fine wire,” Phys. Fluids,5, No. 10 (1962).

  3. F. P. Warren, “Drag on a small sphere moving through a gas,” Phys. Fluids,18, No. 9 (1975).

  4. V. S. Galkin, “Cylindrical Couette flow of a rarefied gas,” Inzh. Zh.,5, No. 3 (1965).

  5. I. N. Ivchenko and Yu. I. Yalamov, “Evaporation and condensation of spherical drops at arbitrary Knudsen numbers,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3 (1974).

  6. L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Addison-Wesley (1939).

  7. V. N. Konstantinesku, Gas Lubrication [in Russian], Mashinostroenie, Moscow (1965).

    Google Scholar 

  8. G. B. Jeffery, “On the steady rotation of a solid of revolution in a viscous fluid,” Proc. Lond. Math. Soc., Ser. 2,14, 327 (1915).

    Google Scholar 

  9. H. Brenner and R. M. Sonshine, “Slow viscous rotation of a sphere in a circular cylinder,” Quart. J. Mech. Appl. Math.,17, Pt. 1 (1964).

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Authors and Affiliations

  1. Moscow

    L. P. Smirnov & V. V. Chekalov

Authors
  1. L. P. Smirnov
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  2. V. V. Chekalov
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Additional information

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 117–124, July–August, 1978.

The authors are grateful to the participants of the seminars guided by G. I. Petrov and A. M. Golovnyi for discussions concerning this work.

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Smirnov, L.P., Chekalov, V.V. Slow rotation of a sphere in a confined volume of a dilute gas. Fluid Dyn 13, 580–586 (1978). https://doi.org/10.1007/BF01055109

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  • DOI: https://doi.org/10.1007/BF01055109

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