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Motion of a spherical particle in a rarefied gas. Part 2. Drag and thermal polarization

Published online by Cambridge University Press:  26 April 2006

S. A. Beresnev ,
V. G. Chernyak  and
G. A. Fomyagin
S. A. Beresnev
Affiliation:
Urals State University, Sverdlovsk, 620083. USSR
V. G. Chernyak
Affiliation:
Urals State University, Sverdlovsk, 620083. USSR
G. A. Fomyagin
Affiliation:
Urals State University, Sverdlovsk, 620083. USSR
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Abstract

Kinetic theory for the drag and thermal polarization of a spherical particle in a low-speed flow of a rarefied gas is presented. The problem is solved on the basis of the linearized kinetic equation (Shakhov 1974) with the correct Prandtl number, $Pr = \frac{2}{3}2$, for monatomic gas. The integral-moment method of solution for arbitrary values of the Knudsen number is employed. The possibility of arbitrary energy, and tangential and normal momentum accommodation of gas molecules on the particle surface is taken into account in the boundary condition. The particle–gas heat conductivity ratio Λ is assumed to be arbitrary.

Numerical results for the isothermal drag, radiometric force affecting a non-uniformly heated particle in a rarefied gas, and temperature drop between the ends of the particle diameter owing to its thermal polarization in a gas flow have been obtained. The analytical expressions approximating the numerical calculations for the whole range of Knudsen numbers are given. The results obtained are compared to the available theoretical and experimental data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 219 , October 1990 , pp. 405 - 421
Copyright
© 1990 Cambridge University Press

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References

Abramovitz, M.: 1953 Evaluation of the integral ∫0∞ e −u2−x/u du. J. Math. Phys. 32, 188–192.Google Scholar
Aoki, K. & Sone, Y., 1987 Temperature field induced around a sphere in a uniform flow of a rarefied gas. Phys. Fluids 30, 2286–2288.Google Scholar
Bakanov, S. P. & Vysotsky, V. V., 1980 Thermal polarization of bodies in a rarefied gas flow. Kolloidn. Zh. 44, 1156–1158.Google Scholar
Bakanov, S. P., Vysotsky, V. V. & Nekrasov, A. N., 1986 Thermal polarization of bodies in the gas current and thermophoresis of aerosols at small Knudsen numbers. Kolloidn. Zh. 48, 851–855.Google Scholar
Bakanov, S. P., Derjaguin, B. V. & Roldughin, V. I. 1979 Thermophoresis in gases. Usp. Phys. Nauk. 129, 255–278.Google Scholar
Bakanov, S. P., Vysotsky, V. V., Derjaguin, B. V., Roldughin, V. I.: 1983 Thermal polarization of bodies in the rarefied gas flow. J. Non-Equilibr. Thermodyn. 8, 75–84.Google Scholar
Basset, A.: 1961 Treatise on Hydrodynamics. Dover.
Batchelor, G. K.: 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Beresnev, S. A., Chernyak, V. G. & Suetin, P. E., 1987 Motion of a spherical particle in a rarefied gas. Part 1. A liquid particle in its saturated vapour. J. Fluid Mech. 176, 295–310.Google Scholar
Bhatnagar, P. L., Gross, E. P. & Krook, M., 1954 A model for collision processes in gases. 1. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511–525.Google Scholar
Brock, J. R.: 1980 The kinetics of ultrafine particles. In Aerosol Microphysics. 1. Particle Interaction (ed. W. H. Marlow), pp. 15–59. Springer.
Cercignani, C. & Pagani, C. D., 1968 Flow of a rarefied gas past an axisymmetric body. 1. General remarks. Phys. Fluids 11, 1395–1399.Google Scholar
Cercignani, C., Pagani, C. D. & Bassanini, P., 1968 Flow of a rarefied gas past an axisymmetric body. 2. Case of a sphere. Phys. Fluids 11, 1399–1403.Google Scholar
Derjaguin, B. V. & Bakanov, S. P., 1962 Theory of thermophoresis of large rigid aerosol particles. Dokl. Akad. Nauk SSSR 147, 139–142.Google Scholar
Epstein, P. S.: 1924 On resistance experienced by spheres in their motion through gases. Phys. Rev. 23, 710–733.Google Scholar
Kogan, M. N.: 1969 Rarefied Gas Dynamics. Plenum.
Landau, L. D. & Lifshitz, E. M., 1966 Fluid Mechanics. Pergamon.
Law, W. S. & Loyalka, S. K., 1986 Motion of a sphere in a rarefied gas. 2. Role of temperature variation in the Knudsen layer. Phys. Fluids 29, 3886–3888.Google Scholar
Lea, K. C. & Loyalka, S. K., 1982 Motion of a sphere in a rarefied gas. Phys. Fluids 25, 1550–1557.Google Scholar
Marchuk, G. I.: 1961 Methods of Calculations of Nuclear Reactors. Moscow: Gosatomizdat.
Mikhlin, S. G.: 1970 Variational Methods in Mathematical Physics. Moscow: Nauka.
Millikan, R. A.: 1923 The general law of fall of a small spherical body through a gas. Phys. Rev. 22, 1–23.Google Scholar
Prigogine, I.: 1955 Introduction to Thermodynamics of Irreversible Processes. Springfield.
Roldughin, V. I.: 1987 On the theory of the thermal polarization of bodies in a rarefied gas current. Kolloidn. Zh. 49, 45–53.Google Scholar
Shakhov, E. M.: 1974 Method of Rarefied Gas Flows Investigation. Moscow: Nauka.
Shen, S. F.: 1967 Parametric representations of gas–surface interaction data and the problem of slip-flow boundary conditions with arbitrary accommodation coefficients. Entropie 18, 138–145.Google Scholar
Schmitt, K. H.: 1961 Modellversuche zur Photophorese in Vakuum. Vakuum-Technik 10, 238–242.Google Scholar
Sone, Y. & Aoki, K., 1977 Forces on a spherical particle in a slightly rarefied gas. In Rarefied Gas Dynamics (ed. J. L. Potter), vol. 1, pp. 417–433. AIAA Progr. Astro. Aero.
Vestner, H. & Waldmann, L., 1977 Generalized hydrodynamics of thermal transpiration, thermal force and frictional force. Physica 86A, 303–336.Google Scholar
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