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The spherical-droplet problem of evaporation and condensation in a vapour-gas mixture

Published online by Cambridge University Press:  21 April 2006

Yoshimoto Onishi
Yoshimoto Onishi
Affiliation:
Department of Mechanical Engineering, University of Osaka Prefecture, Sakai 591, Japan
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Abstract

The behaviour of a binary mixture of a vapour and an inert gas around the spherical condensed-phase droplet is studied analytically using kinetic theory. By the singular-perturbation method, the linearized Boltzmann equation of B–G–K type is first solved for problems with spherical symmetry under the diffusive boundary condition when the Knudsen number of the problem is small. The macroscopic equations and the appropriate boundary conditions in the form of the temperature and partial-pressure jumps on the interface between the droplet and the gas phase, which enable us to treat the problems at the level of ordinary fluid dynamics, are derived together with the Knudsen-layer structure formed near the interface. Then the velocity, temperature and pressure fields around the droplet are explicitly obtained, as well as the mass, heat and energy flows from it. The results obtained are capable of describing the transition from the diffusion-control to the kinetic-control mechanism in the mass-transfer process. The negative-temperature-gradient phenomenon, a common phenomenon for pure-vapour cases (absence of inert gas), is also possible, manifesting itself more easily as the kinetic-control mechanism becomes prevalent and the critical condition for its existence is given. The present analysis could be applied to other problems with spherical symmetry as well.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 163 , February 1986 , pp. 171 - 194
Copyright
© 1986 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1970 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, pp. 1001–1003. U.S. Department of Commerce, National Bureau of Standards.
Cercignani, C. 1975 Theory and Application of the Boltzmann Equation, pp. 245–248. Scottish Academic Press.
Davies, C. N. 1978 Evaporation of airborne droplets. In Fundamentals of Aerosol Science (ed. D. T. Shaw), pp. 135–164. John Wiley.
Fuchs, N. A. 1959 Evaporation and Droplet Growth in Gaseous Media. Pergamon.
Hamel, B. B. 1965 Kinetic model for binary gas mixtures. Phys. Fluids 8, 418–425.Google Scholar
Kogan, M. N. 1969 Rarefied Gas Dynamics, pp. 501–502. Plenum Press.
Landau, L. D. & Lifshitz, E. M. 1969 Statistical Physics, 82. Pergamon.
Lees, L. 1959 A kinetic theory description of rarefied gas flows. Memorandum No. 51, Guggenheim Aero. Lab., C.I.T.
Lees, L. & Liu, C. Y. 1962 Kinetic-theory description of conductive heat transfer from a fine wire. Phys. Fluids 5, 1137–1148.Google Scholar
Matsushita, T. 1976 Kinetic analysis of the problem of evaporation and condensation. Phys. Fluids 19, 1712–1715.Google Scholar
Maxwell, J. C. 1965 The Scientific Papers of James Clerk Maxwell, vol. II, pp. 625–646. Dover.
Onishi, Y. 1977 Kinetic theory of evaporation and condensation of a vapor gas between concentric cylinders and spheres. J. Phys. Soc. Japan 42, 2023–2032.Google Scholar
Onishi, Y. 1979 Asymptotic theory for heat transfer problems of a slightly rarefied gas between coaxial cylinders - hydrodynamic equations and jump conditions. Trans. Japan Soc. Aero. Space Sci. 21, 16–30.Google Scholar
Onishi, Y. 1984 A two-surface problem of evaporation and condensation in a vapor-gas mixture. In Rarefied Gas Dynamics (ed. H. Oguchi), vol. II, pp. 875–884. University of Tokyo Press.
Pao, Y. P. 1971a Application of kinetic theory to the problem of evaporation and condensation. Phys. Fluids 14, 306–312.Google Scholar
Pao, Y. P. 1971b Temperature and density jumps in the kinetic theory of gases and vapors. Phys. Fluids 14, 1340–1346 [Erratum: 1973 Phys. Fluids 16, 15601.Google Scholar
Sampson, R. E. & Springer, G. S. 1969 Condensation on and evaporation from droplets by a moment method. J. Fluid Mech. 36, 577–584.Google Scholar
Shankar, P. N. 1970 A kinetic theory of steady condensation. J. Fluid Mech. 40, 385–400.Google Scholar
Siewert, C. E. & Thomas, J. R. 1973 Half-space problems in the kinetic theory of gases. Phys. Fluids 16, 1557–1559.Google Scholar
Sone, Y. 1964 Kinetic theory analysis of linearized Rayleigh problem. J. Phys. Soc. Japan 19, 1463–1473.Google Scholar
Sone, Y. 1969 Asymptotic theory of flow of rarefied gas over a smooth boundary I. In Rarefied Gas Dynamics (ed. L. Trilling & H. Y. Wachman), vol. I, pp. 243–253. Academic.
Sone, Y. 1971 Asymptotic theory of flow of rarefied gas over a smooth boundary II. In Rarefied Gas Dynamics (ed. D. Dini), vol. II, pp. 737–749, Editrice Tecnico Scientifica.
Sone, Y. 1984 Analytical studies in rarefied gas dynamics. In Rarefied Gas Dynamics (ed. H. Oguchi), vol. I, pp. 71–87. University of Tokyo Press.
Sone, Y. & Onishi, Y. 1973 Kinetic theory of evaporation and condensation. J. Phys. Soc. Japan 35, 1773–1776.Google Scholar
Sone, Y. & Onishi, Y. 1977 Heat transfer through a rarefied gas between coaxial circular cylinders with large temperature difference. In Rarefied Gas Dynamics (Prog. in Astronaut, and Aeronaut. vol. 51, (ed. J. L. Potter), part 1, pp. 295–310. AIAA.
Sone, Y. & Onishi, Y. 1978 Kinetic theory of evaporation and condensation — Hydrodynamic equation and slip boundary condition. J. Phys. Soc. Japan 44, 1981–1994. (See also Research Rep. No. 31, Section of Fluid Dynamics, Department of Aeronautical Engineering, Kyoto Univ. 1977, p. 1.)Google Scholar
Thomas, J. R., Chang, T. S. & Siewert, C. E. 1974 Reverse temperature gradient in the kinetic theory of evaporation. Phys. Rev. Letters 33, 680–682.Google Scholar
Vincenti, W. G. & Kruger, C. H. 1965 Introduction to Physical Gas Dynamics, Chap. X. John Wiley.