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Condensation by homogeneous nucleation in the vapor phase

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Abbreviations

A :

cluster, nozzle cross section

a :

sound speed

C :

concentration

g :

condensate mass fraction

h :

Planck's constant

I :

moment of inertia, Eq. (12)

J :

nucleation rate, Eqs. (21), (27), (28), and (29)

k :

Boltzmann's constant

L :

heat of condensation

M :

Mach number

m :

molecular mass

m r :

mass of drop of radiusr

m :

mass flow

N :

number density of clusters

n :

number of molecules in cluster

O :

surface area

p :

pressure

Q :

partition function

Q rn :

configurational integral, Eq. (8)

q :

heat addition per unit mass

q rep :

“replacement factor”, e. g. Eqs. (18) and (19)

q rot :

rotational partition function, Eq. (11)

q tr :

translational partition function, Eq. (10)

\(\tilde q_{{\text{tr}}} \) :

alternate form ofq tr, Eq. (15)

r :

droplet radius

T :

absolute temperature

U :

potential energy

u :

How speed

V :

volume

v :

molecular volume

x :

nozzle coordinate in flow direction

α:

condensation coefficient

β:

collision rate, Eq. (22)

γ:

specific heat ratio

δ:

length related to surface tension correction, Eq. (23)

μ:

chemical potential

ν:

molecular frequency

ϱ:

density

τ:

molecular coordinate

*:

indicates critical size

0:

reference state

1:

monomer

c :

condensate

n :

cluster withn molecules

r :

cluster with radiusr

∞:

flat interface

Literatur

  1. Becker, R.: Theorie der Wärme. Berlin: Springer 1955.

    Google Scholar 

  2. Dunning, W. J., in: Nucleation (ed. A. C. Zettlemoyer). New York: Marcel Dekker 1969.

    Google Scholar 

  3. Einstein, A.: Ann. Phys.33, 1275 (1910).

    Google Scholar 

  4. Volmer, M., Weber, A.: Z. Phys. Chem.119, 277 (1926).

    Google Scholar 

  5. Volmer, M.: Kinetik der Phasenbildung. Dresden-Leipzig: Steinkopff 1939.

    Google Scholar 

  6. Frenkel, J.: Kinetic Theory of Liquids. New York: Oxford University Press 1946.

    Google Scholar 

  7. Kuhrt, F.: Z. Phys.131, 185, 205 (1952).

    Google Scholar 

  8. Mason, B. J.: The Physics of Clouds. London: Oxford University Press 1957.

    Google Scholar 

  9. Courtney, W. G.: ARS J.31, 751 (1961).

    Google Scholar 

  10. McDonald, J. E.: Am. J. Phys.30, 870 (1962);31, 31 (1963).

    Google Scholar 

  11. Dufour, L., Defay, R.: Thermodynamics of Clouds. New York: Academic Press Inc. 1963.

    Google Scholar 

  12. Hirth, J. P., Pound, G. M.: Progr. Maten Sci., Vol. 11 (ed. by B. Chalmers). Oxford: Pergamon 1963.

    Google Scholar 

  13. Feder, J., et al.: Adv. Phys. (Suppl. Phil. Mag.)15, 111 (1966).

    Google Scholar 

  14. Andres, R. P., in: Nucleation (ed. A. C. Zettlemoyer). New York: Marcel Dekker 1969.

    Google Scholar 

  15. Mayer, J. E., Mayer, M. G.: Statistical Mechanics. New York: John Wiley and Sons 1940.

    Google Scholar 

  16. Fisher, M.: Private communication (1970).

  17. Fisher, M.: Physics3, 255 (1967).

    Google Scholar 

  18. Lothe, J., Pound, G. M.: J. Chem. Phys.48, 1849 (1968).

    Google Scholar 

  19. Lothe, J., Pound, G. M.:ibid.36, 2080 (1962).

    Google Scholar 

  20. Lothe, J., Pound, G. M., in: Molecular Processes on Solid Surfaces, p. 407. (ed. E. Drauglis, R. D. Gretz, R. I. Jaffee, Series in Materials Science and Engineering). New York: McGraw Hill 1969.

    Google Scholar 

  21. Dunning, W. J., in: Colloques Internationaux du Centre National de la Recherche Scientifique, No. 152, p. 369, CNRS Paris 1965.

    Google Scholar 

  22. Reiss, H., Katz, J. L.: J. Chem. Phys.46, 2496 (1967).

    Google Scholar 

  23. Reiss, H., Katz, J. L., Cohen, E. R.:ibit.48, 5553 (1968).

    Google Scholar 

  24. Dunning, W. J.: Progr. Astron. Aeronaut.15, 739 (1964).

    Google Scholar 

  25. Parlange, J.-Y.: J. Chem. Phys.48, 776 (1968).

    Google Scholar 

  26. Miyazawa, Y., et al.: Private communication.

  27. Buckle, E. R.: Trans. Faraday Soc.65, 1267 (1969).

    Google Scholar 

  28. Farkas, L.: Z. Phys. Chem.125, 236 (1927).

    Google Scholar 

  29. Probstein, R. F.: J. Chem. Phys.19, 619 (1951).

    Google Scholar 

  30. Wakeshima, H.: J. Phys. Soc. Japan10, 141 (1955).

    Google Scholar 

  31. Courtney, W. G.: J. Chem. Phys.36, 2009 (1962).

    Google Scholar 

  32. Chakraverty, B. K., in: Colloques Internationaux du Centre National de la Recherche Scientifique, No. 152, p. 375, CNRS Paris 1965.

    Google Scholar 

  33. Kantrowitz, A.: J. Chem. Phys.19, 1097 (1951).

    Google Scholar 

  34. Wegener, P. P.: Phys. Rev.76, 883 (1949).

    Google Scholar 

  35. Andres, R. P., Boudart, M.: J. Chem. Phys.42, 2057 (1965).

    Google Scholar 

  36. Becker, R., Döring, W.: Ann. Phys.24, 719 (1935).

    Google Scholar 

  37. Zeldovich, Y. B.: Zh. Eksper. Teoret. Fiz.12, 525 (1942).

    Google Scholar 

  38. Barnard, A. J.: Proc. Roy. Soc. (London) A220, 132 (1953).

    Google Scholar 

  39. Tolman, R. C.: J. Chem. Phys.17, 333 (1949).

    Google Scholar 

  40. Ono, S., Kondo, S. in: Encyclopedia of Physics, Vol. X, p. 152 (ed. S. Flügge). Berlin-Göttin-en-Heidelberg: Springer 1960.

    Google Scholar 

  41. Kirkwood, J. G., Buff, F. P.: J. Chem. Phys.17, 338 (1949).

    Google Scholar 

  42. Parlange, J.-Y.:ibid.48, 169 (1968).

    Google Scholar 

  43. Oriani, R. A., Sundquist, B. E.:ibid.38, 2082 (1963).

    Google Scholar 

  44. Wegener, P. P., Parlange, J.-Y.: Recent Advances in Aerothermochemistry, Vol. 2, p. 607. Agard Conference Proceedings No. 12; 64, Rùe de Varenne, Paris 1967.

  45. Parlange, J.-Y.: J. Crystal Growth6, 311 (1970).

    Google Scholar 

  46. Thomson, W.: Proc. Roy. Soc. (Edinburgh)7, 63 (1870).

    Google Scholar 

  47. von Helmholtz, R.: Ann. Phys.27, 508 (1886).

    Google Scholar 

  48. Gibbs, J. W.: Trans. Conn. Acad.3, 343 (1875); also Collected Works. New York: Longmans, Green and Co. 1928.

    Google Scholar 

  49. Wilson, C. T. R.: Trans. Roy. Soc. (London)189, 265 (1897); Phil. Mag. A189, 281 (1897); B. Wiedener Ann.21 720 (1897).

    Google Scholar 

  50. Allard, E. F., Kassner, Jr., J. L.: J. Chem. Phys.42, 1401 (1965).

    Google Scholar 

  51. Pound, G. M.: Private communication (1969).

  52. Allen, L. B., Kassner, Jr., J. L.: J. Coll. Int. Sci.30, 81 (1969).

    Google Scholar 

  53. Das Gupta, N. N., Ghosh, S. K.: Revs. Modern Phys.18, 2 (1946).

    Google Scholar 

  54. Volmer, M., Flood, H.: Z. Phys. Chem. A170, 273 (1934).

    Google Scholar 

  55. Langsdorf, A.: Rev. Sci. Instr.10, 91 (1939).

    Google Scholar 

  56. Franck, J. P., Hertz, H. G.: Z. Physik143, 559 (1956).

    Google Scholar 

  57. Katz, J. L., Ostermier, B. J.: J. Chem. Phys.47, 478 (1967).

    Google Scholar 

  58. Katz, J. L.:ibid.52, 4733 (1970).

    Google Scholar 

  59. Wegener, P. P., Lundquist, G.: J. Appl. Phys.22, 233 (1951).

    Google Scholar 

  60. Oswatitsch, K.: Gasdynamik. Wien: Springer 1952.

    Google Scholar 

  61. Higuchi, W. I., O'Konski, C. T.: J. Colloid Sci.15, 14 (1960).

    Google Scholar 

  62. Levine, D., Friedlander, S. K.: Chem. Eng. Sci.13, 49 (1960).

    Google Scholar 

  63. Hidy, G. M., Friedlander, S. K.: Amer. Inst. Chem. Engineers J.10, 115 (1964).

    Google Scholar 

  64. Stodola, A.: Steam and Gas Turbines. New York: McGraw-Hill Book Co. 1927.

    Google Scholar 

  65. Prandtl, L., in: Atti del V Convegno Volta, Reale Accademia D'Italia, Roma 1935, 2nd Ed. 1940, p. 167.

  66. Oswatitsch, K.: Jahrb. Dtsch. Luftfahrtforsch.1, 703 (1941).

    Google Scholar 

  67. Oswatitsch, K.: Z. angew. Math. Mech.22, 1 (1942).

    Google Scholar 

  68. Stever, H. G., in: Fundamentals of Gas Dynamics, Vol. III, p. 526. New Jersey: Princeton University Press 1958.

    Google Scholar 

  69. Wegener, P. P., Mack, L. M., in: Adv. Appl. Mech., Vol. V, p. 307. New York: Academic Press 1958.

    Google Scholar 

  70. Gyarmathy, G., Meyer, H.: VDl-Forschungsheft 508. Düsseldorf: VDI-Verlag GMBH 1965.

    Google Scholar 

  71. Thomann, H.: Phys. Fluids9, 896 (1966).

    Google Scholar 

  72. Hill, P. G.: J. Fluid Mech.25, 593 (1966).

    Google Scholar 

  73. Daum, F. L., Gyarmathy, G.: AIAA J.6, 458 (1958).

    Google Scholar 

  74. Wegener, P. P., in: Gasdynamics, Chapt. 4, Vol. 1, Part I (ed. P. P. Wegener). New York: Marcel Dekker 1969.

    Google Scholar 

  75. Wegener, P. P., Pouring, A. A.: Phys. Fluids7, 352 (1964).

    Google Scholar 

  76. Stein, G. D., Wegener, P. P.: J. Chem. Phys.46, 3685 (1967).

    Google Scholar 

  77. Stein, G. D.:ibid.51, 938 (1969).

    Google Scholar 

  78. Nebrich, E., Mohrmann, H.: Z. Naturforsch.24b, 1226 (1969).

    Google Scholar 

  79. Binnie, A. M., Green, J. R.: Proc. Roy. Soc. A181, 134 (1943).

    Google Scholar 

  80. Clumpner, J. A., Wegener, P. P.: in preparation (1970).

  81. Duff, K. M., Hill, P. G., in: Proc. 1966 Heat Transfer and Fluid Mech. Inst., p. 268 (eds. M. A. Saad and J. A. Miller). Stanford. Calif.: Stanford University Press 1966.

    Google Scholar 

  82. Jaeger, H. L., Willson, E. J., Hill, P. G.: J. Chem. Phys.51, 5380 (1969).

    Google Scholar 

  83. Dawson, D. B., et al.:ibid.51, 5389 (1969).

    Google Scholar 

  84. Abraham, F. F.: Appl. Phys. Letters13, 208 (1968).

    Google Scholar 

  85. Abraham, F. F.: J. Appl. Phys.39, 5811 (1968).

    Google Scholar 

  86. McDonald, J. E.: J. Meteorology10, 416 (1953).

    Google Scholar 

  87. Powell, C. F.: Proc. Roy. Soc. (London) A119, 553 (1928).

    Google Scholar 

  88. Amelin, A. G.: Kolloidn. Zh.10, 169 (1948).

    Google Scholar 

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  1. Department of Engineering and Applied Science, Yale University, New Haven, Connecticut

    Peter P. Wegener & Jean-Yves Parlange

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Wegener, P.P., Parlange, JY. Condensation by homogeneous nucleation in the vapor phase. Naturwissenschaften 57, 525–533 (1970). https://doi.org/10.1007/BF00625319

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