Abstract
A review of the theoretical data accumulated for the last decade on the diffusion kinetics of the stage of homogeneous nucleation of liquid droplets and gas bubbles in multicomponent systems has been presented. In addition to the previously known results, the review contains new relations and discussions that represent the further development of own studies. Thermodynamic expressions that relate the composition of critical droplets and bubbles occurring at unstable equilibrium with metastable multicomponent systems to the sizes of new-phase particles and degrees of supersaturation in the systems have been discussed. The dynamics of the growth of individual multicomponent supercritical droplets and bubbles at the stage of nucleation has been described at arbitrary values of vapor supersaturation for droplets and gas solubility in solutions for bubbles. The kinetics of the nucleation stage has been considered for ensembles of droplets and bubbles within the framework of the mean-field description of supersaturations and the excluded-volume approach. A relation has been shown between the excluded-volume approach to the description of the nucleation stage and the Kolmogorov crystallization theory.
Similar content being viewed by others
REFERENCES
Colloid and Interface Chemistry for Nanotechnology, Kralchevsky, P., Miller, R., and Ravera, F., Eds., Boca Raton: CRC, 2016.
Liu, P.S. and Chen, G.F., Porous Materials: Processing and Applications, Amsterdam: Elsevier, 2014.
Dubrovskii, V.G., Nucleation Theory and Growth of Nanostructures, Berlin: Springer, 2014.
Kelton, K. and Greer, A.L., Nucleation in Condensed Matter: Applications in Materials and Biology, Amsterdam: Elsevier Science & Technology, 2010.
Nucleation: A Transition State to the Directed Assembly of Materials (themed collection)Faraday Discuss., 2015, vol. 179, p. 1.
Kashchiev, D., Nucleation: Basic Theory with Applications, Oxford: Butterworth-Heinemann, 2000.
Onuki, A., Phase Transition Dynamics, Cambridge: Cambridge Univ. Press, 2004.
Nucleation Theory and Applications, Schmelzer, J.W.P., Weinheim: Wiley-VCH, 2005.
Slezov, V.V., Kinetics of First-Order Phase Transitions, Berlin: Wiley-VCH, 2009.
Kalikmanov, V.I., Nucleation Theory,Lecture Notes in Physics, Dordrecht: Springer, 2013.
Ruckenstein, E. and Berim, G., Kinetic Theory of Nucleation, Boca Raton: CRC, Taylor & Francis Group, 2016.
Tunitskii, N.N., Zh. Fiz. Khim., 1941, vol. 15, p. 1061.
Wakeshima, H., J. Phys. Soc. Jpn., 1954, vol. 9, p. 400.
Wakeshima, H., J. Phys. Soc. Jpn., 1954, vol. 9, p. 407.
Kuni, F.M. and Grinin, A.P., Kolloidn. Zh., 1984, vol. 46, p. 23. Colloid Journal of the USSR, 1984, vol. 46, no.1, p. 17.
Kuni, F.M. and Grinin, A.P., Kolloidn. Zh., 1984, vol. 46, p. 460. Colloid Journal of the USSR, 1984, vol. 46, no.3, p. 412.
Kuni, F.M., Melikhov, A.A., and Kon’kov, P.A., in Problemy sovremennoi statisticheskoi fiziki (Problems of Current Statistical Physics), Kiev: Naukova Dumka, 1985, p. 11.
Slezov, V.V. and Schmelzer, J.W.P., in Nucleation Theory and Applications, Schmelzer, J.W.P., Röpke, G., and Priezzhev, V.B., Eds., 1999, Dubna: JINR Publ. House, p. 6.
Lifshits, I.M. and Slezov, P.V., Zh. Eksp. Teor. Fiz., 1958, vol. 35, p. 479.
Piskunov, V.N., Vopr. At. Nauki Tekh., Ser. Teor., 1984, no. 1, p. 24.
Piskunov, V.N., Dinamika aerozolei (Aerosol Dynamics), Moscow: FIZMATLIT, 2010.
Vasil’ev, A.N., Kazanskii, A.K., and Adzhemyan, L.Ts., Colloid J., 2008, vol. 70, p. 703.
Kuni, F.M., Kolloidn. Zh., 1984, vol. 46, p. 682. Colloid Journal of the USSR, 1984, vol. 46, no. 4, 602.
Kuni, F.M., Grinin, A.P., and Kopeikin, K.V., Vestn. Leningr. Univ., 1984, no. 16, p. 74.
Kuni, F.M., Kolloidn. Zh., 1985, vol. 47, p. 284. Colloid Journal of the USSR, 1985, vol. 47, no. 2, p. 238.
Kuni, F.M., Kolloidn. Zh., 1985, vol. 47, p. 498. Colloid Journal of the USSR, 1985, vol. 47, no. 3, p. 418.
Kuni, F.M., A.A. Melikhov, K.V. Kopeikin, Kolloidn. Zh., 1986, vol. 48, p. 270. Colloid Journal of the USSR, 1986, vol. 48, no. 2, p. 227.
Grinin, A.P. and Kuni, F.M., Kolloidn. Zh., 1990, vol. 52, p. 21. Colloid Journal of the USSR, 1990, vol. 52, no. 1, p. 15.
Kuni, F.M. and Grinin, A.P., Kolloidn. Zh., 1990, vol. 52, p. 54. Colloid Journal of the USSR, 1990, vol. 52, no. 1, p. 40.
Kuni, F.M. and Grinin, A.P., Kolloidn. Zh., 1990, vol. 52, p. 277. Colloid Journal of the USSR, 1990, vol. 52, no. 2, p. 229.
Grinin, A.P. and Kuni, F.M., Kolloidn. Zh., 1990, vol. 52, p. 351. Colloid Journal of the USSR, 1990, vol. 52, no. 2, p. 301.
Grinin, A.P., Kuni, F.M., and Feshchenko, N.P., Teor. Mat. Fiz., 1992, vol. 93, p. 138.
Kuni, F.M., in Problemy teoreticheskoi fiziki III (Problems of Theoretical Physics III), Leningrad: Leningr. Gos. Univ., 1988, p. 192.
Dubrovskii, V.G. and Nazarenko, M.V., J. Chem. Phys., 2010, vol. 132, 114507.
Dubrovskii, V.G. and Nazarenko, M.V., J. Chem. Phys., 2010, vol. 132, 114508.
Konobejewski, S., Z. Phys. Chem., 1934, vol. 171A, p. 25.
Konobeevskii, S.T., Izv. Akad. Nauk SSSR, Ser. Khim., 1937, no. 5, p. 1909.
Konobeevskii, S.T., Zh. Eksp. Teor. Fiz., 1943, vol. 13, p. 185.
Rusanov, A.I., Usp. Khim., 1964, vol. 33, p. 873. Russ. Chem. Rev., 1964, vol. 33, p. 385.
Rusanov, A.I., Fazovye ravnovesiya i poverkhnostnye yavleniya (Phase Equilibria and Surface Phenomena), Leningrad: Khimiya, 1967.
Ward, C.A., Tikuisis, P., and Venter, R.D., J. Appl. Phys., 1982, vol. 53, p. 6076.
Schmelzer, J. and Ulbricht, H., J. Colloid Interface Sci., 1987, vol. 117, p. 325.
Ulbricht, H., Schmelzer, J., Mahnke, R., and Schweitzer, F., Thermodynamics of Finite Systems and the Kinetics of First-Order Phase Transitions, Leipzig: Teubner, 1988.
Schmelzer, J.W.P. and Abyzov, A.S., AIP Adv., 2011, vol. 1, 042160.
Grossier, R. and Veesler, S., Cryst. Growth Des., 2009, vol. 9, p. 1917.
Shchekin, A.K., Shabaev, I.V., and Hellmuth, O., J. Chem. Phys., 2013, vol. 138, 054704.
Dubrovskii, V.G., Cryst. Growth Des., 2017, vol. 17, p. 2589.
Philippe, T., Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 2017, vol. 96, 032802.
Sakurai, D., Paul, S., Hsu, W.-L., Daiguji, H., and Takemura, F., J. Phys. Chem. B, 2019, vol. 123, p. 542.
Shchekin, A.K., Koga, K., and Volkov, N.A., J. Chem. Phys., 2019, vol. 151, 244903.
Pesthy, A.J., Flagan, R.C., and Seinfeld, J.H., J. Colloid Interface Sci., 1981, vol. 82, p. 465.
Kurasov, V.B., Phys. A (Amsterdam), 1996, vol. 226, p. 117.
Kurasov, V.B., Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 2001, vol. 63, 056123.
Kuni, F.M., Kuchma, A.E., and Adzhemyan, L.Ts., Colloid J., 2009, vol. 71, p. 360.
Kuchma, A.E., Kuni, F.M., and Shchekin, A.K., Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 2009, vol. 80, 061125.
Kuchma, A.E., Kuni, F.M., and Shchekin, A.K., Vestn. S.-Peterb. Gos. Univ., Ser. 4, 2009, p. 320.
Kuchma, A.E., Markov, M.N., and Shchekin, A.K., Phys. A (Amsterdam), 2014, vol. 402, p. 255.
Kuchma, A.E., Shchekin, A.K., and Markov, M.N., Colloid J., 2014, vol. 76, p. 701.
Kuchma, A.E., Shchekin, A.K., and Markov, M.N., Colloids Surf. A, 2015, vol. 483, p. 307.
Kuchma, A.E., Shchekin, A.K., and Bulgakov, M.Yu., Phys. A (Amsterdam), 2017, vol. 468, p. 228.
Kuchma, A.E., Shchekin, A.K., Martyukova, D.S., and Savin, A.V., Fluid Phase Equilib., 2018, vol. 455, p. 63.
Vehkamäki, H., Classical Nucleation Theory in Multicomponent Systems, Berlin–Heidelberg: Springer, 2006.
Reiss, H., J. Chem. Phys., 1950, vol. 18, p. 840.
Hirschfelder, J.O., J. Chem. Phys., 1974, vol. 35, p. 2690.
Mirabel, P. and Katz, J.L., J. Chem. Phys., 1974, vol. 60, p. 1138.
Stauffer, D., J. Aerosol Sci., 1976, vol. 7, p. 319.
Trinkaus, H., Phys. Rev. B, 1983, vol. 27, p. 7372.
Shi, G. and Seinfeld, J.H., J. Chem. Phys., 1990, vol. 93, p. 9033.
Wu, D.T., J. Chem. Phys., 1993, vol. 99, p. 1990.
Oxtoby, D.W. and Kashchiev, D., J. Chem. Phys., 1994, vol. 100, p. 7665.
McGraw, R., J. Chem. Phys., 1995, vol. 102, p. 2098.
Viisanen, Y., Kulmala, M., and Laaksonen, A., J. Chem. Phys., 1997, vol. 107, p. 920.
Wyslouzil, B.E. and Wilemski, G., J. Chem. Phys., 1996, vol. 105, p. 1090.
Li, J.-S., Nishioka, K., and Maksimov, I.L., Phys. Rev. B, 1998, vol. 58, p. 7580.
Kožíšek, Z. and Demo, P., J. Cryst. Growth, 1998, vol. 194, p. 239.
Wilemski, G., J. Chem. Phys., 1999, vol. 110, p. 6451.
Peeters, P., Hrubý, J., and Van Dongen, M.E.H., J. Phys. Chem. B, 2001, vol. 105, p. 11763.
Chen, B., Siepmann, J.I., and Klein, M.L., J. Am. Chem. Soc., 2003, vol. 125, p. 3113.
Fisenko, S.P. and Wilemski, G., Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 2004, vol. 70, 056119.
Kathmann, S.M., Schenter, G.K., and Garrett, B.C., J. Chem. Phys., 2004, vol. 120, p. 9133.
Kurasov, V., Phys. A (Amsterdam), 2005, vol. 353, p. 159.
Kurasov, V., arXiv preprint. 2007. arXiv:0711.4559.
McGraw, R. and Zhang, R., J. Chem. Phys., 2008, vol. 128, 064508.
Kalikmanov, V.I., Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 2010, vol. 81, 050601.
Van Putten, D.S., Sidin, R.S.R., and Hagmeijer, R., J. Chem. Phys., 2010, vol. 132, 184511.
Alekseechkin, N.V., J. Chem. Phys., 2015, vol. 143, 054502.
Wyslouzil, B.E. and Wolk, J., J. Chem. Phys., 2016, vol. 145, 211702.
Kuni, F.M. and Melikhov, A.A., Teor. Mat. Fiz., 1989, vol. 81, p. 247.
Kuni, F.M., Melikhov, A.A., Novozhilova, T.Yu., and Terent’ev, I.A., Teor. Mat. Fiz., 1990, vol. 83, p. 274.
Melikhov, A.A., Kurasov, V.B., Dzhikaev, Yu.Sh., and Kuni, F.M., Zh. Tekh. Fiz., 1991, vol. 61, no. 1, p. 27.
Dzhikaev, Yu.Sh., Zh. Tekh. Fiz., 1992, vol. 62, no. 7, p. 60.
Dzhikaev, Yu.Sh., Zh. Tekh. Fiz., 1992, vol. 62, no. 7, p. 69.
Djikaev, Y.S., Grinin, A.P., and Kuni, F.M., Phys. A (Amsterdam), 2002, vol. 305, p. 387.
Djikaev, Y.S., J. Chem. Phys., 2002, vol. 116, p. 9865.
Kusaka, I., Talreja, M., and Tomasko, D.L., AIChE J., 2013, vol. 59, p. 3042.
Shardt, N. and Elliott, J.A.W., J. Phys. Chem. A, 2016, vol. 120, p. 2194.
Shardt, N. and Elliott, J.A.W., Langmuir, 2017, vol. 33, p. 11077.
Shardt, N. and Elliott, J.A.W., J. Phys. Chem. B, 2018, vol. 122, p. 2434.
Slezov, V.V. and Schmelzer, J.W.P., Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 2002, vol. 65, 031506.
Rusanov, A.I., Lektsii po termodinamike poverkhnostei (Lectures on Surface Thermodynamics), St. Petersburg: Lan’, 2013.
Kuchma, A.E., Shchekin, A.K., and Martyukova, D.S., J. Chem. Phys., 2018, vol. 148, 234103.
Kuchma, A.E. and Shchekin, A.K., J. Chem. Phys., 2019, vol. 150, 054104.
Kulmala, M., Vesala, T., and Wagner, P.E., Proc. R. Soc. London A, 1993, vol. 441, p. 589.
Vesala, T. and Kulmala, M., Phys. A (Amsterdam), 1993, vol. 192, p. 107.
Vesala, T., Kulmala, M., Rudolf, R., Vrtala, A., and Wagner, P.E., J. Aerosol Sci., 1997, vol. 28, p. 565.
Mattila, T., Kulmala, M., and Vesala, T., J. Aerosol Sci., 1997, vol. 28, p. 553.
Kuchma, A.E., Shchekin, A.K., and Kuni, F.M., Colloid J., 2011, vol. 73, p. 224.
Kuchma, A.E., Shchekin, A.K., and Kuni, F.M., Phys. A (Amsterdam), 2011, vol. 390, p. 3308.
Kuchma, A.E., Martyukova, D.S., Lezova, A.A., and Shchekin, A.K., Colloids Surf. A, 2013, vol. 432, p. 147.
Kuchma, A.E., Shchekin, A.K., Lezova, A.A., and Martyukova, D.S., Colloid J., 2014, vol. 76, p. 576.
Kuchma, A.E., Shchekin, A.K., Martyukova, D.S., and Lezova, A.A., Colloid J., 2016, vol. 78, p. 340.
Martyukova, D.S., Shchekin, A.K., Kuchma, A.E., and Lezova, A.A., Colloid J., 2016, vol. 78, p. 353.
Kuchma, A.E. and Shchekin, A.K., Nanosyst.Phys. Chem. Mat., 2015, vol. 6, p. 479.
Brennen, C.E., Cavitation and Bubble Dynamics, Oxford: Oxford Univ. Press, 1995.
Scriven, L.E., Chem. Eng. Sci., 1959, vol. 10, p. 1.
Scriven, L.E., Chem. Eng. Sci., 1962, vol. 17, p. 55.
Plesset, M.S. and Prosperetti, A., Annu. Rev. Fluid Mech., 1977, vol. 9, p. 145.
Lensky, N.G., Navon, O., and Lyakhovsky, V., J. Volcanol. Geotherm. Res., 2004, vol. 129, p. 7.
Chernov, A.A., Pil’nik, A.A., Davydov, M.N., Ermanyuk, V.E., and Pakhomov, M.A., Int. J. Heat Mass Transfer, 2018, vol. 123, p. 1101.
Chernov, A.A., Pil’nik, A.A., and Davydov, M.N., J. Phys.: Conf. Ser., 2019, vol. 1382, 012107.
Fuks, N.A., Isparenie i rost kapel' v gazoobraznoi srede (Drop Evaporation and Growth in Gaseous Medium), Moscow: Akad. Nauk SSSR, 1958.
Kuchma, A.E. and Shchekin, A.K., in Nucleation Theory and Applications, Schmelzer, J.W.P., Röpke, G., and Priezzhev, V.B., Eds., Dubna: JINR, 2011, p. 203.
Kuchma, A.E. and Shchekin, A.K., Colloid J., 2012, vol. 74, p. 215.
Shchekin, A.K., Kuni, F.M., and Lezova, A.A., Colloid J., 2011, vol. 73, p. 394.
Kuchma, A.E., Shchekin, A.K., and Martyukova, D.S., J. Aerosol Sci., 2016, vol. 102, p. 72.
Grinin, A.P., Kuni, F.M., and Gor, G.Yu., J. Mol. Liq., 2009, vol. 148, p. 32.
Grinin, A.P., Kuni, F.M., and Gor, G.Yu., Colloid J., 2009, vol. 71, p. 46.
Alekseechkin, N.V., J. Non-Cryst. Solids, 2011, vol. 357, p. 3159.
Petukhov, B.V., Phys. Solid State, 2012, vol. 54, p. 1289.
Sinha, I. and Mandal, R.K., J. Non-Cryst. Solids, 2011, vol. 357, p. 919.
Homberg, D., Patacchini, F.S., Sakamoto, K., and Zimmer, J., IMA J. Appl. Math., 2017, vol. 82, p. 763.
Kolmogorov, A.N., Bull. Acad. Sci. USSR,Ser. Mat., 1937, vol. 3, p. 355.
Johnson, W. and Mehl, R., Trans.AIME, 1939, vol. 135, p. 416.
Avrami, M., J. Chem. Phys., 1939, vol. 7, p. 1103.
Avrami, M., J. Chem. Phys., 1940, vol. 8, p. 212.
Avrami, M., J. Chem. Phys., 1941, vol. 9, p. 177.
Filipovich, V.N., Fiz. Khim. Stekla, 1981, vol. 7, p. 364.
Filipovich, V.N., Kalinina, A.M., Fokin, V.M., Shishkina, V.K., and Dmitriev, D.D., Fiz. Khim. Stekla, 1983, vol. 9, p. 58.
Funding
This work was supported by the Russian Foundation for Basic Research, project no. 19-03-00997.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflict of interest.
Additional information
Translated by A. Kirilin
Rights and permissions
About this article
Cite this article
Shchekin, A.K., Kuchma, A.E. The Kinetic Theory for the Stage of Homogeneous Nucleation of Multicomponent Droplets and Bubbles: New Results. Colloid J 82, 217–244 (2020). https://doi.org/10.1134/S1061933X20030102
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1061933X20030102