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Nonlinear dynamics of polydisperse assemblages of particles evolving in metastable media

Abstract

The article addresses theoretical approaches in describing the evolution of particulate assemblages in metastable liquids. The evolutionary model to deal with such processes and phenomena is put forward, which is based on the Fokker–Planck equation for the particle-size distribution function and on the mass/heat balance equation for the degree of metastability. The model is generalized in describing various phase transformation phenomena met in materials science and condensed matter physics. Two general analytical approaches in solving the generalized integro-differential model are considered with special attention to crystallization processes in supercooled and supersaturated liquids, evaporation of liquid droplets and dissolution of dispersed solids. These analytical theories are based on the saddle-point method in solving the integro-differential equation for the degree of system metastability and on the separation of variables in the kinetic and balance equations with subsequent summation or integration over different elementary solutions. The main focus here is to determine the analytical expressions for the particle-size distribution function and the degree of metastability dependent on the evolutionary kinetics of particulate assemblages in metastable media.

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References

  1. 1.

    A.C. Zettlemoyer, Nucleation (Dekker, New York, 1969)

  2. 2.

    J.W. Mullin, Crystallization (Butterworth, London, 1972)

  3. 3.

    V.V. Slezov, V.V. Sagalovich, Sov. Phys. Usp. 30, 23 (1987)

  4. 4.

    V.V. Slezov, Kinetics of first-order phase transitions (Wiley, Weinheim, 2009)

  5. 5.

    V.G. Dubrovskii, Nucleation theory and growth of nanostructures (Springer, Berlin, 2014)

  6. 6.

    D.V. Alexandrov, J. Phys. A: Math. Theor. 48, 035103 (2015).

  7. 7.

    D.V. Alexandrov, J. Phys. Chem. Solids 91, 48 (2016)

  8. 8.

    S.K. Friedlander, Smoke, dust and haze: fundamentals of aerosol behaviour (Wiley-Interscience, New York, 1977)

  9. 9.

    V.S. Solomatov, D.J. Stevenson, J. Geophys. Res. 98, 5407 (1993)

  10. 10.

    K.F. Kelton, A.L. Greer, Nucleation in condensed matter: applications in materials and biology (Elsevier, Amsterdam, 2008)

  11. 11.

    E.V. Makoveeva, D.V. Alexandrov, Phil. Trans. R. Soc. A 376, 20170327 (2018)

  12. 12.

    D.A. Barlow, J. Cryst. Growth 311, 2480 (2009)

  13. 13.

    D.V. Alexandrov, J. Cryst. Growth 457, 11 (2017)

  14. 14.

    D.V. Alexandrov, J. Phys.: Condens. Matter 28, 035102 (2016)

  15. 15.

    A.V. Alyab’eva, Yu.A. Buyevich, V.V. Mansurov, J. Phys. II (France) 4, 951 (1994)

  16. 16.

    E.M. Lifshitz, L.P. Pitaevskii, Physical kinetics (Pergamon, Oxford, 1981)

  17. 17.

    V.V. Mansurov, Math. Comput. Modell. 14, 819 (1990)

  18. 18.

    D.L. Aseev, D.V. Alexandrov, Int. J. Heat Mass Transfer 49, 4903 (2006)

  19. 19.

    D.L. Aseev, D.V. Alexandrov, Dokl. Phys. 51, 291 (2006)

  20. 20.

    V.A. Shneidman, Phys. Rev. E 82, 031603 (2010)

  21. 21.

    V.A. Shneidman, Phys. Rev. E 84, 031602 (2011)

  22. 22.

    YuA Buyevich, A.O. Ivanov, Physica A 193, 221 (1993)

  23. 23.

    A.O. Ivanov, AYu Zubarev, Physica A 251, 348 (1998)

  24. 24.

    C. Connaughton, A. Dutta, R. Rajesh, O. Zaboronski, EPL 117, 10002 (2017)

  25. 25.

    YuA Buyevich, V.V. Mansurov, J. Cryst. Growth 104, 861 (1990)

  26. 26.

    YuA Buyevich, I.A. Natalukha, Chem. Eng. Sci. 49, 3241 (1994)

  27. 27.

    D.V. Alexandrov, Phys. Lett. A 378, 1501 (2014)

  28. 28.

    D.V. Alexandrov, Philos. Mag. Lett. 96, 132 (2016)

  29. 29.

    D.A. Barlow, J. Cryst. Growth 470, 8 (2017)

  30. 30.

    D.V. Alexandrov, J. Phys. A: Math. Theor. 47, 125102 (2014)

  31. 31.

    D.V. Alexandrov, A.P. Malygin, J. Phys. A: Math. Theor. 46, 455101 (2013)

  32. 32.

    M.V. Fedoruk, Saddle-point method (Nauka, Moscow, 1977)

  33. 33.

    YuA Buyevich, D.V. Alexandrov, V.V. Mansurov, Macrokinetics of crystallization (Begell House, New York, 2001)

  34. 34.

    R.F. Strickland-Constable, Kinetics and mechanisms of crystallization (Academic Press, London, 1968)

  35. 35.

    E.B. Treivus, Kinetics of growth and dissolution of crystals (Leningrad State Univ, Leningrad, 1979)

  36. 36.

    P. Bennema, in: Industrial crystallization, edited by J.W. Mullin (Plenum Press, London, 1976)

  37. 37.

    D.V. Alexandrov, J. Phys. A: Math. Theor. 51, 075102 (2018)

  38. 38.

    D.V. Alexandrov, I.G. Nizovtseva, I.V. Alexandrova, Int. J. Heat Mass Transfer. 128, 46 (2019)

  39. 39.

    D.V. Alexandrov, I.V. Alexandrova, Philos. Trans. R. Soc. A 377, 20180209 (2019)

  40. 40.

    G.P. Yasnikov, J. Eng. Phys. 42, 163 (1982)

  41. 41.

    D.R. Dickinson, W.R. Marshall Jr, AIChE J. 14, 541 (1968)

  42. 42.

    G.A. Akselrud, A.D. Molchanov, Dissolution of solids (Izdatelstvo Khimia, Moscow, 1977)

  43. 43.

    J.-P. Hsu, M.-J. Lin, J. Colloid Interface Sci. 141, 60 (1991)

  44. 44.

    H. Wang, J.F. White, D. Sichen, Metall. Mater. Trans. B 49, 688 (2018)

  45. 45.

    B.K. Nikolaeshvili, V.M. Barabash, L.N. Braginskiy, N.N. Kulov, V.A. Malusov, Teor. Osnovy Khim. Tekhnol. 14, 349 (1980)

  46. 46.

    D.V. Alexandrov, I.G. Nizovtseva, Philos. Trans. R. Soc. A 377, 20180214 (2019)

  47. 47.

    E.V. Makoveeva, D.V. Alexandrov, Philos. Trans. R. Soc. A 377, 20180210 (2019)

  48. 48.

    D.V. Alexandrov, A.A. Ivanov, I.V. Alexandrova, Philos. Trans. R. Soc. A 376, 20170217 (2018)

  49. 49.

    M. Herrmann, P. Laurençot, B. Niethammer, C. R. Acad. Sci. Paris, Ser. I 347, 909 (2009)

  50. 50.

    M. Herrmann, B. Niethammer, J.J.L. Velázquez, J. Differ. Equ. 247, 2282 (2009)

  51. 51.

    A.A. Lushnikov, J. Phys. A: Math. Theor. 44, 335001 (2011)

  52. 52.

    V.A. Shneidman, Phys. Rev. E 88, 010401 (2013)

  53. 53.

    M.S. Veshchunov, V.I. Tarasov, Aerosol Sci. Technol. 48, 813 (2014)

  54. 54.

    D.V. Alexandrov, J. Phys. A: Math. Theor. 48, 245101 (2015)

  55. 55.

    O. Sotolongo-Costa, L.M. Gaggero-Sager, M.E. Mora-Ramos, Physica A 438, 74 (2015)

  56. 56.

    D.V. Alexandrov, Philos. Mag. Lett. 96, 355 (2015)

  57. 57.

    J. Orava, A.L. Greer, Acta Mater. 139, 226 (2017)

  58. 58.

    D.V. Alexandrov, A.A. Ivanov, I.V. Alexandrova, J. Phys. A: Math. Theor. 52, 015101 (2019)

  59. 59.

    D.V. Alexandrov, Chem. Eng. Sci. 117, 156 (2014)

  60. 60.

    D.V. Alexandrov, J. Phys. A: Math. Theor. 50, 345101 (2017)

  61. 61.

    YuA Buyevich, N.A. Korolyova, I.A. Natalukha, Int. J. Heat Mass Transfer 36, 2223 (1993)

  62. 62.

    YuA Buyevich, N.A. Korolyova, I.A. Natalukha, Int. J. Heat Mass Transfer 36, 2233 (1993)

  63. 63.

    A.A. Ivanov, I.V. Alexandrova, D.V. Alexandrov, Philos. Trans. R. Soc. A 377, 20180215 (2019)

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Correspondence to Dmitri V. Alexandrov.

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Alexandrov, D.V. Nonlinear dynamics of polydisperse assemblages of particles evolving in metastable media. Eur. Phys. J. Spec. Top. 229, 383–404 (2020). https://doi.org/10.1140/epjst/e2019-900049-4

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