Skip to main content
Log in

Formation of BI- and Polymodal Distributions and the Non-Ostwald Behavior of Disperse Systems

  • HEAT AND MASS TRANSFER IN DISPERSED AND POROUS MEDIA
  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

Consideration has been given to distinctive features of the influence of the chemical and phase composition of a dispersed phase, and also of external conditions on equilibrium size distributions of evaporating solution droplets containing a nonvolatile sparingly soluble component. Equilibrium radii of droplets containing a solid phase or a supersaturated solution have been described on the basis of Kelvin and Freundlich equations and Raoult’s law. Conditions have been shown under which the non-Ostwald behavior of the dispersed phase (mass transfer from large drops to small droplets) develops. Using the model distribution as an example, the possibility of the unimodal distribution transforming into a polymodal one has been demonstrated. A maximum separation of the fractions in the distribution is attained if the partial pressure of a volatile component exceeds the pressure of a vapor above a saturated solution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. N. A. Fuks, Evaporation and Droplet Growth in a Gaseous Medium [in Russian], AN SSSR, Moscow (1958).

    Google Scholar 

  2. G. Amelin, Theoretical Foundations of Formation of a Mist in the Chemical Industry [in Russian], GNTIKhL, Moscow–Leningrad (1951).

    Google Scholar 

  3. S. Sazhin, Droplets and Sprays, Springer, London (2014).

    Book  Google Scholar 

  4. T. A. Yakhno and V. G. Yakhno, Structural evolution of drying drops of biological fluids, Tech. Phys. The Russ. J. Appl. Phys., 54, No. 8, 1219−1227 (2009).

    Google Scholar 

  5. Yu. Yu. Tarasevich, Mechanisms and models of the dehydration self-organization in biological fluids, PhysicsUspekhi, 47, No. 7, 717−728 (2004).

    Article  Google Scholar 

  6. V. A. Nikitin, Methods of substances and organelles introduction in living cell for cell engineering technologies, Tsitologiyia, 49, No. 8, 631−641 (2007).

    Google Scholar 

  7. O. G. Penyazkov, V. I. Saverchenko, and S. P. Fisenko, Low-temperature synthesis of nanoparticles in the process of evaporation of femtoliter droplets of a solution at a low pressure, J. Eng. Phys. Thermophys., 87, No. 4, 796−801 (2014).

    Article  Google Scholar 

  8. L. V. Andreeva, A. S. Novoselova, P. V. Lebedev-Stepanov, D. A. Ivanov, A. V. Koshkin, A. N. Petrov, and M. V. Alfi mov, Crystallization of solutes from droplets. Technical Physics, Tech. Phys. The Russ. J. Appl. Phys., 52, No. 2, 164−172 (2007).

    Google Scholar 

  9. Yu. V. Pakhomova, V. I. Konovalov, and A. N. Pakhomov, Peculiarities of the mechanism and kinetics of drying of dispersion droplets (with the example of drying of distillery stillage), Vestn. Tambovsk. Gos. Univ., 17, No. 1, 70–82 (2011).

    Google Scholar 

  10. E. M. Littringer, R. Paus, A. Mescher, H. Schroettner, P. Walzel, and N. A. Urbanetz, The morphology of spray dried mannitol particles — The vital importance of droplet size, Powder Technol., 239, 162–174 (2013).

    Article  Google Scholar 

  11. V. Burlakov and A. Goriely, Thermodynamic limit for particle monodispersity: How narrow can a particle size distribution be? EPL (Europhysics Lett.), 119, No. 5, 50001-1−50001-7 (2017).

  12. W. Ostwald, Studien über die Bildung und Umwandlung fester Körper. 1. Abhandlung: Übersättigung und Überkaltung, Zeitschrift für Phys. Chemie, 22, No. 2, 289–330 (1897).

    Google Scholar 

  13. V. M. Burlakov, M. S. Bootharaju, T. M. D. Besong, O. M. Bakr, and A. Goriely, Reversing Ostwald Ripening: arXiv preprint arXiv:1412.6280 (2014).

  14. I. Sugimoto, Reversed Ostwald ripening, J. Soc. Photogr. Sci. Technol. Jpn., 46, No. 4, 306–312 (1983).

    Google Scholar 

  15. K.-H. Heinig, B. Schmidt, M. Strobel, and H. Bernas, Inverse Ostwald ripening and self-organization of nanoclusters due to ion irradiation, MRS Proc., 650, R9.6/O14.6 (2000).

    Article  Google Scholar 

  16. G. C. Rizza, M. Strobel, K.-H. Heinig, and H. Bernas, Ion irradiation of gold inclusions in SiO2: Experimental evidence for inverse Ostwald ripening, Nucl. Instrum. Methods Phys. Res. B, 178, 78–83 (2001).

    Article  Google Scholar 

  17. S. Lucas and P. Moskovkin, Simulation at high temperature of atomic deposition, islands coalescence, Ostwald and inverse Ostwald ripening with a general simple kinetic Monte Carlo code, Thin Solid Films, 518, No. 18, 5355–5361 (2010).

    Article  Google Scholar 

  18. I. Leizerson, S. G. Lipson, and A. V. Lyushnin, Wetting properties: When larger drops evaporate faster, Nature, 422, No. 6930, 395–396 (2003).

    Article  Google Scholar 

  19. N. M. Zadymova and G. A. Arshakyan, Inhibition of Ostwald ripening in heptane/water miniemulsions, Colloid J., 76, No. 1, 25−37 (2014).

    Article  Google Scholar 

  20. V. B. Fedoseev and E. N. Fedoseeva, States of a supersaturated solution in limited-size systems, JETP Lett., 97, No. 7, 408–412 (2013).

    Article  Google Scholar 

  21. E. K. Titaeva and V. B. Fedoseev, Specifi c features of crystallization of supersaturated solution in femtoliter volume systems, Crystallogr. Rep., 59, No. 3, 437–441 (2014).

    Article  Google Scholar 

  22. V. B. Fedoseev and M. V. Maksimov, Solution–crystal–solution oscillatory phase transitions in the KCl–NaCl–H2O system, JETP Lett., 101, No. 6, 390–393 (2015).

    Article  Google Scholar 

  23. V. B. Fedoseev, Solution–gas and solution–crystal oscillatory phase transitions in droplets of solutions with one crystallizing component, Nenlinein. Dinam., 13, No. 2, 195–206 (2017).

    Article  Google Scholar 

  24. V. B. Fedoseev, Theory of subdivisions and the size distribution of dispersed particles, Vestn. Nizhegorodsk. Gos. Univ. (NNGU), No. 1, 146–150 (2000).

  25. S. Ya. Frenkel’, Introduction to the Statistical Theory of Polymerization [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  26. S. P. Fisenko, A. A. Brin, and A. I. Petruchik, Evaporative cooling of water in a mechanical draft cooling tower, Int. J. Heat Mass Transf., 47, No. 1, 165−177 (2004).

    Article  Google Scholar 

  27. L. Zigan, I. Schmitz, A. Flügel, M. Wensing, and A. Leipertz, Structure of evaporating single- and multicomponent fuel sprays for 2nd generation gasoline direct injection, Fuel, 90, No. 1, 348–363 (2011).

    Article  Google Scholar 

  28. V. P. Skripov and V. P. Koverda, Spontaneous Crystallization of Supercooled Liquids [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  29. J. Bogovic, S. Stopic, and B. Friedrich, Nanosized metallic oxide produced by Ultrasonic Spray Pyrolysis, Proc. EMC, 1–12 (2011).

  30. M. P. Anisimov and E. G. Fominykh, Modern studies of nucleation: Experiment and semiempirical approaches, Russ. J. Phys. Chem. B, 4, No. 1, 125−134 (2010).

    Article  Google Scholar 

  31. M. P. Anisimov and P. K. Hopke, Nucleation rate surface topologies for binary systems, J. Phys. Chem. B, 105, No. 47, 11817–11822 (2001).

    Article  Google Scholar 

  32. R. Valiullin, D. Vargas-Kruså, and I. Furó, Liquid–liquid phase separation in micropores, Curr. Appl. Phys., 4, Nos. 2–4, 370–372 (2004).

    Article  Google Scholar 

  33. V. M. Burlakovand L. Kantorovich, Ostwald ripening of binary alloy particles, J. Chem. Phys., 134, No. 2, 24521 (2011).

    Article  Google Scholar 

  34. Yu. D. Tyapkin, E. I. Malienko, I. V. Gongadze, and S. M. Komarov, Rearrangement of regular distributions in the process of Ostwald coalescence of Fe−Be alloys, Fiz. Metal. Metalloved., 68, No. 4, 755–763 (1989).

    Google Scholar 

  35. Yu. S. Raguzina and E. N. Fedoseeva, Obtaining resorcinol-formaldehyde oligomer and polymer in dispersed particles, Abstracts of Papers XI All-Russia School-Conference of Young Scientists. Theoretical and Experimental Chemistry of Liquid–Phase Systems (Krestovskii Readings), Ivanovo (2017), p. 163.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. B. Fedoseev.

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 92, No. 5, pp. 2229–2238, September–October, 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fedoseev, V.B., Fedoseeva, E.N. Formation of BI- and Polymodal Distributions and the Non-Ostwald Behavior of Disperse Systems. J Eng Phys Thermophy 92, 1191–1200 (2019). https://doi.org/10.1007/s10891-019-02033-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-019-02033-2

Keywords

Navigation