Stabilization of Dissolved Substance Concentration in Droplet Clusters


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Using a previously developed laboratory technique, a series of experiments was conducted to study the effect of increased concentrations of substances dissolved in water on the condensational growth and equilibrium parameters of droplets in levitating droplet clusters during their stabilization by the combined action of infrared heating and the dissolution of table salt in the water layer under the cluster. The experiments demonstrated that the equilibrium solution in cluster droplets can be reached even for dissolved substances that most strongly prevent equilibrium from being achieved. For the first time, experiments were conducted for mixtures of solutions of various substances. In some cases, a non-additive effect of the solution components on droplet evaporation and stabilization was observed. The results obtained demonstrate the complex interaction of some aqueous solutions in small droplets, highlighting the importance of employing alternative methods and technical means in experimental research.

droplet cluster, aqueous solutions, levitation, equilibrium.

DOI: http://doi.org/10.33257/PhChGD.26.4.1211


Volume 26, issue 4, 2025 year


Стабилизация концентрации растворенных веществ в капельных кластерах

С применением ранее разработанной лабораторной методики проведена серия экс-периментов по изучению влияния повышенной концентрации растворенных в воде веществ на конденсационный рост и равновесные параметры капель в левитирующих капельных кластерах при их стабилизации путем совместного действия инфракрасного нагрева и растворения поваренной соли в слое воды под кластером. Экспериментально показана возможность выхода на равновесную концентрацию примеси в каплях кластера даже для растворенных веществ, которые наиболее сильно препятствуют достижению равновесия. Впервые проведены эксперименты для смесей растворов различных веществ. В ряде случаев наблюдалось неаддитивное влияние компонентов растворов на испарение и стабилизацию капель. Полученные результаты демонстрируют сложное взаимодействие некоторых растворов в малых каплях воды, что указывает на важность использования альтернативных методов и технических средств экспериментальных исследований.

капельный кластер, водные растворы, левитация, равновесие.

DOI: http://doi.org/10.33257/PhChGD.26.4.1211


Volume 26, issue 4, 2025 year



1. Dombrovsky L. A., Levashov V. Yu., Shoval S., Bormashenko Ed., Progress in understanding of evaporation of droplets: Fundamentals and applications, Adv. Colloid Interface Sci., 2025, vol. 344, 103605. https://doi.org/10.1016/j.cis.2025.103605
2. Ziaee A., Albadarin A. B., Padrela L., Femmer T., O’Reilly E., Walker G., Spray drying of pharmaceuticals and biopharmaceuticals: Critical parameters and experimental process optimization approaches, Eur. J. Pharm. Sci., 2019, vol. 127, pp. 300–318. https://doi.org/10.1016/j.ejps.2018.10.026
3. O’Sullivan J. J., Norwood E. A., O’Mahony J. A., Kelly A. L., Atomisation technologies used in spray drying in the dairy industry: A review, J. Food Eng., 2019, vol. 243, pp. 57−69.
https://doi.org/10.1016/j.jfoodeng.2018.08.027
4. Baumann J. M., Adam M. S., Wood J. D., Engineering advances in spray drying for pharmaceuticals, Annu. Rev. Chem. Biomol. Eng., 2021, vol. 12, pp. 217–240.
https://doi.org/10.1146/annurev-chembioeng-091720-034106
5. Hardy D. A., Archer J., Lemaitre P., Vehring R., Reid J. P., Walker J. S., High time resolution measurements of droplet evaporation kinetics and particle crystallization, Phys. Chem. Chem. Phys., 2021, vol. 23, no. 34, pp. 18568–18579. https://doi.org/10.1039/D1CP02840E
6. Hardy D. A., Robinson J. F., Hildich T. G., Neal E., Lemaitre P., Walker J. S., Reid J. P., Accurate measurements and simulations of the evaporation and trajectories of individual solution droplets, J. Phys. Chem. B, 2023, vol. 127, no. 15, pp. 3416–3430. https://doi.org/10.1021/acs.jpcb.2c08909
7. Leung G. R., Saleeby S. M., Sokolowsky G. A., Freeman S.W., van den Heever S. C., Aerosol–cloud impacts on aerosol detrainment and rainout in shallow maritime tropical clouds, Atm. Chem. Phys., 2023, vol. 23, pp. 5263–5278. https://doi.org/10.5194/acp-23-5263-2023
8. Jiang Y., Yang Z., Xu X., Shen D., Jiang T., Xie B., Duan J., Wetting and deposition characteristics of air-assisted spray droplet on large broadleaved crop canopy, Front. Plant Sci., 2023, vol. 14, 1079703. https://doi.org/10.3389/fpls.2023.1079703
9. Aminpour Y., Dehghan D., Playán E., Maroufpoor E., Estimation of wind drift and evaporation losses of sprinkler irrigation systems using dimensional analysis, Agric. Water Manag., 2023, vol. 289, 108518. https://doi.org/10.1016/j.agwat.2023.108518
10. Spaska O. A., Daszykowski M., Bushuev Yu. G., Evaluation of evaporation fluxes for pesticides and low volatile hazardous materials based on evaporation kinetics of net liquids, ACS Omega, 2024, vol. 9, pp. 18617−18623. http://pubs.acs.org/journal/acsodf
11. Dombrovsky L. A., Fedorets A. A., Levashov V. Yu., Kryukov A. P., Bormashenko E., Nosonovsky M., Modeling evaporation of water droplets as applied to survival of airborne viruses, Atmosphere, 2020, vol. 11, no. 9, 965. https://doi.org/10.3390/atmos11090965
12. Hasan S., Sobolev K., Nosonovsky M., Evaporation of droplets capable of bearing viruses airborne and on hydrophobic surfaces, J. Appl. Phys., 2021, vol. 129, 024703.
https://doi.org/10.1063/5.0023501
13. Kaufman Y. J., Koren I., Remer L. A., Rosenfeld D., Rudich Y., The effect of smoke, dust, and pollution aerosol on shallow cloud development over the Atlantic Ocean, PNAS, 2005, vol. 102, no. 32, pp. 11207–11212. https://doi.org/10.1073/pnas.0505191102
14. Nguyen T. B., Lee P. B., Updyke K. M., Bones D. L., Laskin J., Laskim A., Nizkorodov S. A., Formation of nitrogen- and sulfur-containing light-absorbing compounds accelerated by evaporation of water from secondary organic aerosols, J. Geophys. Res.: Atmospheres 2012, vol. 117, no. D1, D01207. https://doi.org/10.1029/2011JD016944
15. Karset I. H. H., Gettelman A., Storelvmo T., Alterskjær K., Berntsen T. K., Exploring impacts of size-dependent evaporation and entrainment in a global model, J. Geophys. Res.: Atmospheres, 2020, vol. 125, no. 4, e2019JD031817. https://doi.org/10.1029/2019JD031817
16. Leung G. R., Saleeby S. M., Sokolowsky G. A., Freeman S.W., van den Heever S. C., Aerosol–cloud impacts on aerosol detrainment and rainout in shallow maritime tropical clouds, Atm. Chem. Phys., 2023, vol. 23, pp. 5263–5278. https://doi.org/10.5194/acp-23-5263-2023
17. Nasarov V. S., The moment method applying for modeling heterogeneous condensation and evaporation, Phys.-Chem. Kinetics in Gas Dynamics, 2021, vol. 22, no. 5, 949.
http://chemphys.edu.ru/issues/2021-22-5/articles/949
18. Kortsenstein N. M., Petrov L. V., Rudov A. V., Yastrebov A. K., Numerical simulation of vapor bulk condensation near the interphase surface under intensive evaporation conditions, Phys.-Chem. Kinetics in Gas Dynamics, 2023, vol. 24, no. 5, 1076. http://chemphys.edu.ru/issues/2023-24-5/articles/1076
19. Fedorets A. A., Kolmakov E. E., Medvedev D. N., Mayorov V. O., Dombrovsky L. A., Effect of dissolved substances on the size of water droplets in levitating droplet clusters, Fluid Dynamics, 2025, vol. 60, no. 3, 50. https://doi.org/10.1134/S001546282560097X
20. Fedorets A. A., Bormashenko E., Dombrovsky L. A., Nosonovsky M., Droplet сlusters: Nature-inspired biological reactors and aerosols, Philos. Trans. Royal Soc. A, 2019, vol. 377, no. 2150, 20190121. DOI: 10.1098/rsta.2019.0121
21. Fedorets A. A., Dombrovsky L. A., Bormashenko E., Nosonovsky M., Levitating Droplet Clusters, New York: Begell House, 2023. 196 pp. https://doi.org/10.1615/978-1-56700-532-5.0
22. Yarin A. L., Brenn G., Kastner O., Rensink D., Tropea C., Evaporation of acoustically levitated droplets, J. Fluid Mech., 1999, vol. 399, pp. 151–204. https://doi.org/10.1017/S0022112099006266
23. Combe N. A., Donaldson D. J., Water evaporation from acoustically levitated aqueous solution droplets, J. Phys. Chem. A, 2017, vol. 121, no. 38, pp. 7197–7204. https://doi.org/10.1021/acs.jpca.7b08050
24. Zang D., Yu Y., Chen Z., Li X., Wu H., Geng X., Acoustic levitation of liquid drops: Dynamics, manipulation and phase transition, Adv. Colloid Interface Sci., 2017, vol. 243, pp. 77–85.
https://doi.org/10.1016/j.cis.2017.03.003
25. Di W., Zhang Z., Li L., Lin K., Li J., Li X., Binks B. P., Chen X., Shape evolution and bubble formation of acoustically levitating drops, Phys. Rev. Fluids, 2018, vol. 3, 103606.
https://doi.org/10.1103/PhysRevFluids.3.103606
26. Maruyama Y., Hasegawa K., Evaporation and drying kinetics of water-NaCl droplets via acoustic levitation, RSC Adv., 2020, vol. 10, pp. 1870–1877. https://doi.org/10.1039/C9RA09395H
27. Yang Z., Yang S., He Y., Shi Z., Dong T., Evaporation issues of acoustically levitated fuel droplets, Ultrasonics Sonochem., 2023, vol. 98, 106480. https://doi.org/10.1016/j.ultsonch.2023.106480
28. Zeng H., Wakata Y., Chao X., Lia M., Sun C., On evaporation dynamics of an acoustically levitated multicomponent droplet: Evaporation-triggered phase transition and freezing, J. Colloid Interface Sci., 2023, vol. 648, pp.736–744. https://doi.org/10.1016/j.jcis.2023.06.012
29. Chen H., Hong Z., Zang D., New insight into suspended drops: When soft matter meets acoustic levitation, Droplet, 2024, vol. 3, No. 1, e95. https://doi.org/10.1002/dro2.95
30. Fedorets A. A., Shcherbakov D. V., Levashov V. Yu., Dombrovsky L. A., Self-stabilization of droplet clusters levitating over heated salt water, Int. J. Therm. Sci., 2022, vol. 182, 107822.
https://doi.org/10.1016/j.ijthermalsci.2022.107822
31. Fedorets A. A., Medvedev D. N., Levashov V. Yu., Dombrovsky L. A., Stabilization of levitating clusters containing saltwater droplets, Int. J. Therm. Sci., 2023, vol. 188, 108222.
https://doi.org/10.1016/j.ijthermalsci.2023.108222
32. Dombrovsky L. A., Fedorets A. A., Medvedev D. N., The use of infrared irradiation to stabilize levitating clusters of water droplets, Infrared Phys. Techn., 2016, vol. 75, pp. 124–132.
https://doi.org/10.1016/j.infrared.2015.12.020
33. Dombrovsky L. A., Fedorets A. A., Levashov V. Yu., Kryukov A. P., Bormashenko E., Nosonovsky M., Stable cluster of identical water droplets formed under the infrared irradiation: Experimental study and theoretical modeling, Int. J. Heat Mass Transf., 2020, vol. 161, 120255.
https://doi.org/10.1016/j.ijheatmasstransfer.2020.120255
34. Fedorets A. A., Kolmakov E. E., Dombrovsky L. A., Experimental study of the effect of water salinity on the parameters of an equilibrium droplet cluster levitating over a water layer, Front. Heat Mass Transf., 2024, vol. 22, no. 1, pp. 1–14. https://doi.org/10.32604/fhmt.2024.049335
35. Fedorets A. A., Dombrovsky L. A., Generation of levitating droplet clusters above the locally heated water surface: A thermal analysis of modified installation, Int. J. Heat Mass Transf., 2017, vol. 104, pp. 1268–1274. https://doi.org/10.1016/j.ijheatmasstransfer.2016.09.087
36. Hale G. M., Querry M. R., Optical constants of water in the 200 nm to 200 µm wavelength region, Appl. Optics, 1973, vol. 12, no. 3, pp. 555–563. https://doi.org/10.1364/AO.12.000555
37. Zolotarev V. M., Demin A. V., Optical constants of water over the broad 0.1Å÷1 m wavelength range, Opt. Spectrosc., 1977, vol. 43, pp. 271–277 [in Russian].
38. Van de Hulst H.C., Light Scattering by Small Particles, New York: Dover Publ., 1981. 496 pp.
39. Bohren C. F., Huffman D. R., Absorption and Scattering of Light by Small Particles, New York: Wiley, 1998. 530 pp.
40. Mishchenko M. I., Travis L. D., Gustav Mie and the evolving discipline of electromagnetic scattering by particles, Bull. Am. Meteorol. Soc., 2008, vol. 89, no. 12, pp. 1853–1862.
https://doi.org/10.1175/2008BAMS2632.1
41. Gouesbet G., Lock J. A., Gréhan G., Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: Localized approximations and localized beam models, a review, J. Quant. Spectrosc. Radiat. Transf., 2011, vol. 112, pp. 1–27.
https://doi.org/10.1016/j.jqsrt.2010.08.012
42. Hergert W., Wriedt T., The Mie Theory: Basics and Applications. Berlin: Springer, 2012. 273 pp.
43. Drolen B. L., Tien C. L., Independent and dependent scattering in packed-sphere systems, J. Thermophys. Heat Transfer, 1987, vol. 1, no. 1, pp. 63–68. https://doi.org/10.2514/3.8
44. Mishchenko M. I., Electromagnetic Scattering by Particles and Particle Groups: An Introduction, Cambridge (UK): Cambridge University Press, 2014. 450 pp.
45. Mishchenko M. I., “Independent” and “dependent” scattering by particles in a multi-particle group, OSA Continuum, 2018, vol. 1, no. 1, pp. 243–260. https://doi.org/10.1364/OSAC.1.000243
46. Fell C. J. D., Hutchison Y. P., Diffusion coefficients for sodium and potassium chlorides in water at elevated temperatures, J. Chem. Eng. Data, 1971, vol. 16, no. 4, pp. 427–429.
https://doi.org/10.1021/je60051a005
47. Hamann C. H., Hamnett A., Vielstich W., Electrochemistry. Second Edition. Weinheim (Germany): Wiley-VCH, 2007. 550 pp.
48. Fedorets A. A., Kolmakov E. E., Nasyrova A. V., Medvedev D. N., Mayorov V. O., Levashov V. Yu., Dombrovsky L. A., Experimental method for studying the effect of dissolved substances on the evaporation rate of water droplets suspended in air, Front. Heat Mass Transf., 2025, in press (published online 07 August 2025), https://doi.org/10.32604/fhmt.2025.068244