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RAS Chemistry & Material ScienceКоллоидный журнал Colloid Journal

  • ISSN (Print) 0023-2912
  • ISSN (Online) 3034-543X

CONVECTION IN A SMALL HEMISPHERICAL DROP OF BINARY SOLVENT: ANALYTICAL SOLUTION AND APPLICATIONS

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PII
S3034543X25040076-1
DOI
10.7868/S3034543X25040076
Publication type
Article
Status
Published
Authors
P.V. Lebedev-Stepanov
  • Affiliation:
Volume/ Edition
Volume 87 / Issue number 4
Pages
346-360
Abstract
A new analytical solution of the linearized Navier–Stokes equations and the diffusion equation is proposed that allows to relate the intensity of Marangoni flow to the surface tension gradient in a droplet of binary solvent and to study the associated mass transfer and self-organization of solvated solutes (nanoparticles, molecules). When deriving the equations, the smallness of the Reynolds number was assumed, which corresponds to the smallness of the drop size and the liquid flow velocity. Evaporation was assumed to be slow enough for the quasi-stationary approximation to be valid. The smallness of the Peclet number was also accepted, which corresponds to relatively small velocity of convective flow in relation to the velocity of diffusion transfer of the impurity. In this case, the Marangoni number can have a value in the range from 1 to several tens. The model was tested on water—ethanol and octanol—hydrogen peroxide systems. The streamlines of convective flows were visualized, and the conditions for their occurrence were considered.
Keywords
капля на горизонтальной подложке бинарный растворитель потоки Марангони конвекция диффузия испарение уравнения Навье—Стокса микрофлюидика ламинарный поток
Date of publication
19.05.2025
Year of publication
2025
Number of purchasers
0
Views
35

References

  1. 1. Hoath S.D. Fundamentals of Inkjet Printing. Wiley-VCH Verlag GmbH & Co.: Weinheim, Germany, 2016.
  2. 2. Lebedev–Stepanov P., Vlasov K. Simulation of self-assembly in an evaporating droplet of colloidal solution by dissipative particle dynamics // Coll. Surf. A Physicochem. Eng. Asp. 2013. V. 432. P. 132–138. https://doi.org/10.1016/j.colsurfa.2013.05.012
  3. 3. Kolegov K., Barash L. Applying droplets and films in evaporative lithography // Adv. Colloid Interface Sci. 2020. V. 285. P. 102271. https://doi.org/10.1016/j.cis.2020.102271
  4. 4. Layani M., Gruchko M., Milo O., Balberg I., Azulay D., Magdassi S. Transparent conductive coatings by printing coffee ring arrays obtained at room temperature // ACS Nano. 2009. V. 3. № 11. P. 3537–3542. https://doi.org/10.1021/m19012392
  5. 5. Kokornaczyk M.O., Bodrova N.B. Baumgartner S. Diagnostic tests based on pattern formation in drying body fluids – A mapping review // Colloids Surf. B Biointerfaces. 2021. V. 208. P. 112092. https://doi.org/10.1016/j.colsurfb.2021.112092
  6. 6. Lebedev–Stepanov P.V., Buzoveva M.E., Vlasov K.O., Potekhina, Yu. P. Morphological analysis of images of dried droplets of saliva for determination the degree of endogenous intoxication // J. Bioinform. Genom. 2018. V. 4. № 9. P. 1. https://doi.org/10.18454/jbg.2018.4.9.2
  7. 7. Barash L.Yu. Marangoni convection in an evaporating droplet: Analytical and numerical descriptions // Int. J. Heat Mass Transf. 2016. V. 102. P. 445–454. https://doi.org/10.1016/j.jheatmasstransfer.2016.06.042
  8. 8. Tarasevich Yu. Simple analytical model of capillary flow in an evaporating sessile drop // Phys. Rev. E 2005. V. 71. P. 027301 https://doi.org/10.1103/PhysRevE.71.027301
  9. 9. Diddens C., Li Y., Lohse D. Competing Marangoni and Rayleigh convection in evaporating binary droplets // J. Fluid Mech. 2021. V. 914. P. A23. https://doi.org/10.1017/jfm.2020.734
  10. 10. Gurrula P., Balusamy S., Banerjee S., Saliu K.C. A Review on the evaporation dynamics of sessile drops of binary mixtures: Challenges and opportunities // Fluid Dynamics & Materials Processing. 2021. V. 17. № 2. P. 253–284. https://doi.org/10.32604/fdmp.2021.014126
  11. 11. Sefiane K., Tadrisi L., Douglas M. Experimental study of evaporating Water-Erhanol mixture sessile drop: influence of concentration // Int. J. Heat Mass Transfer. 2003. V. 46. № 23. P. 4527–4534. https://doi.org/10.1016/S0017-9310 (03)00267-9
  12. 12. Cheng A.K., Soolaman D.M., Yu H.-Z. Evaporation of microdroplets of ethanol-water mixtures on gold surfaces modified with self-assembled monolayers // J. Phys. Chem. B. 2006. V. 110. № 23. P. 11267–11271. https://doi.org/10.1021/jp0572885
  13. 13. Christy J.R.E., Hamamoto Y., Sefiane K. Flow transition within an evaporating binary mixture sessile drop // Phys. Rev. Lett. 2011. V. 106. P. 205701. https://doi.org/10.1103/physrevlett.106.205701
  14. 14. Edwards A.M.J., Atkinson P.S., Cheung C.S., Liang H., Fairhurst D.J., Ouali F.F. Density-driven flows in evaporating binary liquid droplets // Phys. Rev. Lett. 2018. V. 121. P. 184501. https://doi.org/10.1103/PhysRevLett.121.184501
  15. 15. Deegan R.D. Capillary flow as the cause of ring stains from dried liquid drops // Nature. 1997. V. 389. P. 827–829. https://doi.org/10.1038/39827
  16. 16. Batchelor G.K. An introduction to fluid dynamics. Cambridge University Press. Cambridge. 2000.
  17. 17. Левин В.Г. Физико-химическая гидродинамика. Изд. 3-e, испр. и доп. М.-Ижевск: Институт компьютерных исследований. 2016.
  18. 18. Лебедев–Степанов П.В. Введение в самоорганизацию и самооборку ансамблей наночастиц. М.: НИЯУ МИФИ. 2015.
  19. 19. Lebedev–Stepanov P., Appendix in: ArXiv:2411.15853 [physics.flu-dyn].
  20. 20. Агрен С.В., Weber H.-J., Harris F.E. Mathematical methods for physicists: a comprehensive guide. Elsevier. 2012.
  21. 21. Barash L. Influence of gravitational forces and fluid flows on the shape of surfaces of a viscous fluid of capillary size // Phys. Rev. E. 2009. V. 79. P. 025302.
  22. 22. Ландау Л.Д., Лифшиц Е.М. Гидродинамика. М.: Наука. 1986.
  23. 23. Meylan W.M., Howard P.H. Estimating octanol—air partition coefficients with octanol—water partition coefficients and Henry’s law constants // Chemosphere 2005. V. 61. № 5. P. 640–644.
  24. 24. Lide D.R., CRC Handbook of Chemistry and Physics, 84th Edition. CRC Press, Boca Raton, FL. 2004.
  25. 25. Smallwood I. Handbook of organic solvent properties. Arnold Halsted Press. London. 1996.
  26. 26. Daubert T.E., Danner R.P. Physical and thermodynamic properties of pure chemicals data compilation. Washington, D.C.: Taylor and Francis. 1989.
  27. 27. Larranaga M.D., Lewis R.J.Sr., Lewis R.A. Hawley’s Condensed Chemical Dictionary 16th Edition. 2016. John Wiley & Sons, Inc. Hoboken.
  28. 28. ILO-WHO International Chemical Safety Cards (ICSCs) https://chemicalsafety.ilo.org/dyn/icsc/showcard.display?p_version=2&p_card_id=0164
  29. 29. Yaws C.L., Hopper J.R., Sheth S.D., Han M., Pike R.W. Solubility and Henry’s law constant for alcohols in water // Waste Management. 1997. V. 17 № 8. P. 541–547.
  30. 30. Betterton E.A. Gaseous Pollutants. 1992. New York, NY: John Wiley and Sons, Inc.
  31. 31. Иоффе Н.С. Физические величины. Справочник. М.: Энергоатомиздат. 1991.
  32. 32. Vazquez G., Alvarez E., Navaza J.M. Surface tension of alcohol+water from 20 to 50°C // J. Chem. Eng. Data. 1995. V. 40. № 3. P. 611–614. https://doi.org/10.1021/je00019a016
  33. 33. Goor G., et al., Hydrogen Peroxide. Ullmann’s Encyclopedia of Industrial Chemistry. 7th ed. 2017. New York, NY: John Wiley & Sons.
  34. 34. Zang D., Tarafdar S., Tarasevich Yu.Yu., Choudhury M.D., Dutta T. Evaporation of a droplet: from physics to applications // Physics Reports. 2019. V. 804. P. 1–56. https://doi.org/10.1016/J.PHYSREP.2019.01.008
  35. 35. Christy J.R.E., Sefane K., Munro E. A study of the velocity field during evaporation of sessile water and water/ethanol drops // Journal of Bionic Engineering. 2010. V. 7. P. 321–328. https://doi.org/10.1016/S1672-6529 (10)60263-6
  36. 36. Talbot E., Berson A., Yang L., Bain C. Internal flows and particle transport inside picoliter droplets of binary solvent mixtures. NIP & Digital Fabrication Conference. 2013.
  37. 37. Guruda P., Balusamy S., Banerjee S., Saliu K.C. A Review on the evaporation dynamics of sessile drops of binary mixtures: challenges and opportunities // Fluid Dynamics & Materials Processing. 2021. V. 17. № 2. P. 253–284. https://doi.org/10.32604/fdmp.2021.014126
  38. 38. Lebedev-Stepanov P., Savenko O. Evaporation of small sessile drop deposited on a horizontal solid surface: New exact solutions and approximations // Colloids Interfaces. 2024. V. 8. № 1. P. 2. https://doi.org/10.3390/colloids8010002
  39. 39. Caenko O.A., Лебедев-Степанов П.В. Квазистационарное испарение малой капли жидкости на плоской подложке: Аналитическое решение в биполярных координатах // Коллоидный журнал. 2022. Т. 84. № 3. С. 328. https://doi.org/10.31857/S0023291222030119
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