Взаимодействие капли жидкости с супергидрофобной поверхностью

Взаимодействие капли жидкости с супергидрофобной поверхностью

Сомванши П. М., Чеверда В. В., Кабов O. A.
Сибирский журнал индустриальной математики, 26, 2(94), 142-154 (2023)
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УДК 532.5 
DOI: 10.33048/SIBJIM.2023.26.212

Аннотация:

Исследовано взаимодействие капли жидкости с медной поверхностью. Подложка принимается супергидрофобной с краевым углом смачивания 150°. Исходя из объёма капли числа Бонда и Вебера составляют приблизительно 0,23 и 1,6 соответственно. Температура поверхности и окружающего воздуха составляет 298 К, а температура капли жидкости на 5 К ниже. Моделирование сопряжённого теплообмена выполняется с использованием осесимметричной системы координат. Модель контактной линии Кистлера используется для определения динамического угла контакта капли при растекании. Исследуется изменение напряжения сдвига на подложке и теплового потока, индуцированного во время распространения капли в зависимости от времени.

Литература:
  1. Worthington A. M. On the forms assumed by drops of liquids falling vertically on a horizontal plate // Proc. Royal Soc. 1876. V. 25. P. 261–272.
     
  2. Yarin A. L. Drop impact dynamics: splashing, spreading, receding, bouncing // Ann. Rev. Fluid Mech. 2006. V. 38. P. 159–192.
     
  3. Josserand C., Thoroddsen S.T. Drop impact on a solid surface // Ann. Rev. Fluid Mech. 2016. V. 48. P. 365–391.
     
  4. Khandekar S., Sahu G., Muralidhar K., Gatapova E. Y., Kabov O. A., Hu R., Luo X., Zhao L. Cooling of high-power LEDs by liquid sprays: Challenges and prospects // Appl. Thermal Engrg. 2021. V. 184. Article 115640.
     
  5. Karchevsky A.L., Marchuk I.V., Kabov O.A. Calculation of the heat flux near the liquid-gas-solid contact line // Appl. Math. Model. 2016. V. 40, N 2. P. 1029–1037.
     
  6. Чеверда В.В., Марчук И.В., Карчевский А.Л., Орлик Е.В., Кабов О.А. Экспериментальное исследование теплообмена в стекающем по наклонной фольге ручейке // Теплофизика и аэромеханика. 2016. Т. 23, № 3. C. 431–436.
     
  7. Karchevsky A.L. Development of the heated thin foil technique for investigating nonstationary transfer processes // Interfacial Phenomena and Heat Transfer. 2018. V. 6, N 3. P. 179–185.
     
  8. Jaiswal A.K., Benard B., Garg V., Khandekar S. Evaporation dynamics of liquid bridge formed between two heated hydrophilic and hydrophobic flat surfaces // Interfacial Phenomena and Heat Transfer. 2022. V. 10, N 1. P. 1–14.
     
  9. Karchevsky A.L., Cheverda V.V., Marchuk I.V., Kabov O.A., Ponomarenko T.G., Sulyaeva V. S. Heat flux density evaluation in the region of contact line of drop on a sapphire surface using infrared thermography measurements // Microgravity Sci. Technology. 2021. V. 33. N 53; https://doi.org/10.1007/s12217-021-09892-6 
  10. Чеверда В.В., Карчевский А.Л., Марчук И.В., Кабов О.А. Плотность теплового потока в области контактной линии капли, лежащей на горизонтальной поверхности тонкой нагреваемой фольги // Теплофизика и аэромеханика. 2017. Т. 24, № 5(107). С. 825–828.
     
  11. Stephan P.C., Busse C. A. Analysis of the heat transfer coefficient of grooved heat pipe evaporator walls // Internat. J. Heat and Mass Transfer. 1992. V. 35. P. 383–391.
     
  12. Wang J-X., Guo W., Xiong K., Wang S-N. Review of aerospace-oriented spray cooling technology // Progress in Aerospace Sci. 2020. V. 116. Article 100635.
     
  13. Chen C., Tang Z. Investigation of the spray formation and breakup process in an open-end swirl injector // Sci. Progress. 2020. V. 103. P. 1–19.
     
  14. Mudawar I., Estes K. Optimizing and predicting CHF in spray cooling of a square surface // ASME J. Heat Transfer. 1996. V. 118. P. 672–679.
     
  15. Wang Y.Q., Liu M.H., Liu D., Xu K., Chen Y.L. Experimental study on the effects of spray inclination on water spray cooling performance in non-boiling regime // Experimental Thermal and Fluid Sci. 2010. V. 34. P. 933–942.
     
  16. Visaria M., Mudawar I. Theoretical and experimental study of the effects of spray inclination on two-phase spray cooling and critical heat flux // Internat. J. Heat and Mass Transfer. 2008. V. 51. P. 2398– 2410.
     
  17. Zhang Z., Jiang P.X., Ouyang X.L., Chen J.N., Christopher D.M. Experimental investigation of spray cooling on smooth and micro-structured surfaces // Internat. J. Heat and Mass Transfer. 2014. V. 76. P. 366–375.
     
  18. Liang G., Mudawar I. Review of drop impact on heated walls // Internat. J. Heat and Mass Transfer. 2017. V. 106. P. 103–126.
     
  19. Gholijani A., Schlawitschek C., Gambaryan-Roisman T., Stephan P. Heat transfer during drop impingement onto a hot wall: The influence of wall superheat, impact velocity, and drop diameter // Internat. J. Heat and Mass Transfer. 2020. V. 153. Article 119661.
     
  20. Liu L., Zhang Y., Cai G., Tsai P. A. High-speed dynamics and temperature variation during drop impact on a heated surface // Internat. J. Heat and Mass Transfer. 2022. V. 189. Article. 122710.
     
  21. Gatapova E.Y., Kirichenko E.O.,Bai B., Kabov O.A. Interaction of impacting water drop with a heated surface and breakup into microdrops // Interfacial Phenomena and Heat Transfer. 2018. V. 6, N 1. P. 75–88.
     
  22. Biolè D., Bertola V. Measuring fluid interfaces, corners, and angles from high-speed digital images of impacting drops // J. Flow Visualization and Image Processing. 2021. V. 28, N 1. P. 1–19.
     
  23. Yue P., Zhou C., Feng J.J. Sharp-interface limit of the Cahn—Hilliard model for moving contact lines // J. Fluid Mech. 2010. V. 645. P. 279–294.
     
  24. Yue P., Zhou C., Feng J.J. Spontaneous shrinkage of drops and mass conservation in phase-filed simulations // J. Comput. Phys. 2007. V. 223. P. 1–9.
     
  25. Somwanshi P.M., Muralidhar K., Khandekar S., Vyacheslav C. Mixing and wall heat transfer during vertical coalescence of drops placed over a superhydrophobic surface // Interfacial Phenomenon and Heat Transfer. 2020. V. 8, N 3. P. 207–224.
     
  26. Kistler S.F. Hydrodynamics of Wetting in Wettability. N. Y.: Marcel Dekker, 1993.
     
  27. Schremb M., Borchert S., Berberovic E., Jakirlic S., Roisman I. V., Tropea C. Computational modelling of flow and conjugate heat transfer of a drop impacting onto a cold wall // Internat. J. Heat and Mass Transfer. 2017. V. 109. P. 971–980.
     
  28. Jaiswal A.K., Khandekar S. Dynamics of a droplet impacting a sessile droplet on a superhydrophobic surface: role of boundary conditions during droplet placement // J. Flow Visualization and Image Processing. 2021. V. 28, N 4. P. 69–89.

Работа выполнена при финансовой поддержке Российского научного фонда (проект 21-79-10373; https://www.rscf.ru/project/21-79-10373/). Измерение краевого угла смачивания выполнено в рамках государственного задания Института теплофизики СО РАН

П. М. Сомванши
  1. Институт теплофизики им. С. С. Кутателадзе СО РАН, 
    просп. Акад. Лаврентьева, 1, г. Новосибирск 630090, Россия

E-mail: praveen.somwanshi@gmail.com

В. В. Чеверда
  1. Институт теплофизики им. С. С. Кутателадзе СО РАН, 
    просп. Акад. Лаврентьева, 1, г. Новосибирск 630090, Россия
  2. Новосибирский государственный университет, 
    ул. Пирогова, 1, г. Новосибирск 630090, Россия

E-mail: slava.cheverda@gmail.com

О. А. Кабов
  1. Институт теплофизики им. С. С. Кутателадзе СО РАН, 
    просп. Акад. Лаврентьева, 1, г. Новосибирск 630090, Россия
  2. Новосибирский государственный технический университет, 
    просп. К. Маркса, 20, г. Новосибирск 630073, Россия

Статья поступила 22.11.2022 г.
После доработки — 05.12.2022 г.
Принята к публикации 12.01.2023 г.

Abstract:

The impact of a liquid drop over a copper surface is investigated. The substrate is assumed to be superhydrophobic with a equilibrium contact angle of 150°. Based on the volume of the drop, the Bond and Weber numbers are 0.23 and 1.6, respectively. Surface temperature and ambient air is at 298 K, and the temperature of the liquid drop is 5 K lower than the ambient. Simulation of conjugate heat transfer is performed using the axi-symmetric coordinate system. The Kistler contact line model is used to predict the dynamic contact angle of the drop during spreading. In the present work, we investigate the temporal variation of the shear stress and the wall heat flux induced over a substrate during the drop spreading.

References:
  1. Worthington A. M. On the forms assumed by drops of liquids falling vertically on a horizontal plate. Proc. Royal Soc., 1876, Vol. 25, pp. 261–272.
     
  2. Yarin A. L. Drop impact dynamics: splashing, spreading, receding, bouncing. Ann. Rev. Fluid Mech., 2006, Vol. 38, pp. 159–192.
     
  3. Josserand C., Thoroddsen S.T. Drop impact on a solid surface. Ann. Rev. Fluid Mech., 2016, Vol. 48, pp. 365–391.
     
  4. Khandekar S., Sahu G., Muralidhar K., Gatapova E. Y., Kabov O. A., Hu R., Luo X., Zhao L. Cooling of high-power LEDs by liquid sprays: Challenges and prospects. Appl. Thermal Engrg., 2021, Vol. 184, article 115640.
     
  5. Karchevsky A.L., Marchuk I.V., Kabov O.A. Calculation of the heat flux near the liquid-gas-solid contact line. Appl. Math. Model., 2016, Vol. 40, No. 2, pp. 1029–1037.
     
  6. Cheverda V.V., Marchuk I.V., Karchevskii A.L., Orlik E.V., Kabov O.A. Eksperimental’noe issledovanie teploobmena v stekayushchem po naklonnoi fol’ge rucheike [Experimental study of heat transfer in a stream flowing down an inclined foil]. Teplofiz. Aeromekhanika, 2016, Vol. 23, No. 3, pp. 431–436 (in Russian).
     
  7. Karchevsky A.L. Development of the heated thin foil technique for investigating nonstationary transfer processes. Interfacial Phenomena and Heat Transfer, 2018, Vol. 6, No. 3, pp. 179–185.
     
  8. Jaiswal A.K., Benard B., Garg V., Khandekar S. Evaporation dynamics of liquid bridge formed between two heated hydrophilic and hydrophobic flat surfaces. Interfacial Phenomena and Heat Transfer, 2022, Vol. 10, No. 1, pp. 1–14.
     
  9. Karchevsky A.L., Cheverda V.V., Marchuk I.V., Kabov O.A., Ponomarenko T.G., Sulyaeva V. S. Heat flux density evaluation in the region of contact line of drop on a sapphire surface using infrared thermography measurements. Microgravity Sci. Technology, 2021, Vol. 33, No. 53; https://doi.org/10.1007/s12217-021-09892-6
     
  10. Cheverda V.V., Karchevskii A.L., Marchuk I.V., Kabov O.A. Plotnost’ teplovogo potoka v oblasti kontaktnoi linii kapli, lezhashchei na gorizontal’noi poverkhnosti tonkoi nagrevaemoi fol’gi [The heat flux density in the area of the contact line of a drop lying on the horizontal surface of a thin heated foil]. Teplofiz. Aeromekhanika, 2017, Vol. 24, No. 5(107), pp. 825–828 (in Russian).
     
  11. Stephan P.C., Busse C. A. Analysis of the heat transfer coefficient of grooved heat pipe evaporator walls. Internat. J. Heat and Mass Transfer, 1992, Vol. 35, pp. 383–391.
     
  12. Wang J-X., Guo W., Xiong K., Wang S-N. Review of aerospace-oriented spray cooling technology. Progress in Aerospace Sci., 2020, Vol. 116, article 100635.
     
  13. Chen C., Tang Z. Investigation of the spray formation and breakup process in an open-end swirl injector. Sci. Progress, 2020, Vol. 103, pp. 1–19.
     
  14. Mudawar I., Estes K. Optimizing and predicting CHF in spray cooling of a square surface. ASME J. Heat Transfer, 1996, Vol. 118, pp. 672–679.
     
  15. Wang Y.Q., Liu M.H., Liu D., Xu K., Chen Y.L. Experimental study on the effects of spray inclination on water spray cooling performance in non-boiling regime. Experimental Thermal and Fluid Sci., 2010, Vol. 34, pp. 933–942.
     
  16. Visaria M., Mudawar I. Theoretical and experimental study of the effects of spray inclination on two-phase spray cooling and critical heat flux. Internat. J. Heat and Mass Transfer, 2008, Vol. 51, pp. 2398– 2410.
     
  17. Zhang Z., Jiang P.X., Ouyang X.L., Chen J.N., Christopher D.M. Experimental investigation of spray cooling on smooth and micro-structured surfaces. Internat. J. Heat and Mass Transfer, 2014, Vol. 76, pp. 366–375.
     
  18. Liang G., Mudawar I. Review of drop impact on heated walls. Internat. J. Heat and Mass Transfer, 2017, Vol. 106, pp. 103–126.
     
  19. Gholijani A., Schlawitschek C., Gambaryan-Roisman T., Stephan P. Heat transfer during drop impingement onto a hot wall: The influence of wall superheat, impact velocity, and drop diameter. Internat. J. Heat and Mass Transfer, 2020, Vol. 153, article 119661.
     
  20. Liu L., Zhang Y., Cai G., Tsai P. A. High-speed dynamics and temperature variation during drop impact on a heated surface. Internat. J. Heat and Mass Transfer, 2022, Vol. 189, article. 122710.
     
  21. Gatapova E.Y., Kirichenko E.O.,Bai B., Kabov O.A. Interaction of impacting water drop with a heated surface and breakup into microdrops. Interfacial Phenomena and Heat Transfer, 2018, Vol. 6, No. 1, pp. 75–88.
     
  22. Biolè D., Bertola V. Measuring fluid interfaces, corners, and angles from high-speed digital images of impacting drops. J. Flow Visualization and Image Processing, 2021, Vol. 28, No. 1, pp. 1–19.
     
  23. Yue P., Zhou C., Feng J.J. Sharp-interface limit of the Cahn–Hilliard model for moving contact lines. J. Fluid Mech., 2010, Vol. 645, pp. 279–294.
     
  24. Yue P., Zhou C., Feng J.J. Spontaneous shrinkage of drops and mass conservation in phase-filed simulations. J. Comput. Phys., 2007, Vol. 223, pp. 1–9.Som
     
  25. Somwanshi P.M., Muralidhar K., Khandekar S., Vyacheslav C. Mixing and wall heat transfer during vertical coalescence of drops placed over a superhydrophobic surface. Interfacial Phenomenon and Heat Transfer, 2020, Vol. 8, No. 3, pp. 207–224.
     
  26. Kistler S.F. Hydrodynamics of Wetting in Wettability. N. Y.: Marcel Dekker, 1993.
     
  27. Schremb M., Borchert S., Berberovic E., Jakirlic S., Roisman I. V., Tropea C. Computational modelling of flow and conjugate heat transfer of a drop impacting onto a cold wall. Internat. J. Heat and Mass Transfer, 2017, Vol. 109, pp. 971–980.
     
  28. Jaiswal A.K., Khandekar S. Dynamics of a droplet impacting a sessile droplet on a superhydrophobic surface: role of boundary conditions during droplet placement. J. Flow Visualization and Image Processing, 2021, Vol. 28, No. 4, pp. 69–89.