TO THE THEORY OF HYDRAULIC JUMPS IN FILM FLOWS ON ORDINARY AND SUPERHYDROPHOBIC SURFACES

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The paper analyzes the asymptotic formulations of the problems of thin-film flow structure on ordinary and superhydrophobic surfaces (SHS) with a given localized liquid mass supply into the film with the formation of "hydraulic jumps", i.e., sharp jumps in the film thickness. The analysis is restricted to the case of laminar flows without surface waves. The similarity parameters are obtained and the equations of the hydraulic approximation for viscous liquid film flows on a horizontal SHS in a gravity field are derived. A partial analogy is discussed with subsonic and supersonic flows of a compressible gas in the presence of external forces, according to which hydraulic jumps in a film are analogous to shock waves in gases. However, in the general case, changes in the total momentum flux (calculated based on the average velocity) and in the tangential velocity component in the film should be taken into account in the conditions on the hydraulic jump. Refined relations are derived for normal and oblique hydraulic jumps, taking into account the above mentioned changes in total pressure and tangential velocity, which depend on the liquid "slip length" on the SHS. Approximate models are proposed for determining the location of hydraulic jumps in steady-state one-dimensional flows with plane and axial symmetry. The fundamental role of the boundary condition for the film thickness (or velocity) in the "subcritical" region behind the hydraulic jump is emphasized in calculating the position of the jump. Examples of numerical calculations of one-dimensional flows with hydraulic jumps on SHS are given. The limits of the parameter region of existence of one-dimensional stationary solutions with flat or cylindrical hydraulic jumps are discussed. Outside these limits, the jump surface may take a polygonal shape, corresponding to the appearance of a system of oblique hydraulic jumps.

作者简介

A. Ageev

M.V. Lomonosov Moscow State University, Research Institute of Mechanics

Email: aaiageev@mail.ru
Moscow, Russia

A. Osiptsov

M.V. Lomonosov Moscow State University, Research Institute of Mechanics

Email: osiptsov@imec.msu.ru
Moscow, Russia

K. Smirnov

M.V. Lomonosov Moscow State University, Research Institute of Mechanics

Moscow, Russia

参考

  1. Гилинский М.М., Лебедев М.Г., Якубов И.Р. Моделирование течений газа с ударными волнами. М.: Машиностроение, 1984.
  2. Bélanger J.B. Essai sur la Solution Numérique de Quelques Problèmes Relatifs au Mouvement Permanent des Eaux Courantes (“Essay on the Numerical Solution of Some Problems relative to Steady Flow of Water”); Carilian-Goeury: Paris, France, 1828.
  3. Boussinesq J.V. Essai sur la Théorie des Eaux Courantes, Mémoires présentés par divers savants à l’Académie des Sciences, Paris, France. V. 23, Série 3 (1), supplément 24, 1877. P. 1–680 (in French).
  4. Rayleigh L. On the theory of long waves and bores // Proc. R. Soc. Lond. 1914. A 90. P. 324.
  5. Gilmore F.R., Plesset M.S., and Crossley Jr. H.E. The analogy between hydraulic jumps in liquids and shock wave in gases // J. Appl. Phys. 1950. V. 21. P. 243–249. https://doi.org/10.1063/1.1699641
  6. Saint-Venant A.J.C. Barré de. Théorie du mouvement non permanent des eaux, avec application aux crues des rivières et a l’introduction de marées dans leurs lits // Comptes Rendus de l’Académie des Sciences. 1871. V. 73. Р. 147–154 and 237–240.
  7. Watson E. The spread of a liquid jet over a horizontal plane // J. Fluid Mech. 1964. V. 20. P. 481–499. https://doi.org/10.1017/S0022112064001367
  8. Bowles R.I., Smith F.T. The standing hydraulic jump: theory, computations and comparisons with experiments // J. Fluid Mech. 1992. V. 242. P. 145–168. https://doi.org/10.1017/S0022112092002313
  9. Bohr T., Putkaradze V., and Watanabe S. Averaging theory for the structure of hydraulic jumps and separation in laminar free-surface flows // Phys. Rev. Lett. 1997. V. 79. P. 1038. https://doi.org/10.1103/PhysRevLett.79.1038
  10. Watanabe S., Putkaradze V., and Bohr T. Integral methods for shallow free-surface flows with separation // J. Fluid Mech. 2003. V. 480. P. 233–265. https://doi.org/10.1017/S0022112003003744
  11. Bush J.W.M., Aristoff J.M. The influence of surface tension on the circular hydraulic jump // J. Fluid Mech. 2003. V. 489. P. 229–238. https://doi.org/10.1017/S0022112003005159
  12. Ellegaard C. et al. Creating corners in kitchen sink flows // Nature. 1998. V. 392. P. 767–768. https://doi.org/10.1038/33820
  13. Bush J.W.M., Aristoff J.M., and Hosoi A.E. An experimental investigation of the stability of the circular hydraulic jump // J. Fluid Mech. 2006. V. 558. P. 32–52. https://doi.org/10.1017/S0022112006009839
  14. Foglizzo T., Masset F., Guilet J., and Durand G. Shallow water analogue of the standing accretion shock instability: Experimental demonstration and a two-dimensional model // Phys. Rev. Lett. 2012. V. 108. P. 051103–051108. https://doi.org/10.1103/PhysRevLett.108.051103
  15. Kasimov A.R. A stationary circular hydraulic jump, the limits of its existence and its gasdynamic analogue // J. Fluid Mech. 2008. V. 601. P. 189–198. https://doi.org/10.1017/S0022112008000773
  16. Rojas N., Tirapegui E. Harmonic solutions for polygonal hydraulic jumps in thin fluid films // J. Fluid Mech. 2015. V. 780. P. 99–119. https://doi.org/10.1017/jfm.2015.458
  17. Rothstein J.P. Slip on superhydrophobic surfaces // Annu. Rev. Fluid Mech. 2010. V. 42. P. 89. https://doi.org/10.1146/annurev-fluid-121108-145558
  18. Агеев А.И., Осипцов А.Н. Макро- и микрогидродинамика течений вблизи супергидрофобных поверхностей // Коллоидный журнал. 2022. Т. 84. № 4. С. 380–395. https://doi.org/10.31857/S0023291222040024
  19. Celestini F., Kofman R., Noblin X., and Pellegrin M. Water jet rebounds on hydrophobic surfaces: a first step to jet micro-fluidics // Soft Matter. 2010. V. 6. P. 5872–5876. https://doi.org/10.1039/C0SM00794C
  20. Prince J.F., Maynes D., and Crockett J. Analysis of laminar jet impingement and hydraulic jump on a horizontal surface with slip // Phys. Fluids. 2012. V. 24. P. 102103–102118. https://doi.org/10.1063/1.4757659
  21. Prince J.F., Maynes D., and Crockett J. Jet impingement and the hydraulic jump on horizontal surfaces with anisotropic slip // Phys. Fluids. 2014. V. 26. P. 042104. https://doi.org/10.1063/1.4870650
  22. Maynes D., Johnson M., and Webb B.W. Free-surface liquid jet impingement on rib patterned superhydrophobic surfaces // Phys. Fluids. 2011. V. 22. P. 052104–052114. https://doi.org/10.1063/1.3593460
  23. Седов Л.И. Механика сплошной среды. Т. 1. М.: Наука, 1994. 528 с.
  24. Gavrilyuk S., Ivanova K., and Favrie N. Multi-dimensional shear shallow water flows: Problems and solutions // J. Comput. Phys. 2019. V. 366. P. 252–280. https://doi.org/10.1016/j.jcp.2018.04.011
  25. Tani I. Water jump in the boundary layer // J. Phys. Soc. Japan. 1949. V. 4. P. 212–215.
  26. Черный Г.Г. Газовая динамика. М.: Наука, 1988. 424 с.
  27. Стокер Дж. Волны на воде. М.: Изд-во иностр. лит-ра, 1959. 620 c.
  28. Кудрявцев А.Н., Михайлова У.В. Явление гистерезиса при взаимодействии косых гидравлических прыжков на мелкой воде // Теплофизика и аэромеханика. 2023. Т. 30. № 6. С. 1135–1145.

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