Modeling of an axisymmetric shape of an equilibrium drop resting on a horizontal plane

Мұқаба

Дәйексөз келтіру

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Рұқсат жабық Тек жазылушылар үшін

Аннотация

The problem of calculating the equilibrium axisymmetric shape of a liquid drop resting on a non-deformable horizontal plane is formulated. For the first time, an equation for the balance of forces acting on a drop in the vertical direction has been obtained, which completes the formulation of the problem under consideration. A high-precision numerical method for solving the formulated nonlinear problem has been developed. The dependence of the wetting angles of drops on variation of the input data of the problem: the chemical composition of the drop, gas pressure, and the strength of additional weak interaction (for example, van der Waals or electrochemical origin) is studied. For drops of small diameters, the possibility of the existence of two solutions is shown, which correspond to significantly different contact angles: in the first solution, the contact angles are less than 90°, and in the second, they are greater than 90°, reaching values of 160° and more. The existence of two equilibrium forms of a small-diameter drop is confirmed by full-scale experiments. Equilibrium forms of droplets of large diameters can exist only in the presence of an additional weak repulsive force between the liquid and the supporting surface, having an intensity of the order of 10–7…10–5 Pa. In this case, for drops of large diameters, there is only one solution.

Толық мәтін

Рұқсат жабық

Авторлар туралы

A. Yankovskii

Khristianovich Institute of Theoretical and Applied Mechanics of the SB RAS

Хат алмасуға жауапты Автор.
Email: yankovsky_ap@itam.nsc.ru
Ресей, Novosibirsk

Әдебиет тізімі

  1. Voitik O.L., Delendik K.I., Kolyago N.V., Roshchin L.Yu. Factors influencing the wetting characteristics of parts of the steam chamber // J. of Engng. Phys.&Thermophys., 2020, vol. 93, no. 5, pp. 1126–1133. (in Russian)
  2. Matyukhin S.I., Frolenkov K.Yu. Shape of liquid drops placed on a solid horizontal surface // Condensed Matter&Interphase Boundaries, 2013, vol. 15, no. 3, pp. 292–304. (in Russian)
  3. Marchuk I.V., Cheverda V.V., Strizhak P.A., Kabov O.A. Determination of surface tension and contact angle by the axisymmetric bubble and droplet shape analysis // Thermophys. & Aeromech., 2015, vol. 22, no. 3, pp. 297–303.
  4. Bai M., Kazi H., Zhang X., Liu J., Hussain T. Robust hydrophobic surfaces from suspension HVOF thermal sprayed rare-earth oxide ceramics coatings // Article in Sci. Rep., 2018, vol. 8, no. 1, pp. 6973-1–6973-8.
  5. Xu P., Coyle T.W., Pershin L., Mostaghimi J. Fabrication of superhydrophobic ceramic coatings via solution precursor plasma spray under atmospheric and low-pressure conditions // J. Therm. Spray Tech., 2019, vol. 28, pp. 242–254.
  6. Gulyaev I.P., Kuzmin V.I., Kovalev O.B. Highly hydrophobic ceramic coatings produced by plasma spraying of powder materials // Thermophys.&Aeromech., 2020, vol. 27, no. 4, pp. 585–594.
  7. Contact Angle, Wettability, and Adhesion / ed. by Gould R.F. Washington: Amer. Chem. Soc. Advances in Chem. Ser., 1964.
  8. Finn R. Equilibrium Capillary Surfaces. N.Y.: Springer, 1986 p.
  9. Rusakov A.I., Prokhorov V.A. Interfacial Tensometry. St. Petersburg: Chemistry, 1994. 398 p. (in Russian)
  10. Saranin V.A. Equilibrium of Liquids and Its Stability. Simple Theory and Accessible Experiments. Moscow: Inst. for Comput. Res., 2002. pp. 73–76. (in Russian)
  11. De Gennes P.G., Brochard-Wyart F., Quere D. Capillarity and Wetting Phenomena. Berlin: Springer, 2004.
  12. Kupershtokh A.L., Lazebryi D.B. Contact angles in the presence of an electrical field // J. of Phys.: Conf. Ser., 2020, 1675, 012106, pp. 1–6. https://doi.org/10.1088/1742-6596/1675/1/012106
  13. Del Rio O.I., Neumann A.W. Axisymmetric drop shape analysis: computational methods for the measurement of interfacial properties from the shape and dimensions of pendant and sessile drops // J. of Colloid&Interface Sci., 1997, vol. 196, no. 2, pp. 136–147.
  14. Zholob S.A., Makievski A.V., Miller R., Fainerman V.B. Optimization of calculation methods for determination of surface tensions by drop profile analysis tensiometry // Advances in Colloid&Interface Sci., 2007, no. 134, 135, pp. 322–329.
  15. Carmo M.P. Differential Geometry of Curves and Surfaces. New Jersey: Prentice-Hall Inc., 1976.
  16. Novozhilov V.V. Theory of Thin Shells. St. Petersburg.: St. Petersburg Univ. Pyb., 2010. 380 p. (in Russian)
  17. Vlasov V.Z., Leontiev N.N. Beams, Slabs and Shells on an Elastic Base. Moscow: Fizmatgiz, 1960. 491 p. (in Russian)
  18. Nowacki W. Teoria sprężystości. Warszawa: PAN, 1970.
  19. Hall G., Watt J.M. Modern Numerical Methods for Ordinary Differential Equations. Oxford: Clarendon, 1976.
  20. Dekker K., Verwer J.G. Stability of Runge–Kutta Methods for Stiff Nonlinear Differential Equation. Amsterdam: North-Holland, 1984. 308 p.

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Әрекет
1. JATS XML
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2. Fig. 1. Meridional cross-section of an equilibrium axisymmetric droplet resting on a horizontal non-deformable substrate

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3. Fig. 2. The edge point and its vicinity in a drop and substrate (a), only in a drop (b) and only in the substrate (c) with an indication of the system of forces applied to this point

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4. Fig. 3. The shape of the drop meridian and its geometric characteristics

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5. Fig. 4. Meridional cross-section of a drop with a contact angle of less than 90° and the system of forces applied to it

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6. Fig. 5. Profile of a drop with a contact angle greater than 90° (a) and the lower part of this drop after applying the section method (b) indicating the system of forces applied to it

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7. Fig. 6. Dependence of the residual in the force balance equation (2.20) on the magnitude of excess pressure at the top of a water drop: a) for drops with a standard diameter of 1 and 2 mm; b) for drops with a standard diameter of 3 and 3.894 mm.

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8. Fig. 7. Calculated meridional cross-sections of water droplets of different standard diameters: a) first type of solution; b) second type of solution

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9. Fig. 8. Calculated meridional cross-sections of ethyl alcohol droplets of different standard diameters: a) first type of solution; b) second type of solution

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10. Fig. 9. Two equilibrium shapes of water droplets of the same reference diameter, resting on a polycarbonate substrate

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11. Fig. 10. Calculated meridional cross-sections of water droplets with a standard diameter in the presence of additional interaction between the liquid and the substrate

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12. Fig. 11. Calculated meridional cross-sections of water droplets of large standard diameters

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