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Modeling of an axisymmetric shape of an equilibrium drop resting on a horizontal plane
- Authors: Yankovskii A.P.1
-
Affiliations:
- Khristianovich Institute of Theoretical and Applied Mechanics of the SB RAS
- Issue: Vol 88, No 4 (2024)
- Pages: 594-621
- Section: Articles
- URL: https://journals.rcsi.science/0032-8235/article/view/275959
- DOI: https://doi.org/10.31857/S0032823524040079
- EDN: https://elibrary.ru/WVWAMI
- ID: 275959
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Abstract
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.
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About the authors
A. P. Yankovskii
Khristianovich Institute of Theoretical and Applied Mechanics of the SB RAS
Author for correspondence.
Email: yankovsky_ap@itam.nsc.ru
Russian Federation, Novosibirsk
References
- 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)
- 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)
- 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.
- 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.
- 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.
- 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.
- Contact Angle, Wettability, and Adhesion / ed. by Gould R.F. Washington: Amer. Chem. Soc. Advances in Chem. Ser., 1964.
- Finn R. Equilibrium Capillary Surfaces. N.Y.: Springer, 1986 p.
- Rusakov A.I., Prokhorov V.A. Interfacial Tensometry. St. Petersburg: Chemistry, 1994. 398 p. (in Russian)
- 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)
- De Gennes P.G., Brochard-Wyart F., Quere D. Capillarity and Wetting Phenomena. Berlin: Springer, 2004.
- 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
- 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.
- 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.
- Carmo M.P. Differential Geometry of Curves and Surfaces. New Jersey: Prentice-Hall Inc., 1976.
- Novozhilov V.V. Theory of Thin Shells. St. Petersburg.: St. Petersburg Univ. Pyb., 2010. 380 p. (in Russian)
- Vlasov V.Z., Leontiev N.N. Beams, Slabs and Shells on an Elastic Base. Moscow: Fizmatgiz, 1960. 491 p. (in Russian)
- Nowacki W. Teoria sprężystości. Warszawa: PAN, 1970.
- Hall G., Watt J.M. Modern Numerical Methods for Ordinary Differential Equations. Oxford: Clarendon, 1976.
- 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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