Geodesic
An analytical and numerical study of capillary menisci
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 36 (2021) no. 3, pp. 80-93 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the current paper we consider the mathematical models of axisymmetric capillary menisci — sessile and pendant drops, rolled out meniscus, taking into account the size dependence of surface tension. Existence and uniqueness theorems for solutions of problems describing equilibrium meniscus surfaces are proved. Effective numerical methods have been developed and tested for the approximate calculation of meniscus profiles. A computer program is written in the Wolfram Language, with the help of which large-scale computational experiments were carried out to reveal the degree and nature of the influence of the model parameters on the equilibrium shape of each type of menisci.
Keywords: mathematical modeling, sessile drop, capillary meniscus, size dependence, mean curvature, numerical scheme
Mots-clés : pendant drop, surface tension, convergence. 
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     title = {An analytical and numerical study of capillary menisci},
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A. A. Sokurov. An analytical and numerical study of capillary menisci. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 36 (2021) no. 3, pp. 80-93. http://geodesic.mathdoc.fr/item/VKAM_2021_36_3_a6/

[1] Robert F., Equilibrium Capillary Surfaces, Springer-Verlag, New York, 1986, 245 pp. | Zbl

[2] Rusanov A. I., Prokhorov V. A., Interfacial Tensiometry, Elsevier, Amsterdam, 1996, 407 pp.

[3] Bashforth F., Adams J. C., An Attempt to Test The Theories of Capillary Action by Comparing the Theoretical and Measured Forms of Drops of Fluid, Cambridge University Press, London, 1883, 158 pp.

[4] Tolman R. C., “The effect of droplet size on surface tension”, The Journal of Chemical Physics, 17:3 (1949), 333–337 | DOI

[5] Rekhviashvili S. Sh., Sokurov A. A., “Modeling of sessile droplet with the curvature dependence of surface tension”, Turkish journal of physics, 42:6 (2018), 699–705 | DOI

[6] Baranov S. A., Rekhviashvili S. Sh., Sokurov A. A., “Some Problems in Simulation of the Thermodynamic Properties of Droplets”, Surface Engineering and Applied Electrochemistry, 55:3 (2019), 286–293 | DOI

[7] Freud B. B., Freud H. Z., “A Theory of the Ring Method for the Determination of Surface Tension”, Journal of the American Chemical Society, 52:5 (1930), 1772–1782 | DOI