Geodesic
Equilibrium of liquid drop on rotating disc
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2020), pp. 43-50 
P. N. Konon; E. I. Mogilevskii; G. N. Sitsko; V. Ya. Shkadov. Equilibrium of liquid drop on rotating disc. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2020), pp. 43-50. http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a5/
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     author = {P. N. Konon and E. I. Mogilevskii and G. N. Sitsko and V. Ya. Shkadov},
     title = {Equilibrium of liquid drop on rotating disc},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {43--50},
     year = {2020},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider the equilibrium of a finite volume of liquid on a horizontal rotation surface due to gravity and centrifugal forces under the action of surface tension. It is shown that a solution exits if the angular velocity is less than a critical value. For large droplets, the angular velocity is estimated analytically.

[1] Scriven L., “Physics and applications of dip coating and spin coating”, Mat. Res. Soc. Proc., 121 (1988), 717–729 | DOI

[2] Konon P. N., Kulago A. E., Sitsko G. N., Konon N. P., “Eksperimentalnoe i teoreticheskoe issledovanie povedeniya sloya zhidkosti na vraschayuschemsya diske”, Teor. i prikl. mekhan., 31 (2016), 155–160

[3] Melo F., Joanny J. F., Fauve S., “Fingering instability of spinning drops”, Phys. Rev. Lett., 63:18 (1989), 1958–1961 | DOI

[4] Takagi D., Huppert H., “Flow and instability of thin films on a cylinder and sphere”, J. Fluid Mech., 647 (2010), 221–238 | DOI | MR | Zbl

[5] Chandrasekhar S., “The stability of a rotating liquid drop”, Proc. Roy. Soc. London A, 286:1404 (1965), 1–26 | DOI | MR | Zbl

[6] Hocking L., Michael D., “The stability of a column of rotating liquid”, Mathematika, 6:1 (1959), 25–32 | DOI | MR | Zbl

[7] Gillis J., “Stability of a column of rotating viscous liquid”, Math. Proc. Cambridge Phil. Soc., 57:1 (1961), 152–159 | DOI | MR | Zbl

[8] Mogilevskii E. I., Shkadov V. Ya., “Techeniya tonkikh plenok vyazkoi zhidkosti po krivolineinym vraschayuschimsya poverkhnostyam”, Izv. RAN. Mekhan. zhidkosti i gaza, 2009, no. 2, 18–32

[9] A. D. Myshkis (red.), Gidromekhanika nevesomosti, Nauka, M., 1976

[10] Mogilevskii E. I., Shkadov V. Ya., Shutov A. A., “Ravnovesnye formy visyaschei kapli v elektrostaticheskom pole”, Izv. RAN. Mekhan. zhidkosti i gaza, 2012, no. 5, 23–31

[11] Rienstra S. W., “The shape of a sessile drop for small and large surface tension”, J. Eng. Math., 24:3 (1990), 193–202 | DOI | MR | Zbl

[12] Nurse A. K., Coriell S. R., McFadden G. B., “On the stability of rotating drops”, J. Res. Nat. Inst. Stand. Technol., 120 (2015), 74–101 | DOI