Abstract
Analytical solutions for the time evolution of a capillary-gravitational wave in a charged layer of a viscous conducting liquid on a solid support are found. It is shown that the velocity field eddy component of the wave-induced liquid flow arises not only near the free surface of the liquid, but also at the solid bottom. The ratio between the amplitudes of these eddy components depends on the relationship between the thickness of the layer and the wavelength. If the wavelength far exceeds the thickness, the eddy flow amplitude near the bottom exceeds that near the free surface and the eddy flow occupies the whole volume of the liquid.
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References
Chr. Boyadjiev and V. Beschkov, Mass Transfer in Moving Liquid Films (Bulg. Acad. Sci., Sofia, 1984; Mir, Moscow, 1988) [translated from Bulgarian].
S. A. Kurochkina, D. F. Belonozhko, and A. N. Grigor’ev, Elektrokhim. Obrab. Met., No. 3, 26 (2003).
D. F. Belonozhko, A. I. Grigor’ev, A. V. Klimov, et al., Elektrokhim. Obrab. Met., No. 4, 66 (2004).
A. I. Grigor’ev, A. V. Klimov, S. V. Chernikova, and A. V. Prisyazhnyuk, Parametritic and Nonlinear Waves on Charged Liquid Surface (Yaroslavsk. Gos. Univ., Yaroslavl’, 2007) [in Russian].
A. I. Grigor’ev, S. O. Shiryaeva, V. A. Koromyslov, and D. F. Belonozhko, Zh. Tekh. Fiz. 67(8), 27 (1997) [Tech. Phys. 42, 877 (1997)].
A. I. Grigor’ev, V. A. Koromyslov, and S. O. Shiryaeva, Zh. Tekh. Fiz. 67(9), 8 (1997) [Tech. Phys. 42, 991 (1997)].
D. F. Belonozhko, A. I. Grigor’ev, M. I. Munichev, and S. O. Shiryaeva, Pis’ma Zh. Tekh. Fiz. 22(10), 84 (1996) [Tech. Phys. Lett. 22, 425 (1996)].
A. Gonzalez and A. Castellanos, Phys. Rev. E 49, 2935 (1994).
A. Gonzalez and A. Castellanos, Phys. Rev. E 53, 3573 (1996).
A. Zhakin, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 94 (1984).
V. S. Krylov, V. P. Vorotilin, and V. G. Levich, Teor. Osn. Khim. Tekhnol. 3, 499 (1969).
D. F. Belonozhko, A. I. Grigor’ev, and S. O. Shiryaeva, Pis’ma Zh. Tekh. Fiz. 28(19), 1 (2002) [Tech. Phys. Lett. 28, 795 (2002)].
D. F. Belonozhko and A. I. Grigor’ev, Zh. Tekh. Fiz. 73(4), 28 (2003) [Tech. Phys. 48, 404 (2003)].
A. V. Klimov, D. F. Belonozhko, and A. I. Grigor’ev, Zh. Tekh. Fiz. 75(10), 9 (2005) [Tech. Phys. 50, 1259 (2005)].
A. V. Klimov and A. I. Grigor’ev, Zh. Tekh. Fiz. 78(4), 10 (2008) [Tech. Phys. 53, 399 (2008)].
A. I. Grigor’ev, Zh. Tekh. Fiz. 77(2), 31 (2007) [Tech. Phys. 52, 173 (2007)].
Ya. I. Frenkel’, Zh. Éksp. Teor. Fiz. 6, 348 (1936).
D. F. Belonozhko and A. I. Grigor’ev, Zh. Tekh. Fiz. 78(3), 21 (2008) [Tech. Phys. 53, 306 (2008)].
V. G. Levich, Physicochemical Hydrodynamics (Fizmatgiz, Moscow, 1959) [in Russian].
Ya. I. Frenkel’, Zh. Éksp. Teor. Fiz. 6, 348 (1936).
A. I. Grigor’ev, O. A. Grigor’ev, and S. O. Shiryaeva, Zh. Tekh. Fiz. 62(9), 12 (1992) [Tech. Phys. 37, 904 (1992)].
A. I. Grigor’ev, S. O. Shiryaeva, D. F. Belonozhko, and A. V. Klimov, Elektrokhim. Obrab. Met., No. 4, 34 (2004).
A. I. Grigor’ev, S. O. Shiryaeva, D. F. Belonozhko, and A. V. Klimov, Zh. Tekh. Fiz. 75(2), 19 (2005) [Tech. Phys. 50, 158 (2005)].
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Original Russian Text © A.I. Grigor’ev, D.M. Pozharitskii, S.O. Shiryaeva, 2009, published in Zhurnal Tekhnicheskoĭ Fiziki, 2009, Vol. 79, No. 2, pp. 51–57.
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Grigor’ev, A.I., Pozharitskii, D.M. & Shiryaeva, S.O. Flow pattern due to capillary-gravitational waves in a charged layer of a viscous conducting liquid on a solid support. Tech. Phys. 54, 214–220 (2009). https://doi.org/10.1134/S1063784209020091
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DOI: https://doi.org/10.1134/S1063784209020091