Abstract
The problem of surface wave propagation over the interface between a nematic liquid crystal and an ideal isotropic fluid is considered. For the nematic liquid crystal the Frank-Oseen model with an isotropic viscous stress tensor is used. Anisotropic surface tension is described by the Rapini model. In this formulation, for the problem of harmonic small-amplitude surface wave propagation, in the case of infinite depths of both phases, an analytical solution is obtained. The dispersion relation is derived and its properties are investigated.
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References
L.D. Landau and E.M. Lifshits, Theoretical Physics, Vol. 6: Hydrodynamics (Nauka, Moscow, 1986) [in Russian].
P.N. Antonyuk, “Dispersion Equation for a Plane Capillary-Gravity Wave on the Free Surface of a Viscous Incompressible Fluid”, Dokl. Akad. Nauk SSSR, 286(6), 1324–1328 (1986).
U.S. Jeng, L. Ensibov, L. Crow, and A. Steyerl, “Viscosity Effect on Capillary Waves at Liquid Interfaces,” J. Phys.: Condens. Matter, 10(23), 4955–4962 (1998).
A.N. Golubiatnikov and G.I. Subkhankulov, “On the Surface Tension of a Magnetic Fluid,” Magnitnaya Gidrodinamika, No. 1, 73–78 (1986).
L.M. Blinov, E.I. Kats, and A.A. Sonin, “Surface Physics of Thermotropic Liquid Crystals,” Uspekhi Fiz. Nauk 152(3), 449–477 (1987).
A.N. Golubiatnikov and A.G. Kalugin, “On Short Surface Waves in Nematic Liquid Crystals,” Mol. Cryst. Liq. Cryst. 366, 2731–2736 (2001).
M. Igosheva and A. Kalugin, “Capillary Waves in Nematic Liquid Crystal,” Mol. Cryst. Liq. Cryst. 526, 10–17 (2010).
V. Popa-Nita and P. Oswald, “Waves at the Nematic-Isotropic Interface: The Role of Surface Tension Anisotropy, Curvature Elasticity, and Backflow Effects,” Phys. Rev. E. 68, 061707:1–12 (2003).
P.-G. de Gennes, The Physics of Liquid Crystals (Clarendon, New York, 1974).
A.S. Sonin, Introduction to the Physics of Liquid Crystals (Nauka, Moscow, 1983) [in Russian].
J.L. Ericksen, “Equilibrium Theory of Liquid Crystals”, in Advances in Liquid Crystals 2, Ed. by G. Brown (Acad. Press, NY, 1976), pp. 233–299.
V.V. Belyaev, Viscosity of Nematic Liquid Crystals (Fizmatgiz, Moscow, 2002) [in Russian].
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Original Russian Text © A. G. Kalugin, 2011, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2011, Vol. 46, No. 6, pp. 130–134.
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Kalugin, A.G. Waves on the interface between a nematic liquid crystal and an ideal isotropic fluid. Fluid Dyn 46, 953–957 (2011). https://doi.org/10.1134/S0015462811060123
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DOI: https://doi.org/10.1134/S0015462811060123