Abstract
An exact solution is obtained to the problem of axisymmetric normal modes and natural frequencies characterizing surface perturbations of a drop that sits with an arbitrary wetting angle on a substrate and experiences only gravity and surface tension. The resulting mode solutions are used to calculate and analyze different shapes of the perturbed surface for the same drop placed on a vibrating base. The distinctive feature of the present study is the explicit representation of the results in the form of calculated shapes of the surface of a vibrating drop, comparison of the parameters of actual drops with resonance frequencies, and comparison with experimental data.
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References
Lord Kelvin, in Mathematical and Physical Papers, vol. 3, art. XCVI (Clay and Sond, Cambridge Univ., 1890), p. 530.
Lord Rayleigh, The Theory of Sound, vol. 2 (Macmillan, London, 1896), p. 504
Lord Rayleigh, Phil. Mag. 34, 94 (1917).
R. Clift, J. R. Grace, and M. E. Weber, Bubbles, Drops, and Particles (Academic Press, 1978), p. 380.
A. Prosperetti, J. Fluid Mech. 100, 333 (1980).
E. H. Trinh, D. B. Thiessen, and R. G. Holt, J. Fluid Mech. 364, 253 (1998).
R. E. Apfel, J. Acoust. Soc. Am. 101, 1227 (1997).
T. G. Leighton, The Acoustic Bubble (Academic Press, 1994), p. 613.
Y. N. Makov, Acoust. Phys. 55, 547 (2009).
P. L. Marston and R. E. Apfel, J. Acoust. Soc. Am. 67(2), 27 (1980).
T. Shi and R. E. Apfel, Phys. Fluids 7, 1545 (1995).
Z. C. Feng and Y. H. Su, Phys. Fluids 9, 519 (1997).
Y. Abe, D. Hyuga, S. Yamada, and K. Aoki, Ann. (N.Y.) Acad. Sci. 1077, 49 (2006).
H. Frenzel and H. Schultes, Z. Phys. Chem. B 27, 421 (1934).
M. P. Brenner, S. Hilgenfeldt, and D. Lohse, Rev. Mod. Phys. 74, 425 (2002).
R. I. Nigmatulin and R. P. Taleyarkhan, Proc. Inst. Mech. Eng. A: J. Power Energy 218, 345 (2004).
P. G. De Gennes, Rev. Mod. Phys. 57, 827 (1985).
E. G. Rapis, Pis’ma Zh. Tekh. Fiz. 14, 1560 (1988) [Sov. Tech. Phys. Lett. 14, 679 (1988)].
Yu. Yu. Tarasevich, Usp. Fiz. Nauk 174, 779 (2004) [Phys. Usp. 47, 717 (2004)].
L. V. Andreeva, A. S. Novoselova, P. V. Lebedev-Stepanov, et al., Zh. Tekh. Fiz. 77(2), 22 (2007) [Tech. Phys. 52, 164 (2007)].
J. Dutta and H. Hofmann, in Encyclopedia of Nanoscience and Nanotechnology, Ed. by H. S. Nalwa (Am. Sci. Publ. 2003), Vol. 10, pp. 1–23.
H. Li, J. R. Friend, and L. Y. Yeo, Biomed. Microdev. 9, 647 (2007).
D. V. Lyubimov, N. P. Lyubimova, and S. V. Shklyaev, Phys. Fluids 18, 012101 (2006).
I. S. Fayzrakhmanova and A. V. Straube, http://arxiv.org/abs/0903.2580.
L. D. Landau and M. E. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, New York, 1987).
B. Vukasinovic, M. K. Smit, and A. Glezer, J. Fluid Mech. 587, 395 (2007).
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Ilyukhina, M.A., Makov, Y.N. Analysis of shape perturbations of a drop on a vibrating substrate for different wetting angles. Acoust. Phys. 55, 722–728 (2009). https://doi.org/10.1134/S1063771009060050
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DOI: https://doi.org/10.1134/S1063771009060050