- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Submit a Manuscript
- Table of Contents
ISRN Mathematical Physics
Volume 2012 (2012), Article ID 869070, 19 pages
Generalizing the Multimodal Method for the Levitating Drop Dynamics
1Institute of Mathematics, National Academy of Sciences of Ukraine, Tereschenkivska 3 St., 01601 Kiev, Ukraine
2CeSOS, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Received 23 April 2012; Accepted 30 July 2012
Academic Editors: S. Ansoldi, K. Netocny, K.-E. Thylwe, and G. F. Torres del Castillo
Copyright © 2012 M. O. Chernova et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- R. Eberhardt and B. Neidhart, “Acoustic levitation device for sample pretreatment in microanalysis and trace analysis,” Fresenius' Journal of Analytical Chemistry, vol. 365, no. 6, pp. 475–479, 1999.
- E. H. Brandt, “Suspended by sound,” Nature, vol. 413, no. 6855, pp. 474–475, 2001.
- F. Priego-Capote and L. de Castro, “Ultrasound-assisted levitation: lab-on-a-drop,” Trends in Analytical Chemistry, vol. 25, no. 9, pp. 856–867, 2006.
- T. G. Wang, A. V. Anilkumar, and C. P. Lee, “Oscillations of liquid drops: results from USML-1 experiments in Space,” Journal of Fluid Mechanics, vol. 308, pp. 1–14, 1996.
- C. P. Lee, A. V. Anilkumar, A. B. Hmelo, and T. G. Wang, “Equilibrium of liquid drops under the effects of rotation and acoustic flattening: results from USML-2 experiments in Space,” Journal of Fluid Mechanics, vol. 354, pp. 43–67, 1998.
- Y. Liu, D. M. Zhu, D. M. Strayer, and U. E. Israelsson, “Magnetic levitation of large water droplets and mice,” Advances in Space Research, vol. 45, no. 1, pp. 208–213, 2010.
- T. Shi and R. E. Apfel, “Oscillations of a deformed liquid drop in an acoustic field,” Physics of Fluids, vol. 7, no. 7, pp. 1545–1552, 1995.
- W. J. Xie and B. Wei, “Dynamics of acoustically levitated disk samples,” Physical Review E, vol. 70, Article ID 046611, pp. 1–11, 2004.
- C. L. Shen, W. J. Xie, and B. Wei, “Parametrically excited sectorial oscillation of liquid drops floating in ultrasound,” Physical Review E, vol. 81, no. 4, Article ID 046305, pp. 1–10, 2010.
- E. Becker, W. J. Hiller, and T. A. Kowalewski, “Experimental and theoretical investigation of large-amplitude oscillations of liquid droplets,” Journal of Fluid Mechanics, vol. 231, pp. 189–210, 1991.
- E. Trinh and T. G. Wang, “Large-amplitude free and driven drop-shape oscillations: experimental observations,” Journal of Fluid Mechanics, vol. 122, pp. 315–338, 1982.
- E. Trinh and T. G. Wang, “Large amplitude drop shape oscillations,” in Proceedings of the 2nd International Colloquium on Drops and Bubbles, pp. 82–87, JPL Publication, Pasadena, Calif, USA, 1982.
- E. Becker, W. J. Hiller, and T. A. Kowalewski, “Nonlinear dynamics of viscous droplets,” Journal of Fluid Mechanics, vol. 258, pp. 191–216, 1994.
- Lord Rayleigh, “On the capillary phenomena of jets,” Proceedings of the Royal Society, London, vol. 29, pp. 71–97, 1879.
- L. D. Landau and E. M. Lifschitz, Hydrodynamics, Verlag Harri Deutsch, Berlin, Germany, 1991.
- O. A. Basaran, “Nonlinear oscillations of viscous liquid drops,” Journal of Fluid Mechanics, vol. 241, pp. 169–198, 1992.
- T. W. Patzek, R. E. Benner Jr., O. A. Basaran, and L. E. Scriven, “Nonlinear oscillations of inviscid free drops,” Journal of Computational Physics, vol. 97, no. 2, pp. 489–515, 1991.
- X. Chen, T. Shi, Y. Tian, J. Jankovsky, R. G. Holt, and R. E. Apfel, “Numerical simulation of superoscillations of a Triton-bearing drop in microgravity,” Journal of Fluid Mechanics, vol. 367, pp. 205–220, 1998.
- J. A. Tsamopoulos and R. A. Brown, “Nonlinear oscillations of inviscid drops and bubbles,” Journal of Fluid Mechanics, vol. 127, pp. 519–537, 1983.
- J. A. Tsamopoulos and R. A. Brown, “Resonant oscillations of inviscid charged drops,” Journal of Fluid Mechanics, vol. 147, pp. 373–395, 1984.
- R. Natarajan and R. A. Brown, “Third-order effects and the nonlinear stability of drop oscillations,” Journal of Fluid Mechanics, vol. 183, pp. 95–121, 1987.
- I. A. Lukovsky, “Variational method in the nonlinear problems of the dynamics of a limited liquid volume with free surface,” in Oscillations of Elastic Constructions with Liquid, pp. 260–264, Volna, Moscow, Russia, 1976.
- J. W. Miles, “Nonlinear surface waves in closed basins,” Journal of Fluid Mechanics, vol. 75, no. 3, pp. 419–448, 1976.
- I. A. Lukovsky, Introduction to the Nonlinear Dynamics of Solid Bodies with Cavities Filled by a Liquid, Naukova dumka, Kiev, Ukraine, 1990.
- O. M. Faltinsen and A. N. Timokha, Sloshing, Cambridge University Press, 2009.
- M. Hermann and A. Timokha, “Modal modelling of the nonlinear resonant fluid sloshing in a rectangular tank. I. A single-dominant model,” Mathematical Models and Methods in Applied Sciences, vol. 15, no. 9, pp. 1431–1458, 2005.
- O. M. Faltinsen, O. F. Rognebakke, and A. N. Timokha, “Resonant three-dimensional nonlinear sloshing in a square-base basin,” Journal of Fluid Mechanics, vol. 487, pp. 1–42, 2003.
- I. Gavrilyuk, I. Lukovsky, Yu. Trotsenko, and A. Timokha, “Sloshing in a vertical circular cylindrical tank with an annular baffle. II. Nonlinear resonant waves,” Journal of Engineering Mathematics, vol. 57, no. 1, pp. 57–78, 2007.
- I. Lukovsky, D. Ovchynnykov, and A. Timokha, “Asymptotic nonlinear multimodal modeling of liquid sloshing in an upright circular cylindrical tank. I. Modal equations,” Nonlinear Oscillations, vol. 14, no. 4, pp. 512–525, 2012.
- H. Takahara and K. Kimura, “Frequency response of sloshing in an annular cylindrical tank subjected to pitching excitation,” Journal of Sound and Vibration, vol. 331, no. 13, pp. 3199–3212, 2012.
- O. M. Faltinsen, O. F. Rognebakke, I. A. Lukovsky, and A. N. Timokha, “Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth,” Journal of Fluid Mechanics, vol. 407, pp. 201–234, 2000.
- J. S. Love and M. J. Tait, “Non-linear multimodal model for tuned liquid dampers of arbitrary tank geometry,” International Journal of Non-Linear Mechanics, vol. 46, no. 8, pp. 1065–1075, 2011.
- G. B. Foote, “A numerical method for studying liquid drop behavior: simple oscillation,” Journal of Computational Physics, vol. 11, no. 4, pp. 507–530, 1973.
- C. T. Alonso, “The dynamics of colliding and oscillating drops,” in Proceedings of the International Colloquium on Drops and Bubbles, D. J. Collins, M. S. Plesset, and M. M. Saffren, Eds., p. 14, Jet Propulsion Laboratory, 1974.
- V. Berdichevsky, Variational Principles of Continuum Mechanics, Springer, 2010.
- I. N. Vekua, “On completeness of a system of harmonic polynomials in space,” Doklady Akademii Nauk SSSR (NS), vol. 90, pp. 495–498, 1953.
- I. N. Vekua, New Methods for Solving Elliptic Equations, John Wiley & Sons, 1967.
- E. Zaarur, Y. Peleg, and R. Pnini, Quantum Mechanics, Schaums Easy Oulines Crash Course, Mc Graw Hill.