Modulation equations for strongly nonlinear oscillations of an incompressible viscous drop

Journal of Fluid Mechanics

Volumn 654, Issue , 2010, Pages 141-159

  Smith, Warren R ^a  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DECAY (ORGANIC); DIFFERENCE EQUATIONS; DROPS; EXCITONS; MODULATION; NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS;

CAPILLARY NUMBERS; CONSERVATION OF ENERGY; LARGE AMPLITUDE OSCILLATION; MODULATION EQUATIONS; PROLATE SPHEROID; STRONGLY NONLINEAR OSCILLATIONS; VORTICITY VECTORS; WEAKLY NON-LINEAR;

NAVIER STOKES EQUATIONS;

ACCELERATION; AMPLITUDE; FLUID MECHANICS; INCOMPRESSIBLE FLOW; NAVIER-STOKES EQUATIONS; NONLINEARITY; NUMERICAL METHOD; PERTURBATION; SIMULATION;

EID: 77957112783     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112010000480     Document Type: Article

References (23)

1. Basaran, O. A. 1992 Nonlinear oscillations of viscous liquid drops. J. Fluid Mech. 241, 169-198.
2. Becker, E., Hiller, W. J. & Kowalewski, T. A. 1991 Experimental and theoretical investigation of large-amplitude oscillations of liquid droplets. J. Fluid Mech. 231, 189-210.
3. Becker, E., Hiller, W. J. & Kowalewski, T. A. 1994 Nonlinear dynamics of viscous droplets. J. Fluid Mech. 258, 191-216.
4. Bostwick, J. B. & Steen, P. H. 2009 Capillary oscillations of a constrained liquid drop. Phys. Fluids 21, 032108.
5. Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
6. Kuzmak, G. E. 1959 Asymptotic solutions of nonlinear second-order differential equations with variable coefficients. Prikl. Mat. Mekh. 23, 515-526 (in Russian);
7. J. Appl. Math. Mech. 23 (1959), pp. 730-744 (in English).
8. Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
9. Lundgren, T. S. & Mansour, N. N. 1988 Oscillation of drops in zero gravity with weak viscous effects. J. Fluid Mech. 194, 479-510.
10. Natarajan, R. & Brown, R. A. 1986 Quadratic resonance in the three-dimensional oscillations of inviscid drops with surface tension. Phys. Fluids 29, 2788-2797.
11. Notz, P. K. & Basaran, O. A. 2004 Dynamics and breakup of a contracting liquid filament. J. Fluid Mech. 512, 223-256.
12. Patzek, T. W., Brenner, R. E., Basaran, O. A. & Scriven, L. E. 1991 Nonlinear oscillations of inviscid free drops. J. Comput. Phys. 97, 489-515.
13. Prosperetti, A. 1977 Viscous effects on perturbed spherical flows. Quart. Appl. Math. 34, 339-352.
14. Prosperetti, A. 1980 Free oscillations of drops and bubbles: the initial-value problem. J. Fluid Mech. 100, 333-347.
15. Rayleigh, J. W. S. 1879 On the capillary phenomena of jets. Phil. Trans. R. Soc. Lond. A 29, 71-97.
16. Schulkes, R. M. S. M. 1996 The contraction of liquid filaments. J. Fluid Mech. 309, 277-300.
17. Smith, W. R. 2005 On the sensitivity of strongly nonlinear autonomous oscillators and oscillatory waves to small perturbations. IMA J. Appl. Math. 70, 359-385.
18. Smith, W. R. 2007 Modulation equations and Reynolds averaging for finite-amplitude nonlinear waves in an incompressible fluid. IMA J. Appl. Math. 72, 923-945.
19. Suryo, R. & Basaran, O. A. 2006 Dripping of a liquid from a tube in the absence of gravity. Phys. Rev. Lett. 96, 034504.
20. Theisen, E. A., Vogel, M. J., López, C. A., Hirsa, A. H. & Steen, P. H. 2007 Capillary dynamics of coupled spherical-cap droplets. J. Fluid Mech. 580, 495-505.
21. Trinh, E. & Wang, T. G. 1982 Large-amplitude free and driven drop-shape oscillations: experimental observations. J. Fluid Mech. 122, 315-338.
22. Tsamopoulos, J. A. & Brown, R. A. 1983 Nonlinear oscillations of inviscid drops and bubbles. J. Fluid Mech. 127, 519-537.
23. Wang, T. G., Anilkumar, A. V. & Lee, C. P. 1996 Oscillations of liquid drops: results from USML-1 experiments in Space. J. Fluid Mech. 308, 1-14.