Abstract
The non-linear oscillations of a viscous drop is a fundamental problem in diverse areas of science and technology. In this paper, we analyze the large-amplitude oscillations of an initially elongated liquid drop in two-dimensions by solving the free boundary problem comprised of the Navier-Stokes equations, using two different numerical codes. The drop models all start from the same deformation in vacuum with zero gravity and varied Reynolds numbers (Re). We find that non-isothermal drops undergo stronger damping than isothermal ones due to the additional dissipative effects of heat conduction. Regardless of the drop parameters and physical mechanisms of dissipation, the transition from periodic to aperiodic decay is seen to occur for \(\mathrm{Re} \le 1.5\) in good agreement with linear theory and previous numerical simulations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Apfel RE, Tian Y, Jankovsky J, Shi T, Chen X, Holt RG, Trinh E, Croonquist A, Thornton KC, Sacco A Jr, Coleman C, Leslie FW (1997) Free oscillations and surfactant studies of superdeformed drops in microgravity. Phys Rev Lett 78:1912–1915
Basaran OA (1992) Nonlinear oscillations of viscous liquid drops. J Fluid Mech 241:169–198
Becker E, Hiller WJ, Kowalewski TA (1991) Experimental and theoretical investigation of large-amplitude oscillations of liquid droplets. J Fluid Mech 231:189–210
Becker E, Hiller WJ, Kowalewski TA (1994) Nonlinear dynamics of viscous droplets. J Fluid Mech 258:191–216
Bonometti T, Magnaudet J (2007) An interface-capturing method for incompressible two-phase flow: validation and application to bubble dynamics. Int J Multiph Flow 33:109–133
Legendre D, Magnaudet J (1998) The lift force on a spherical bubble in a viscous linear shear flow. J Fluid Mech 368:81–126
Legendre D, Magnaudet J, Mougin G (2003) Hydrodynamic interactions between two spherical bubbles rising side by side in a viscous liquid. J Fluid Mech 497:133–166
López H, Sigalotti L Di G, (2006) Oscillations of viscous drops with smoothed particle hydrodynamics. Phys Rev E 73:051201
Lundgren TS, Mansour NN (1988) Oscillations of drops in zero gravity with weak viscous effects. J Fluid Mech 194:479–510
Magnaudet J, Rivero M, Fabre J (1995) Accelerated flows around a rigid sphere or a spherical bubble. Part I: steady straining flow. J Fluid Mech 284:97–135
Mashayek F, Ashgriz N (1998) Nonlinear oscillations of drops with internal circulation. Phys Fluids 10:1071–1082
Meradji S, Lyubimova TP, Lyubimov DV, Roux B (2001) Numerical simulation of a liquid drop freely oscillating. Cryst Res Technol 36:729–744
Merle A, Legendre D, Magnaudet J (2005) Forces on a high-Reynolds-number spherical bubble in a turbulent flow. J Fluid Mech 532:53–62
Miller AC, Scriven LE (1968) The oscillation of a fluid droplet immersed in another fluid. J Fluid Mech 32:417–435
Moran K, Yeung A, Masliyah J (2003) Shape relaxation of an elongated viscous drop. J Colloid Interface Sci 267:483–493
Prosperetti A (1980) Free oscillations of drops and bubbles: the initial-value problem. J Fluid Mech 100:333–347
Rayleigh JWS (1879) On the capillary phenomena of jets. Proc R Soc Lond 29:71–97
Reid WH (1960) The oscillations of a viscous liquid drop. Q Appl Math 18:86–89
Sigalotti L Di G, Daza J, Donoso A (2006) Modelling free surface flows with smoothed particle hydrodynamics. Condens Matter Phys 9:359–366
Sigalotti L Di G, López H (2008) Adaptive kernel estimation and SPH tensile instability. Comput Math Appl 55:23–50
Trinh E, Wang TG (1982) Large-amplitude free and driven drop-shape oscillations: experimental observations. J Fluid Mech 122:315–338
Tsamopoulos JA, Brown RA (1983) Nonlinear oscillations of inviscid drops and bubbles. Int J Fluid Mech 127:519–537
Twiss RJ, Moores EM (1992) Structural geology. Freeman, New York
Wang TG, Anilkumar AV, Lee CP (1996) Oscillations of liquid drops: results from USML-1 experiments in space. J Fluid Mech 308:1–14
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Troconis, J., Blanco, A., Legendre, D., Trujillo, L., Sigalotti, L.D.G. (2014). Numerical Simulations of Freely Oscillating Drops. In: Sigalotti, L., Klapp, J., Sira, E. (eds) Computational and Experimental Fluid Mechanics with Applications to Physics, Engineering and the Environment. Environmental Science and Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-00191-3_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-00191-3_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-00190-6
Online ISBN: 978-3-319-00191-3
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)