Linear oscillations of a supported bubble or drop

Physics of Fluids

Volumn 25, Issue 6, 2013, Pages

  Vejrazka, Jiri ^a   Vobecka, Lucie ^a   Tihon, Jaroslav ^a  

^a INSTITUTE OF CHEMICAL PROCESS FUNDAMENTALS   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; FREQUENCY RESPONSE; PHASE INTERFACES; VIBRATION ANALYSIS;

IRROTATIONAL FLOW; LINEAR OSCILLATIONS; PARTIAL CONTACT; PERIODIC FORCING; SHAPE OSCILLATION; SIMPLE STRUCTURES; SPHERICAL BUBBLES; VARIATIONAL METHODS;

DROPS;

EID: 84880115979     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4810959     Document Type: Article

References (40)

1. Miller R. Liggieri L. Bubble and Drop Interfaces 2011, and (Brill, Leiden-Boston,).
2. Abi Chebel N. Risso F. Masbernat O. Inertial modes of a periodically forced buoyant drop attached to a capillary. Phys. Fluids 2011, 23:102104. 10.1063/1.3646930.
3. Meier W. Greune G. Meyboom A. Hofmann K.P. Surface tension and viscosity of surfactant from the resonance of an oscillating drop. Eur. Biophys. J. 2000, 29:113-124. 10.1007/s002490050256.
4. Tian Y. Holt R.G. Apfel R.E. Investigations of liquid surface rheology of surfactant solutions by droplet shape oscillations: Theory. Phys. Fluids 1995, 7:2938-2949. 10.1063/1.868671.
5. Tian Y. Holt R.G. Apfel R.E. A new method for measuring liquid surface tension with acoustic levitation. Rev. Sci. Instrum. 1995, 66:3349-3354. 10.1063/1.1145506.
6. Asaki T.J. Thiessen D.B. Marston P.L. Effect of an insoluble surfactant on capillary oscillations of bubbles in water: Observation of a maximum in the damping. Phys. Rev. Lett. 1995, 75:2686-2689. 10.1103/PhysRevLett.75.2686.
7. Asaki T.J. Marston P.L. Free decay of shape oscillations of bubbles acoustically trapped in water and sea water. J. Fluid Mech. 1995, 300:149-167. 10.1017/S0022112095003648.
8. Abi Chebel N. Vejrazka J. Masbernat O. Risso F. Free oscillations of an oil drop rising in water: Effect of surface contamination. J. Fluid Mech. 2012, 702:533-542. 10.1017/Jfm.2012.205.
9. Rayleigh J.W. S. On the capillary phenomena of jets. Proc. R. Soc. London 1879, 29:71-97. 10.1098/rspl.1879.0015.
10. Lamb H. Hydrodynamics 1932, 6th ed. (Cambridge University Press, Cambridge, England,).
11. Batchelor G.K. An Introduction to Fluid Dynamics 1967, (Cambridge University Press, Cambridge,).
12. Miller C.A. Scriven L.E. Oscillations of a fluid droplet immersed in another fluid. J. Fluid Mech. 1968, 32:417-435. 10.1017/S0022112068000832.
13. Marston P.L. Shape oscillation and static deformation of drops and bubbles driven by modulated radiation stresses: Theory. J. Acoust. Soc. Am. 1980, 67:15-26. 10.1121/1.383798.
14. Tsamopoulos J.A. Brown R.A. Non-linear oscillations of inviscid drops and bubbles. J. Fluid Mech. 1983, 127:519-537. 10.1017/S0022112083002864.
15. Natarajan R. Brown R.A. Quadratic resonance in the three-dimensional oscillations of inviscid drops with surface tension. Phys. Fluids 1986, 29:2788-2797. 10.1063/1.865475.
16. Basaran O.A. Nonlinear oscillations of viscous liquid drops. J. Fluid Mech. 1992, 241:169-198. 10.1017/S002211209200199X.
17. Trinh E.H. Thiessen D.B. Holt R.G. Driven and freely decaying nonlinear shape oscillations of drops and bubbles immersed in a liquid: Experimental results. J. Fluid Mech. 1998, 364:253-272. 10.1017/S0022112098001153.
18. Stone H.A. Leal L.G. The effects of surfactants on drop deformation and breakup. J. Fluid Mech. 1990, 220:161-186. 10.1017/S0022112090003226.
19. Lu H.L. Apfel R.E. Shape oscillations of drops in the presence of surfactants. J. Fluid Mech. 1991, 222:351-368. 10.1017/S0022112091001131.
20. Tian Y. Holt R.G. Apfel R.E. Investigation of liquid surface rheology of surfactant solutions by droplet shape oscillations: Experiments. J. Colloid Interface Sci. 1997, 187:1-10. 10.1006/jcis.1996.4698.
21. Strani M. Sabetta F. Free vibrations of a drop in partial contact with a solid support. J. Fluid Mech. 1984, 141:233-247. 10.1017/S0022112084000811.
22. Strani M. Sabetta F. Viscous oscillations of a supported drop in an immiscible fluid. J. Fluid Mech. 1988, 189:397-421. 10.1017/S0022112088001077.
23. Bostwick J.B. Steen P.H. Capillary oscillations of a constrained liquid drop. Phys. Fluids 2009, 21:032108. 10.1063/1.3103344.
24. Ramalingam S. Ramkrishna D. Basaran O.A. Free vibrations of a spherical drop constrained at an azimuth. Phys. Fluids 2012, 24:082102. 10.1063/1.4742339.
25. Prosperetti A. Linear oscillations of constrained drops, bubbles, and plane liquid surfaces. Phys. Fluids 2012, 24:032109. 10.1063/1.3697796.
26. Bisch C. Lasek A. Rodot H. Hydrodynamic behavior of spherical semifree liquid volumes in simulated weightlessness. J. Méc. Théor. Appl. 1982, 1:165-183.
27. Rodot H. Bisch C. Lasek A. Zero gravity simulation of liquids in contact with a solid surface. Acta Astronaut. 1979, 6:1083-1092. 10.1016/0094-5765(79)90057-2.
28. Smithwick R.W. Boulet J.A. M. Vibrations of microscopic mercury droplets on glass. J. Colloid Interface Sci. 1989, 130:588-596. 10.1016/0021-9797(89)90134-3.
29. Smithwick R.W. Boulet J.A. M. Electrically driven oscillations of a mercury-droplet electrode. J. Colloid Interface Sci. 1992, 150:567-574. 10.1016/0021-9797(92)90225-B.
30. DePaoli D.W. Scott T.C. Basaran O.A. Oscillation frequencies of droplets held pendant on a nozzle. Sep. Sci. Technol. 1992, 27:2071-2082. 10.1080/01496399208019466.
31. DePaoli D.W. Feng J.Q. Basaran O.A. Scott T.C. Hysteresis in forced oscillations of pendant drops. Phys. Fluids 1995, 7:1181-1183. 10.1063/1.868576.
32. Vukasinovic B. Smith M.K. Glezer A. Dynamics of a sessile drop in forced vibration. J. Fluid Mech. 2007, 587:395-423. 10.1017/S0022112007007379.
33. Basaran O.A. Depaoli D.W. Nonlinear oscillations of pendant drops. Phys. Fluids 1994, 6:2923-2943. 10.1063/1.868120.
34. Wilkes E.D. Basaran O.A. Forced oscillations of pendant (sessile) drops. Phys. Fluids 1997, 9:1512-1528. 10.1063/1.869276.
35. Wilkes E.D. Basaran O.A. Hysteretic response of supported drops during forced oscillations. J. Fluid Mech. 1999, 393:333-356. 10.1017/S0022112099005819.
36. Abi Chebel N. Dynamique et rhéologie interfaciales à haute fréquence d'une goutte oscillante. 2009, "," Ph.D. dissertation, Université de Toulouse.
37. See supplementary material at E-PHFLE6-25-017306 for more details of some principal steps of the analysis. They include some useful relations for Legendre polynomials, detailed derivations of the linearized volume constraint and of the constraint of Strani and Sabetta,2122 calculations of the change in interfacial area, of the kinetic energy, and of the energy dissipation rate. Detailed expressions for the elements of matrices M, D, K and vectors f and fs are provided. The solution for the linearized static shape is given. Details about the eigenproblem evaluation are given.
38. Taylor J.R. Classical Mechanics 2005, (University Science Books, Sausalito,).
39. Lanczos C. The Variational Principles of Mechanics 1970, 4th ed. (University of Toronto Press, Toronto,).
40. Bostwick J.B. Steen P.H. Coupled oscillations of deformable spherical-cap droplets. Part 1. Inviscid motions. J. Fluid Mech. 2013, 714:312-335. 10.1017/jfm.2012.483.