Weakly nonlinear oscillations of nearly inviscid axisymmetric liquid bridges

Journal of Fluid Mechanics

Volumn 328, Issue , 1996, Pages 95-128

  Nicolás, José A ^a   Vega, José M ^a  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

AXIAL FLOW; BOUNDARY LAYERS; FLOW PATTERNS; NUMERICAL ANALYSIS; VIBRATIONS (MECHANICAL);

AMPLITUDE EQUATIONS; AXISYMMETRIC LIQUID BRIDGES; NONLINEAR ANALYSIS; STEADY FLOW;

CAPILLARY FLOW;

BOUNDARY LAYERS; BRIDGES; OSCILLATION(FLUID);

EID: 0030427379     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S002211209600866X     Document Type: Article

References (42)

1. ANILKUMAR, A. V., GRUGEL, R. N., SHEN, X. P., LEE, C. P. & WANG, T. G. 1993 Control of thermocapillary convection in a liquid bridge by vibration. J. Appl. Phys. 73, 4165-4170.
2. BATCHELOR, G. K. 1967 Introduction to Fluid Dynamics. Cambridge University Press.
3. BORKAR, A. & TSAMOPOULOS, J. 1991 Boundary layer analysis of the dynamics of axisymmetric capillary bridges. Phys. Fluids A 3, 2866-2874.
4. BROWN, R. 1988 Theory of transport processes in single crystal growth from the melt. AIChE J. 34, 881-911.
5. CHEN, T. Y. & TSAMOPOULOS, J. A. 1993 Nonlinear dynamics of capillary bridges: theory. J. Fluid Mech. 255, 373-409.
6. CHEN, T. Y., TSAMOPOULOS, J. A. & GOOD, R. J. 1992 Capillary bridges between parallel and non-parallel surfaces and their stability. J. Colloid Interface Sci. 151, 49-69.
7. DEPAOLI, D. W., FENG, J. Q., BASARAN, O. A. & SCOTT, T. C. 1995 Hysteresis in forced oscillations of pendant drops. Phys. Fluids 7, 1181-1183.
8. FOWLE, A. A., WANG, C. A. & STRONG, P. F. 1979 Experiments on the stability of conical and cylindrical columns at low Bond numbers. Arthur D. Little Co.
9. GRASMAN, J. 1987 Asymptotic Methods for Relaxation Oscillations and Applications. Springer-Verlag.
10. HIGUERA, M. 1996 Oscilaciones Débilmente no Lineales en Puentes Líquidos no Axilsimétricos. Doctoral Thesis, Universidad Politécnica de Madrid. In progress.
11. HIGUERA, M., NICOLÁS, J. A. & VEGA, J. M. 1994 Linear oscillations of weakly dissipative axisymmetric liquid bridges. Phys. Fluids A 6, 438-450.
12. 0 single crystals due to non-steady thermocapillary convection. J. Cryst. Growth 102, 214-222.
13. KAMOTANI, Y. S., OSTRACH, S. & VARGAS, M. 1984 Oscillatory thermocapillary convection in a simulated floating-zone configuration. J. Cryst. Growth 66, 83-90.
14. KELLER, H. B. 1987 Lectures on Numerical Methods in Bifurcation Problems. Tata Institute of Fundamental Research, Bombay.
15. LAPLACE, P. S. 1805 Theory of Capillary Attractions, supplement to the Tenth Book of Celestial Mechanics. Reprinted by Chelsea, 1966.
16. MANCEBO, F. J., NICOLÁS, J. A. & VEGA, J. M. 1996 Chaotic mechanical oscillations in a nearly-inviscid liquid bridge at second-order 2:1 resonance, in preparation.
17. MEI, C. C. & LIU, L. F. 1973 The damping of surface gravity waves in a bounded liquid. J. Fluid Mech. 59, 239-256.
18. MELROSE, J. C. 1966 Model calculations for capillary condensation. AIChE J. 12, 986-994.
19. MESEGUER, J. 1983 The breaking of axisymmetric slender liquid bridges. J. Fluid Mech. 130, 123-151.
20. MESEGUER, J. & PERALES, J. M. 1991 A linear analysis of g-jitter effects on viscous cylindrical liquid bridges. Phys. Fluids A 3, 2332-2336.
21. MOLLOT, D. J., TSAMOPOULOS, J., CHEN, T. Y. & ASHGRIZ, N. 1993 Nonlinear dynamics of capillary bridges: experiments. J. Fluid Mech. 255, 411-435.
22. NICOLÁS, J. A. 1992 Hydrodynamic stability of high-viscosity cylindrical liquid bridges. Phys. Fluids A 4, 1-7.
23. NICOLÁS, J. A. & VEGA, J. M. 1996 Linear viscous oscillations of axisymmetric liquid bridges, in preparation.
24. NICOLÁS, J. A., RIVAS, D. & VEGA, J. M. 1996a The interaction of thermocapillary convection and low-frequency vibration in nearly-inviscid liquid bridges, Z. Angew. Math. Phys. (submitted).
25. NICOLÁS, J. A., RIVAS, D. & VEGA, J. M. 1996b On the steady streaming flow due to high-frequency vibration in nearly-inviscid liquid bridges. J. Fluid Mech. (submitted).
26. PERALES, J. M. & MESEGUER, J. 1992 Theoretical and experimental study of vibration of axisymmetric viscous liquid bridges. Phys. Fluids A 4, 1110-1130.
27. PERKO, L. 1991 Differential Equations and Dynamical Systems. Springer-Verlag
28. PLATEAU, J. A. F. 1849 Sur les figures d'equilibre d'une masse liquide sans pesanteur. Mem. Acad. R. Belgique, Nonv. Ser. 23.
29. PLATEAU, J. A. F. 1863 Experimental and theoretical researches on the figures of equilibrium of a liquid mass withdrawn from the action of gravity. Transl. in Ann. Rep. Smithsonian Inst. (1863-1866) 207-285.
30. PREISER, F., SCHWABE, D. & SHARMAN, A. 1983 Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface. J. Fluid Mech. 126, 545-567.
31. RAYLEIGH, LORD 1879 On the instability of jets. Proc. London Math. Soc. 10, 4-13.
32. RAYLEIGH, LORD 1892 On the stability of cylindrical fluid surfaces. Phil. Mag. 34, 177-180.
33. RIVAS, D. & MESEGUER, J. 1984 One-dimensional self-similar solution of the dynamics of axisymmetric slender liquid bridges J. Fluid Mech. 138, 417-429.
34. SANZ, A. 1985 The influence of the outer bath in the dynamics of axisymmetric liquid bridges. J. Fluid Mech. 156, 101-140.
35. SANZ, A. & DÍEZ, J. L. 1989 Non-axisymmetric oscillation of liquid bridges. J. Fluid Mech. 205, 503-521.
36. SCHULKES, R. M. S. M. 1993a Nonlinear dynamics of liquid columns: A comparative study. Phys. Fluids A 5, 2121-2130.
37. SCHULKES, R. M. S. M. 1993b Dynamics of liquid jets revisited. J. Fluid Mech. 250, 635-651.
38. TSAMOPOULOS, J., CHEN, T. & BORKAR, A. 1992 Viscous oscillations of capillary bridges. J. Fluid Mech. 235, 579-609.
39. URSELL, F. 1952 Edge waves on a sloping beach. Proc. R. Soc. Lond. A 214, 79-97.
40. YOUNG, X. 1805 Essay on the cohesion of fluids. Phil. Trans. R. Soc. Lond. A 306, 347-370.
41. ZHANG, Y. & ALEXANDER, J. I. D. 1990 Sensitivity of liquid bridges subjected to axial residual acceleration. Phys. Fluids A 2, 1966-1974.
42. ZASADZINSKI, J. N., SWEENEY, J. B., DAVIS, H. T. & SCRIVEN, L. E. 1987 Finite element calculation of fluid menisci and thin-films in model porous media. J. Colloid Interface Sci. 119, 108-116.