Analytical and numerical studies of the stability of thin-film rimming flow subject to surface shear

Journal of Fluid Mechanics

Volumn 541, Issue , 2005, Pages 317-344

  Villegas Diaz M ^a   Power, H ^a   Riley, David S ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

LUBRICATION; MATHEMATICAL MODELS; NUMERICAL METHODS; SHEAR STRESS; SURFACE TENSION;

LUBRICATION THEORY; SURFACE TENSION EFFECTS; THIN FILM RIMMING FLOW;

VISCOUS FLOW;

FILM LUBRICANT; FLUID FLOW; FLUID MECHANICS; LUBRICATION THEORY; MATHEMATICAL ANALYSIS;

EID: 27744542350     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112005006142     Document Type: Article

References (26)

1. Ashmore, J. J., Hosoi, A. H. & Stone, H. A. 2003 The effect of surface tension on rimming flows in a partially filled rotating cylinder. J. Fluid Mech. 479, 65-98.
2. Balmer, R. T. 1970 The hygrocyst, a stability phenomenon in continuum mechanics. Nature 227, 600-601.
3. Benilov, E. S., O'Brien, S. B. G. & Sazonov, I. A. 2003 A new type of instability: Explosive disturbances in a liquid film inside a rotating horizontal cylinder. J. Fluid Mech. 497, 201-224.
4. Benjamin, T. B., Pritchard, W. G. & Tavener, S. J. 1993 Steady and unsteady flows of a highly viscous liquid inside a rotating horizontal cylinder. Preprint.
5. Bertozzi, A. L., Munch, A. & Shearer, M. 1999 Undercompressive waves in driven film flow: Theory, computation, and experiment. Stud. Adv. Maths 13, 43-67.
6. Bertozzi, A. L., Munch, A., Shearer, M. & Zumbrun, K. 2001 Stability of compressive and undercompressive thin film travelling waves. Eur. J. Appl. Maths 12, 253-291.
7. Black, G. J. B. 2002 Theoretical studies of thin-film flows. MSc thesis, University of Strathclyde.
8. Hosoi, A. E. & Mahadevan, L. 1999 Axial instability of a free surface front in a partially filled horizontal rotating cylinder. Phys. Fluids 11, 97-106.
9. Johnson, R. E. 1988 Steady-state coating flows inside a rotating horizontal cylinder. J. Fluid Mech. 190, 321-342.
10. Johnson, R. E. 1990 In Engineering Science, Fluid Dynamics: A Symposium to Honor T. Y. Wu. World Scientific, Singapore.
11. Moffatt, H. K. 1977 Behaviour of a viscous film on the outer surface of a rotating cylinder. J. Méc. 16, 651-673.
12. Noakes, C. J. 2001 The dynamics of liquid films on rotating surfaces. PhD thesis, University of Nottingham.
13. Noakes, C. J., King, J. R. & Riley, D. S. 2005 On three-dimensional stability of a uniform, rigidly rotating film on a rotating cylinder. Q. J. Mech. Appl. Maths 58, 229-256.
14. O'Brien, S. B. G. 2002a Linear stability of rimming flow. Q. Appl. Maths 40, 201-211.
15. O'Brien, S. B. G. 2002b A mechanism for linear instability in two-dimensional rimming flow. Q. Appl. Maths 40, 283-299.
16. O'Brien, S. B. G. & Gath, E. G. 1998 The location of a shock in a rimming flow. Phys. Fluids 10, 1040-1042.
17. Orr, F. M. & Scriven, L. E. 1978 Rimming flow: Numerical simulation of steady, viscous, free-surface flow with surface tension. J. Fluid Mech. 84, 145-165.
18. Revallo, M. & Riley, D. S. 2004 On two-dimensional rapidly rotating rimming flow subject to gravitational perturbation and a constant surface shear. Preprint.
19. Ruschak, K. J. & Scriven, L. E. 1976 Rimming flow of liquid in a rotating horizontal cylinder. J. Fluid Mech. 76, 113-125.
20. Thoroddsen, S. T. & Mahadevan, L. 1997 Experimental study of coating flows in a partially-filled horizontally rotating cylinder. Exps. Fluids 23, 1-13.
21. Tirumkudulu, M. & Acrivos, A. 2001 Coating flows within a rotating horizontal cylinder: Lubrication analysis, numerical computations, and experimental measurements. Phys. Fluids 13, 14-19.
22. Villegas-Díaz, M., Power, H. & Riley, D. S. 2003 On the stability of rimming flows to two-dimensional disturbances. Fluid Dyn. Res. 33, 141-172.
23. Wilson, S. D. R. & Williams, J. 1997 The flow of a liquid film on the inside of a rotating cylinder, and some related problems. Phys. Fluids 9, 2184-2190.
24. Wilson, S. K. & Duffy, B. R. 1999 Thin-film and curtain flows on the outside of a rotating horizontal cylinder. J. Fluid Mech. 394, 29-49.
25. Wilson, S. K., Duffy, B. R. & Black, G. J. B. 2004 Thin-film flow on a stationary or uniformly rotating horizontal cylinder subject to a prescribed uniform shear stress at the free surface of the film. Preprint.
26. Wilson, S. K., Hunt, R. & Duffy, B. R. 2002 On the critical solutions in coating and rimming flow on a uniformly rotating horizontal cylinder. Q. J. Mech. Appl. Maths 55, 357-387.