Steady and unsteady solutions for coating flow on a rotating horizontal cylinder: Two-dimensional theoretical and numerical modeling

Physics of Fluids

Volumn 16, Issue 8, 2004, Pages 2742-2756

  Evans, P L ^a   Schwartz, L W ^a   Roy, R V ^a  

^a UNIVERSITY OF DELAWARE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CYLINDERS (CONTAINERS); NUMERICAL ANALYSIS; PARAMETER ESTIMATION; SURFACE TENSION;

LUBRICATION THEORY; UNIFORM COATINGS; VISCOUS COATINGS;

FLUID DYNAMICS;

CYLINDER; ROTATING FLOW; STEADY FLOW; UNSTEADY FLOW;

EID: 4344625603     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1758943     Document Type: Article

References (47)

1. C.-S. Yih, "Instability of a rotating liquid film with a free surface," Proc. Soc. London, Ser. A 258, 63 (1960).
2. E. D. Cohen and E. B. Gutoff, Modern Coating and Drying Technology, Vol. 1 of Interfacial Engineering Series (VCH, New York, 1992).
3. H. K. Moffatt, "Behavior of a viscous film on the outer surface of a rotating cylinder," J. Mec. 16, 651 (1977).
4. K. J. Ruschak and L. E. Scriven, "Rimming flow of liquid in a rotating horizontal cylinder," J. Fluid Mech. 76, 113 (1976).
5. S. B. G. O'Brien, "A model for the coating of cylindrical light bulbs," in Progress in Industrial Mathematics at ECMI 98, edited by L. Arkeryd, J. Bergh, P. Brenner, and R. Pettersson (Teubner, Stuttgart, 1999), pp. 45-54.
6. M. Ehmann and J. Siekmann, "Numerical study of the oscillations of axially excited liquid annuli with rotational symmetry enclosed in revolving circular cylindrical containers," J. Fluid Mech. 297, 215 (1995).
7. R. E. White, "Residual condensate, condensate behavior, and siphoning in paper driers," Tech. Assoc. Pulp Paper Ind. 39, 228 (1956).
8. S. K. Wilson, R. Hunt, and B. R. Duffy, "On the critical solutions in coating and rimming flow on a uniformly rotating horizontal cylinder," Q. J. Mech. Appl. Math. 55, 357 (2002).
9. V. V. Pukhnachev, "Motion of a liquid film on the surface of a rotating cylinder in a gravitational field," Prikl. Mekh. Tekh. Fiz. (USSR) 18, 78 (1977) [J. Appl. Mech. Tech. Phys. 18, 344 (1977)].
10. B. R. Duffy and S. K. Wilson, "Thin-film and curtain flows on the outside of a rotating horizontal cylinder," J. Fluid Mech. 394, 29 (1999).
11. O. H. Campanella and R. L. Cerro, "Viscous flow on the outside of a horizontal rotating cylinder-the roll coating regime with a single fluid," Chem. Eng. Sci. 39, 1443 (1984).
12. E. B. Hansen and M. A. Kelmanson, "Steady, viscous, free-surface flow on a rotating cylinder," J. Fluid Mech. 272, 91 (1994).
13. M. A. Kelmanson, "Theoretical and experimetal analyses of the maximum-supportable fluid load on a rotating cylinder," J. Eng. Math. 29, 271 (1995).
14. L. Preziosi and D. D. Joseph, "The run-off condition for coating and rimming flows," J. Fluid Mech. 187, 99 (1988).
15. R. C. Peterson, P. K. Jimack, and M. A. Kelmanson, "On the stability of viscous free-surface flow supported by a rotating cylinder," Proc. R. Soc. London, Ser. A 457, 1427 (2001).
16. E. J. Hinch and M. A. Kelmanson, "On the decay and drift of free-surface perturbations in viscous thin-film flow exterior to a rotating cylinder," Proc. R. Soc. London, Ser. A 459, 1193 (2003).
17. J. A. Dieber and R. L. Cerro, "Viscous flow with a free surface inside a horizontal rotating drum," Ind. Eng. Chem. Fundam. 15, 102 (1976).
18. R. E. Johnson, "Steady-state coating flows inside a rotating horizontal cylinder," J. Fluid Mech. 190, 321 (1988).
19. R. E. Johnson, "Coating instability in rotational molding," in Engineering Science: Fluid Dynamics, edited by G. T. Yates (World Scientific, Singapore, 1990), pp. 435-449.
20. S. D. R. Wilson and J. Williams, "The flow of a liquid film on the inside of a rotating cylinder, and some related problems," Phys. Fluids 9, 2184 (1997).
21. S. B. G. O'Brien and E. G. Gath, "The location of a shock in rimming flow," Phys. Fluids 10, 1040 (1998).
22. M. Tirumkudulu and A. Acrivos, "Coating flows within a rotating horizontal cylinder: Lubrication analysis, numerical computations, and experimental measurements," Phys. Fluids 13, 14 (2001).
23. S. Fomin, J. Watterson, S. Raghunathan, and E. Harkin-Jones, "Steady-state rimming flow of the generalized Newtonian fluid," Phys. Fluids 14, 3350 (2002).
24. S. B. G. O'Brien, "Linear stability of rimming flow," Q. Appl. Math. 60, 201 (2002).
25. S. B. G. O'Brien, "A mechanism for linear instability in two-dimensional rimming flow," Q. Appl. Math. 60, 283 (2002).
26. M. Villegas-Díaz, H. Power, and D. S. Riley, "On the stability of rimming flows to two-dimensional disturbances," Fluid Dyn. Res. 33, 141 (2003).
27. J. Ashmore, A. E. Hosoi, and H. A. Stone, "The effect of surface tension on rimming flows in a partially filled rotating cylinder," J. Fluid Mech. 479, 65 (2003).
28. F. M. Orr and L. E. Scriven, "Rimming flow: Numerical simulation of steady, viscous, free-surface flow with surface tension," J. Fluid Mech. 84, 145 (1978).
29. D. Rajagopalan, R. J. Phillips, R. C. Armstrong, R. A. Brown, and A. Bose, "The influence of viscoelasticity on the existence of steady solutions in 2-dimensional rimming flow," J. Fluid Mech. 235, 611 (1992).
30. S. Fomin, T. Hashida, and J. Watterson, "Fundamentals of steady-state non-Newtonian rimming flow," J. Non-Newtonian Fluid Mech. 111, 19 (2003).
31. H. L. Reed, "Gallery of fluid motion," Phys. Fluids 8, S1 (1996); see page S10.
32. S. T. Thoroddsen and L. Mahadevan, " Experimental study of coating flows in a partially-filled horizontally rotating cylinder," Exp. Fluids 23, 1 (1997).
33. S. M. Troian, E. Herbolzheimer, S. A. Safran, and J. F. Joanny, "Fingering instabilities of driven spreading films," Europhys. Lett. 10, 25 (1989).
34. F. Melo, "Localized states in a film-dragging experiment," Phys. Rev. E 48, 2704 (1993).
35. A. E. Hosoi and L. Mahadevan, "Axial instability of a free-surface front in a partially filled horizontal rotating cylinder," Phys. Fluids 11, 97 (1999).
36. M. J. Karweit and S. Corrsin, "Observations of cellular patterns in a partly filled, horizontal cylinder," Phys. Fluids 18, 111 (1975).
37. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Clarendon, Oxford, 1961).
38. S. L. Goren, "The instability of an annular thread of fluid," J. Fluid Mech. 12, 309 (1962).
39. S. G. Yiantsios and B. G. Higgins, "Rayleigh-Taylor instability in thin viscous films," Phys. Fluids A 1, 1484 (1989).
40. J. P. Kovac and R. T. Balmer, "Experimental studies of external hygrocysts," J. Fluids Eng. 102, 226 (1980).
41. D. D. Joseph and L. Preziosi, "Stability of rigid motions and coating films in bicomponent flows of immiscible liquids," J. Fluid Mech. 185, 323 (1987).
42. H. Ockendon and J. R. Ockendon, Viscous Flow (Cambridge University Press, Cambridge, 1995).
43. D. E. Weidner, L. W. Schwartz, and M. H. Eres, "Simulation of coating layer evolution and drop formation on horizontal cylinders," J. Colloid Interface Sci. 187, 243 (1997).
44. R. V. Roy and L. W. Schwartz, "Coating flows over curved substrates," in Fluid Mechanics of Coating Processes, edited by P. Bourgin, Proceedings of the Second European Coating Symposium, Strasbourg, 1997.
45. J. A. Moriarty, L. W. Schwartz, and E. O. Tuck, "Unsteady spreading of thin liquid films with small surface tension," Phys. Fluids A 3, 733 (1991).
46. J. H. Ahlberg, E. N. Nilson, and J. L. Walsh, The Theory of Splines and Their Applications (Academic, New York, 1967).
47. P. L. Evans, "Mathematical and numerical investigations of coating flows," Ph.D. thesis, University of Delaware (2000).