Three-dimensional solutions for coating flow on a rotating horizontal cylinder: Theory and experiment

Physics of Fluids

Volumn 17, Issue 7, 2005, Pages 1-20

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

^a UNIVERSITY OF DELAWARE   (United States)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; MATHEMATICAL MODELS; SURFACES;

CIRCUMFERENCE; COATING FLOW; LUBRICATION MODELS; THIN COATINGS;

FLOW OF FLUIDS;

THREE-DIMENSIONAL FLOW;

EID: 23044484779     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1942523     Document Type: Article

References (39)

1. H. K. Moffatt, "Behaviour of a viscous film on the outer surface of a rotating cylinder," J. Mec.JOMCAR0021-7832 16, 651 (1977).
2. J. P. Kovac and R. T. Balmer, "Experimental studies of external hygrocysts," J. Fluids Eng.JFEGA40098-2202 102, 226 (1980).
3. D. D. Joseph and L. Preziosi, "Stability of rigid motions and coating films in bicomponent flows of immiscible liquids," J. Fluid Mech.JFLSA70022-1120 185, 323 (1987).
4. L. Preziosi and D. D. Joseph, "The run-off condition for coating and rimming flows," J. Fluid Mech.JFLSA70022-1120 187, 99 (1988).
5. M. A. Kelmanson, "Theoretical and experimetal analyses of the maximum-supportable fluid load on a rotating cylinder," J. Eng. Math.JLEMAU0022-0833 29, 271 (1995).
6. C.-S. Yih, "Instability of a rotating liquid film with a free surface," Proc. R. Soc. London, Ser. APRLAAZ1364-5021 258, 63 (1960).
7. 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.
8. P. L. Evans, L. W. Schwartz, and R. V. Roy, "Steady and unsteady solutions for coating flow on a rotating horizontal cylinder: Two-dimensional theoretical and numerical modeling," Phys. FluidsPHFLE61070-663110.1063/1.1758943 16, 2742 (2004).
9. E. B. Hansen and M. A. Kelmanson, "Steady, viscous, free-surface flow on a rotating cylinder," J. Fluid Mech.JFLSA70022-1120 272, 91 (1994).
10. 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. APRLAAZ1364-5021 457, 1427 (2001).
11. S. L. Goren, "The instability of an annular thread of fluid," J. Fluid Mech.JFLSA70022-1120 12, 309 (1962).
12. 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.JCISA50021-979710.1006/ jcis.1996.4711 187, 243 (1997).
13. E. D. Cohen and E. B. Gutoff, Modern Coating and Drying Technology, Interfacial Engineering Series, Vol. 1 (VCH, New York, 1992).
14. 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. FluidsPHFLE61070-663110.1063/1.869476 9, 2184 (1997).
15. S. B. G. O'Brien and E. G. Gath, "The location of a shock in rimming flow," Phys. FluidsPHFLE61070-663110.1063/1.869630 10, 1040 (1998).
16. 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.JFLSA70022-112010.1017/S0022112002003312 479, 65 (2003).
17. J. A. Dieber and R. L. Cerro, "Viscous flow with a free surface inside a horizontal rotating drum," Ind. Eng. Chem. Fundam.IECFA70196-4313 15, 102 (1976).
18. 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.JFLSA70022-1120 297, 215 (1995).
19. H. L. Reed, "Gallery of fluid motion," Phys. FluidsPHFLE61070-6631 8, S1 (1996); H. L. Reed, Phys. FluidsPHFLE61070-66318, S10 (1996).
20. S. T. Thoroddsen and L. Mahadevan, "Experimental study of coating flows in a partially-filled horizontally rotating cylinder," Exp. FluidsEXFLDU0723-486410.1007/s003480050080 23, 1 (1997).
21. S. M. Troian, E. Herbolzheimer, S. A. Safran, and J. F. Joanny, "Fingering instabilities of driven spreading films," Europhys. Lett.EULEEJ0295-5075 10, 25 (1989).
22. A. E. Hosoi and L. Mahadevan, "Axial instability of a free-surface front in a partially filled horizontal rotating cylinder," Phys. FluidsPHFLE61070-663110.1063/1.869905 11, 97 (1999).
23. F. Melo, "Localized states in a film-dragging experiment," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.48.2704 48, 2704 (1993).
24. M. J. Karweit and S. Corrsin, "Observations of cellular patterns in a partly filled, horizontal cylinder," Phys. FluidsPFLDAS0031-917110.1063/1.860983 18, 111 (1975).
25. O. A. M. Boote and P. J. Thomas, "Effects of granular additives on transition boundaries between flow states of rimming flows," Phys. FluidsPHFLE61070-663110.1063/1.870065 11, 2020 (1999).
26. M. Tirumkudulu, A. Mileo, and A. Acrivos, "Particle segregation in monodisperse sheared suspensions in a partially filled rotating horizontal cylinder," Phys. FluidsPHFLE61070-663110.1063/1.870411 12, 1615 (2000).
27. E. Fried, A. Q. Shen, and S. T. Thoroddsen, "Wave patterns in a thin layer of sand within a rotating horizontal cylinder," Phys. FluidsPHFLE61070-663110.1063/1.869539 10, 10 (1998).
28. J. A. Moriarty, L. W. Schwartz, and E. O. Tuck, "Unsteady spreading of thin liquid films with small surface tension," Phys. Fluids APFADEB0899-821310.1063/1.858006 3, 733 (1991).
29. H. Lamb, Hydrodynamics (Dover, New York, 1932).
30. S. G. Yiantsios and B. G. Higgins, "Rayleigh-Taylor instability in thin viscous films," Phys. Fluids APFADEB0899-821310.1063/1.857327 1, 1484 (1989).
31. J. R. de Bruyn, "Crossover between surface tension and gravity-driven instabilities of a thin fluid layer on a horizontal cylinder," Phys. FluidsPHFLE61070-663110.1063/1.869280 9, 1599 (1997).
32. F. Bashforth and J. C. Adams, An Attempt to Test the Theories of Capillary Action (Cambridge University Press, New York, 1883).
33. C. D. Hodgman, CRC Handbook of Chemistry and Physics, 36th ed. (CRC, Cleveland, 1954).
34. M. A. Spaid and G. M. Homsy, "Stability of Newtonian and viscoelastic dynamic contact lines," Phys. FluidsPHFLE61070-663110.1063/1.868800 8, 460 (1996).
35. M. H. Eres, L. W. Schwartz, and R. V. Roy, "Fingering phenomena for driven coating films," Phys. FluidsPHFLE61070-663110.1063/1.870382 12, 1278 (2000).
36. L. W. Schwartz, "Viscous flows down an inclined plane: Instability and finger formation," Phys. Fluids APFADEB0899-821310.1063/ 1.857466 1, 443 (1989).
37. A. Q. Shen, "Granular fingering patterns in horizontal rotating cylinders," Phys. FluidsPHFLE61070-663110.1063/1.1428748 14, 462 (2002).
38. N. N. Yanenko, Metod Drobnykh Shagov Resheniya Mnogomernykh Zadach Matematicheskoi Fiziki, The Method of Fractional Steps, edited by M. Holt (Springer, New York, 1971).
39. P. L. Evans, "Mathematical and numerical investigations of coating flows," Ph.D. thesis, University of Delaware, 2000.