Three-dimensional ribbing instability in symmetric forward-roll film-coating processes

Journal of Fluid Mechanics

Volumn 335, Issue , 1997, Pages 323-359

  Gurfinkel Castillo, Mariano E ^a,b   Patera, Anthony T ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

^b PDVSA INTEVEP   (Venezuela)

Author keywords

[No Author keywords available]

Indexed keywords

CAPILLARY FLOW; COATING TECHNIQUES; COMPUTER SIMULATION; STABILITY; SURFACE TENSION; TRANSITION FLOW; VISCOUS FLOW;

SPLITTING MENISCUS INSTABILITY; SYMMETRIC FORWARD ROLL FILM COATING; THREE DIMENSIONAL RIBBING INSTABILITY;

UNSTEADY FLOW;

FLUID FLOW; INSTABILITY; VISCOUS FLUIDS; WAVES;

EID: 0031104555     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112096004600     Document Type: Article

References (49)

1. BENKREIRA, H., EDWARDS, M. & WILKINSON, W. 1982 Ribbing instability in the roll coating of Newtonian fluids. Plastics Rubber Proc. Applics. 2, 137-144.
2. BRUYN, J. & PAN, L. 1995 Delayed onset of ribbing instability due to finite-size effects. Phys. Fluids 7, 2185-2190.
3. CANEDO, E. L. & DENSON, C. D. 1989 Flow in driven cavities with a free surface. AIChE J. 35, 129-38.
4. CHRISTODOLOU, K. & SCRIVEN, L. 1989 The fluid mechanics of slide coating. J. Fluid Mech. 208, 321-354.
5. COHEN, E. & GUTOFF, E. 1992 Modern Coating and Drying Technology. VCH Publishers, New York.
6. COYLE, D. 1992 Roll coating. In Modern Coating and Drying Technology (ed. E. D. Cohen & E. B. Gutoff), chap. 3, pp. 63-115. VCH Publishers, New York.
7. COYLE, D., MACOSKO, C. & SCRIVEN, L. 1986 Film splitting flows in forward roll coating J. Fluid Mech. 171, 183-208.
8. COYLE, D., MACOSKO, C. & SCRIVEN, L. 1990a The fluid dynamics of reverse roll coating. AIChE J. 36, 161-174.
9. COYLE, D., MACOSKO, C. & SCRIVEN, L. 1990b Stability of symmetric film-splitting between counter-rotating cylinders. J. Fluid Mech. 216, 437-458.
10. DECRÉ, M., GAILLY, E. & BUCHLIN, J.-M. 1995 Meniscus shape experiments in forward roll coating. Phys. Fluids 7, 458-467.
11. DONEA, J. 1983 Arbitrary Lagrangian-Eulerian finite element methods. In Computational Methods for Transient Analysis (ed. T. Belytschko & T. Hughes), chap. 10. North Holland.
12. DOWSON, D. & TAYLOR, C. 1979 Cavitation in bearings. Ann. Rev. Fluid Mech. 11, 35-66.
13. DUSSAN V., E. & DAVIS, S. 1986 Stability in systems with moving contact lines. J. Fluid Mech. 173, 115-130.
14. FISCHER, P. F. & PATERA, A. T. 1991 Parallel spectral element solution of the Stokes problem. J. Comput. Phys. 92, 380-421.
15. FISCHER, P. F. & PATERA, A. T. 1994 Parallel simulation of viscous incompressible flows. Ann. Rev. Fluid Mech. 26, 483-527.
16. GURFINKEL CASTILLO, M. E. 1995 Modelling and parallel simulation of three-dimensional ribbing instability in symmetric forward-roll coating processes. PhD thesis, Massachusetts Institute of Technology.
17. GUTOFF, E. B. 1993 Avoid coating and drying defects. Chem. Engng Prog., Jan, 49-55.
18. HAKIM, V., RABAUD, M., THOMÉ, H. & COUDER, Y. 1990 Directional growth in viscous fingering. In New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena (ed. P. Huerre), vol. 237, pp. 327-337. Plenum.
19. HASEGAWA, T. & SORIMACHI, K. 1993 Wavelength and depth of ribbing in roll coating and its elimination. AIChE J. 39, 935-945.
20. Ho, L. 1989 A Legendre spectral element method for simulation of incompressible unsteady viscous free-surface flows. PhD thesis, Massachusetts Institute of Technology.
21. Ho, L.-W. & PATERA, A. T. 1990 A Legendre spectral element method for simulation of unsteady incompressible viscous free-surface flows. Comput. Meth. Appl. Mech. Engng 80, 355-366.
22. Ho, L.-W. & PATERA, A. T. 1991 Variational formulation of three dimensional viscous free-surface flows: Natural imposition of surface tension boundary conditions. Intl J. Numer. Meth. Fluids 13, 691-698.
23. Ho, L.-W. & RØNQUIST, E. 1992 Spectral element solution of steady incompressible viscous free-surface flows. In Proc. Intl Conf. on Spectral and High Order Methods for Partial Differential Equations, Le Corum, Montpellier, France, pp. 347-367. North-Holland.
24. KHESHGI, H. S. 1989 Profile equations for film flows at moderate Reynolds numbers. AIChE J. 35, 1719-1727.
25. KISTLER, S. & SCRIVEN, L. 1983 Coating flows. In Computational Analysis of Polymers (ed. J. Pearson & S. Richardson), chap. 8, pp. 243-299. Barking, Essex, England.
26. KISTLER, S. & SCRIVEN, L. 1994 The teapot effect: sheet-forming flows with deflection, wetting and hysteresis. J. Fluid Mech. 263, 19-62.
27. LEE, K.-Y., LIU, L.-D. & LIU, T.-J. 1992 Minimum wet thickness in extrusion slot coating. Chem. Engng Sci. 47, 1703-1713.
28. LEVICH, B. 1962 Physicochemical Hydrodynamics. Prentice Hall.
29. MADAY, Y. & PATERA, A. T. 1989 Spectral element methods for the Navier-Stokes equations. In State-of-the-art Surveys on Computational Mechanics (ed. J. Oden & A. Noor), pp. 71-143. ASME.
30. NEKTON™ Users Guide. Nektonics, Inc. Version 2.85.
31. MILL, C. & SOUTH, G. 1967 Formation of ribs on rotating rollers. J. Fluid Mech. 28, 523-529.
32. ORCHARD, S. 1962 On surface levelling in viscous liquids and gels. Appl. Sci. Res. 11, 451-464.
33. PEARSON, J. 1960 The instability of uniform viscous flow under rollers and spreaders. J. Fluid Mech. 7, 481-500.
34. PITTS, E. & GREILLER, B. 1961 The flow of thin liquid films between rollers. J. Fluid Mech. 11, 33-50.
35. PRANCKH, F. & SCRIVEN, L. 1990 Elastohydrodynamics of blade coating. AIChE J. 36, 587-597.
36. PROBSTEIN, R. F. 1995 Physicochemical Hydrodynamics: An Introduction. John Wiley and Sons.
37. RABAUD, M., COUDER, Y. & MICHALLAND, S. 1991 Wavelength selection and transients in the one-dimensional array of cells of the printer's instability. Eur. J. Mech. B/Fluids 10, 253-260.
38. REINELT, D. 1995 The primary and inverse instabilities of directional viscous fingering. J. Fluid Mech. 285, 303-327.
39. RØNQUIST, E. 1988 Optimal spectral element methods for the unsteady three-dimensional incompressible Navier-Stokes equations. PhD thesis, Massachusetts Institute of Technology.
40. RØNQUIST, E. 1991 A domain decomposition method for elliptic boundary value problems: Application to unsteady incompressible fluid flow. In Proc. Fifth Intl Conf. on Domain Decomposition Methods for Partial Differential Equations. Norfolk, Virginia, (ed. D. E. Keyes, T. F. Chan, G. A. Meurant, J. S. Scroggs & R. G. Voigt), pp. 545-557. SIAM, Philadelphia.
41. RUSCHAK, K. 1980 A method for incorporating free boundaries with surface tension in finite element fluid flow simulators. Intl J. Numer. Meth. Engng 15, 639-648.
42. RUSCHAK, K. 1983 A three-dimensional linear stability analysis for two dimensional free boundary flows by the finite element method. Comput. Fluids 11, 391-401.
43. RUSCHAK, K. 1985 Coating flows. Ann. Rev. Fluid Mech. 17, 65-89.
44. SAFFMAN, P. G. 1986 Viscous fingering in Hele-Shaw cells. J. Fluid Mech. 173, 73-94.
45. SAFFMAN, P. G. & TAYLOR, G. I. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245, 312-342.
46. SAVAGE, M. 1977 Cavitation in lubrication. J. Fluid Mech. 80, 743-768.
47. TAYLOR, G. I. 1963 Cavitation of a viscous fluid in narrow passages. J. Fluid Mech. 14, 595-619.
48. TSIVERIOTIS, K. & BROWN, R. 1992 Boundary-conforming mapping applied to computations of highly deformed solidification interfaces. Intl J. Numer. Meth. Fluids 14, 981-1003.
49. WANG, F. & DOMOTO, G. 1994 Free surface Taylor vortices. J. Fluid Mech. 261, 169-198.