A model for gravity driven flow of a thin liquid-solid solution with evaporation effects

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 56, Issue 5, 2005, Pages 852-873

  Hayes, M ^a   O'Brien, S B G ^a  

^a UNIVERSITY OF LIMERICK   (Ireland)

Author keywords

Evaporation; Solution; Thin film

Indexed keywords

EID: 24144443191     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-005-3098-3     Document Type: Article

References (33)

1. Acheson D. J., Elementary Fluid Dynamics, O.U.P. 1990.
2. Anturkar N. R., Papanastasiou T. C., Wilkes J. O. Lubrication theory for n-layer thin film flow with applications to multilayer extrusion and coating, Chemical Engineering Science 45 (1990), 3271-3282.
3. Burelbach J. P., Bankoff S. G. & Davis S. H., Nonlinear stability of evaporating/condensing films, J. Fluid Mech. 195 (1988), 463-194.
4. Chen B. T., Investigation of the solvent-evaporation effect on spin-coating of thin films, Polymer Engineering and Science 23 (1983), 399-403.
5. Davis S. H., Interfacial fluid dynamics. Perspectives in Fluid Dynamics, CUP (2000), 1-51.
6. Deryagin B. V. and Levi, S. M., Film Coating Theory. Focal Press, London 1964.
7. Emslie A. G., Bonner F. T., Peck L. G., Flow of a viscous liquid on a rotating disc. J. Appl. Phys. 29 (1958), 858-862.
8. Groenveld P., Drainage and withdrawal of liquid films. AIChE J. 17 (1971), 489-490.
9. Hayes M., Models for coating flows, Ph. D. thesis, University of Limerick, 2001.
10. Howison S. D., Moriarty J. A., Ockendon J. R., Terrill E. L., Wilson S. K., A Mathematical model for drying paint layers. J. Eng. Math. 32 (1997), 377-394.
11. Huppert, H. E., Flow and instability of a viscous current down a slope. Nature 300 (1982), 427-429.
12. Jeffreys H., Draining of a vertical plate. Proc. Camb. Phil. Soc. 26 (1930), 204-205.
13. rd Eur. Coating Symp., Erlangen-Nurnberg, (Editors: F. Durst, H. Raszillier), (1999), 253-258.
14. Lammers J. H., O'Brlen S. B. G., Effects of evaporation during spin-coating, in The mechanics of thin film coatings (Editors: P. H. Gaskell, M. D Savage, J. L. Summers), World Scienciflc Press 1999, 397-403.
15. Lammers J. H., Decre M., O'Brien S. B. G., Spin-coating over topography. Second European Coating Symposium. Strasbourg. (Editors: P. Bourgin), 1997, 278-290.
16. Lammers J. H., private communication.
17. Lang K. C., Tallmadge J. A., A postwithdrawal expression for drainage on flat plates. Ind. Eng. Chem. Fundam. 10 (1971), 648-650.
18. Meyerhofer D., Characteristics of resist films produced by spinning. J. Appl. Physics. 49 (1978), 3993-3997.
19. Moriarty J. A., Schwartz L. W., Tuck E. O., Unsteady spreading of thin liquid films with small surface tension. Physics of Fluids 3 (1991), 733-742.
20. Myers T. G., Thin films with high surface tension. SIAM Rev. 40 (1998), 441-462.
21. O'Brien S. B. G. and Gath E. G., The location of a shock in rimming flow. Phys. Fluids 10 (1998), 1040-1042.
22. O'Brien S. B. G., Marangoni drying: non-linear waves in a thin film, J. Fluid Mech. 254 (1993), 649-670.
23. O'Brien S. B. G., Schwartz L. W., Theory and modelling of thin liquid films, Encyclopedia of Surface and Colloid Science, 2000, 5283-5297.
24. Overdiep W. S., The levelling of paints, Prog. Org. Coatings. 14 (1986), 159-169.
25. Oron A., Davis S. H., Bankoff S. G., Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69 (1997), 931-980.
26. Peurrung, L. M., Graves, D. B., Film thickness profiles over topography in spin-coating. Journal of the electrochemical society 138(7) (1991), 2115-2124.
27. Rauscher J. W., Kelly R. E., Cole J. D., An asymptotic solution for the laminar flow of a thin film on a rotating disc. Transactions of the ASME (Journal of Applied Mechanics), March 1973, 200-205.
28. Reisfeld B., Bankoff S. G., Davis S. H., The dynamics and stability of thin liquid-films during spin coating. 1. Films with constant rates of evaporation or absorption. J. Appl. Phys. 70 (1991), 5258-5266.
29. Reisfeld B., Bankoff S. G., Davis S. H., The dynamics and stability of thin liquid-films during spin coating. 2. Films with unit-order and large Peclet numbers. J. Appl. Phys. 70, 5267-5277.
30. Rosenberg, L. D. and Beiter, R. L., Impact of New Technology and Changing Practices in the Automotive Coating Business. AIChE Symposium Series on New Polymer Technology for Auto Body Exteriors, 1989, 33-36.
31. Van Rossum, J., Viscous lifting and drainage of liquid. Appl. Sci. Res. A. 7 (1958), 121-144.
32. Saito H., Scriven L. E., Study of coating flow by the finite element method. J. Comp. Phys. 42 (1981), 53-76.
33. Weidner, D. E., Schwartz, L. W., Eley, R. R., Role of surface tension gradients in correcting coating defects in corners. J. Colloid Interface Sci. 179 (1996), 66-75.