Surface-tension-driven flow on a moving curved surface

Journal of Engineering Mathematics

Volumn 45, Issue 3-4, 2003, Pages 283-308

  Howell, P D ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Asymptotic expansions; Surface tension; Thin liquid films

Indexed keywords

LUBRICATION; SUBSTRATES; THIN FILMS; VISCOSITY;

SURFACE-TENSION-DRIVEN FLOW;

SURFACE TENSION;

FILM THICKNESS; LIQUID FILM; LUBRICATION; SURFACE TENSION; VISCOSITY;

EID: 0037387528     PISSN: 00220833     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022685018867     Document Type: Article

References (32)

1. L. D. Landau and V. G. Levich, Dragging of a liquid by a moving plate. Acta Physicochim. URSS 17 (1942) 42-54.
2. S. D. R. Wilson, The drag-out problem in film coating theory. J. Engng. Math. 16 (1982) 209-221.
3. W. S. Overdiep, The levelling of paints. Prog. Org. Coat. 14 (1986) 159-175.
4. H. Wong, I. Fatt and C. J. Radke, Deposition and thinning of the human tear film. J. Colloid Interface Sci. 184 (1996) 44-51.
5. D. Halpern and J. B. Grotberg, Fluid-elastic instabilities of liquid-lined flexible tubes. J. Fluid Mech. 244 (1992) 615-632.
6. A. Oron, S. H. Davis and S. G. Bankoff, Long-scale evolution of thin liquid films. Rev. Modern Phys. 69 (1997) 931-980.
7. T. G. Myers, Thin films with high surface tension. SIAM Rev. 40 (1998) 441-462.
8. L. E. Stillwagon and R. G. Larson, Fundamentals of topographic substrate levelling. J. Appl. Phys. 63 (1988) 5251-5258.
9. L. E. Stillwagon and R. G. Larson, Leveling of thin films over uneven substrates during spin coating. Phys. Fluids A 2 (1990) 1937-1944.
10. S. Kalliadasis, C. Bielarz and G. M. Homsy, Steady free-surface thin film flows over topography. Phys. Fluids 12 (2000) 1889-1898.
11. A. Mazouchi and G. M. Homsy, Free surface Stokes flow over topography. Phys. Fluids 13 (2001) 2751-2761.
12. L. W. Schwartz and D. E. Weidner, Modelling of coating flows on curved surfaces. J. Engng. Math. 29 (1995) 91-103.
13. M. Hayes, S. B. G. O'Brien and J. H. Lammers, Green's function for steady flow over a small two-dimensional topography. Phys. Fluids 12 (2000) 2845-2858.
14. F. P. Bretherton, The motion of long bubbles in tubes. J. Fluid Mech. 10 (1961) 166-188.
15. P. S. Hammond, Nonlinear adjustment of a thin annular film of viscous fluid surrounding a thread of another within a circular pipe. J. Fluid Mech. 137 (1983) 363-384.
16. R. W. Atherton and G. M. Homsy, On the derivation of evolution equations for interfacial waves. Chem. Engng. Comm. 2 (1976) 57-77.
17. M. Cheng and H.-C. Chang, Stability of axisymmetric waves on liquid films flowing down a vertical column to azimuthal and streamwise disturbance. Chem. Engng. Comm. 118 (1992) 327-334.
18. A. L. Frenkel, On evolution equations for thin films flowing down solid surfaces. Phys. Fluids A 5 (1993) 2342-2347.
19. B. Reisfeld and S. G. Bankoff, Non-isothermal flow of a liquid film on a horizontal cylinder. J. Fluid Mech. 236 (1992) 167-196.
20. P. A. Gauglitz and C. J. Radke, The dynamics of liquid film breakup in constricted cylindrical capillaries. J. Colloid Interface Sci. 134 (1990) 14-40.
21. O. E. Jensen, The thin liquid lining of a weakly curved cylindrical tube. J. Fluid Mech. 331 (1997) 373-403.
22. Lord Rayleigh, On the instability of jets. Proc. London Math. Soc. 10 (1878) 4-13.
23. R. V. Roy, A. J. Roberts and M. E. Simpson, A lubrication model of coating flows over a curved substrate in space. J. Fluid Mech. 454 (2002) 235-261.
24. H. E. Huppert, Flow and instability of a viscous current down a slope. Nature 300 (1982) 427-429.
25. S. M. Troian, E. Herbolzheimer, S. A. Safran and J. F. Joanny, Fingering instabilities of driven spreading films. Euro. Phys. Lett. 10 (1989) 25-30.
26. J. A. Moriarty, L. W. Schwartz and E. O. Tuck, Unsteady spreading of thin liquid films with small surface tension. Phys. Fluids A 3 (1991) 733-742.
27. B. W. van de Fliert, P. D. Howell and J. R. Ockendon, Pressure-driven flow of a thin viscous sheet. J. Fluid Mech. 292 (1995) 359-376.
28. P. D. Howell, S. L. Waters and J. B. Grotberg, The propagation of a liquid bolus along a liquid-lined flexible tube. J. Fluid Mech. 406 (2000) 309-335.
29. E. Kreyszig, Differential Geometry. New York: Dover (1991) 352pp.
30. S. D. R. Wilson and A. F. Jones, The entry of a falling film into a pool and the air-entrainment problem. J. Fluid Mech. 128 (1983) 219-230.
31. A. L. Bertozzi and M. P. Brenner, Linear stability and transient growth in driven contact lines. Phys. Fluids 9 (1997) 530-539.
32. S. Kalliadasis and G. M. Homsy, Stability of free-surface thin-film flows over topography. J. Fluid Mech. 448 (2001) 387-410.