Rupture of a surfactant-covered thin liquid film on a flexible wall

SIAM Journal on Applied Mathematics

Volumn 64, Issue 6, 2004, Pages 2144-2166

  Matar, Omar K ^a   Kumar, Satish ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Flexible walls; Rupture; Surfactants; Thin liquid films

Indexed keywords

FLEXIBLE WALLS; LINEAR STABILITY; RUPTURE; THIN LIQUID FILMS;

COMPUTER SIMULATION; DAMPING; DEFLECTION (STRUCTURES); ELECTROSTATICS; FLEXIBLE STRUCTURES; FLOW OF FLUIDS; LUBRICATION; PHASE INTERFACES; STRESSES; SURFACE ACTIVE AGENTS; VAN DER WAALS FORCES; WALLS (STRUCTURAL PARTITIONS);

THIN FILMS;

EID: 11044224589     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S003613990242002X     Document Type: Article

References (40)

1. A. ORON, S. H. DAVIS, AND S. G. BANKOFF, Long-scale evolution of thin liquid films, Rev. Modern Phys., 69 (1997), pp. 931-980.
2. E. RUCKENSTEIN AND R. K. JAIN, Spontaneous rupture of thin liquid films, Chem. Soc. Farad. Trans., 70 (1974), pp. 132-147.
3. A. SHARMA AND E. RUCKENSTEIN, An analytical nonlinear theory of thin film rupture and its applications to wetting films, J. Coll. Int. Sci., 113 (1986), pp. 456-479.
4. O. E. JENSEN AND J. B. GROTBERG, Insoluble surfactant spreading on a thin viscous film: Shock evolution and film rupture, J. Fluid Mech., 240 (1992), pp. 259-288.
5. A. L. BERTOZZI, M. P. BRENNER, T. F. DUPONT, AND L. P. KADANOFF, Singularities and similarities in interface flows, in Trends and Perspectives in Applied Mathematics, Appl. Math. Sci. 100, Springer-Verlag, New York, 1994, pp. 155-208.
6. A. L. BERTOZZI AND M. PUGH, The lubrication approximation for thin viscous films: The moving contact line with a "porous media" cut-off of van der Waals interactions, Nonlinearity, 7 (1994), pp. 1535-1564.
7. A. L. BERTOZZI AND M. PUGH, Long-wave instabilities and saturation in thin film equations, Comm. Pure Appl. Math., 51 (1998), pp. 625-661.
8. C.-C. HWANG, C.-K. LIN, AND W.-Y. UEN, A nonlinear three-dimensional rupture theory of thin liquid films, J. Coll. Int. Sci., 190 (1997), pp. 250-252.
9. W. W. ZHANG AND J. R. LISTER, Similarity solutions for van der Waals rupture of a thin film on a solid substrate, Phys. Fluids A, 11 (1999), pp. 2454-2462.
10. T. P. WITELSKI AND A. J. BERNOFF, Stability of self-similar solutions for van der Waals driven thin film rupture, Phys. Fluids A, 11 (1999), pp. 2443-2445.
11. T. P. WITELSKI AND A. J. BERNOFF, Dynamics of three-dimensional thin film rupture, Phys. D, 147 (2000), pp. 155-176.
12. M. R. E. WARNER, R. V. CRASTER, AND O. K. MATAR, Unstable van der Waals driven line rupture in Marangoni driven thin liquid films, Phys. Fluids, 14 (2002), pp. 1642-1654.
13. O. K. MATAR, R. V. CRASTER, AND M. R. E. WARNER, Surfactant transport on highly viscous surface films, J. Fluid Mech., 466 (2002), pp. 85-111.
14. B. T. ERNEUX AND S. H. DAVIS, Nonlinear rupture of free films, Phys. Fluids A, 5 (1993), pp. 1117-1122.
15. A. DEWIT, D. GALLEZ, AND C. CHRISTOV, Nonlinear evolution equations for thin liquid films with insoluble surfactants, Phys. Fluids, 6 (1994), pp. 3256-3266.
16. J. R. LISTER AND H. A. STONE, Capillary breakup of a viscous thread surrounded by another viscous fluid, Phys. Fluids A, 10 (1998), pp. 2758-2764.
17. S. NAIRE, R. J. BRAUN, AND S. A. SNOW, Limiting cases of gravitational drainage of a vertical free film for evaluating surfactants, SIAM J. Appl. Math., 61 (2000), pp. 889-913.
18. D. VAYNBLAT, J. R. LISTER, AND T. P. WITELSKI, Rupture of thin viscous films by van der Waals forces: Evolution and self-similarity, Phys. Fluids A, 13 (2001), pp. 1130-1140.
19. O. K. MATAR, Nonlinear evolution of a thin free viscous film in the presence of soluble surfactant, Phys. Fluids, 14 (2002), pp. 4216-4234.
20. E. RAMOS DE SOUZA AND D. GALLEZ, Pattern formation in thin liquid films with insoluble surfactant, Phys. Fluids, 10 (1998), pp. 1804-1820.
21. W. T. COAKLEY, D. GALLEZ, E. RAMOS DE SOUZA, AND H. GAUCI, Ionic strength dependence of localized contact formation between membranes: Nonlinear theory and experiment, Biophys. J., 77 (1999), pp. 817-828.
22. E. RAMOS DE SOUZA, C. ANTENEODO, D. GALLEZ, AND P. M. BISCH, Long-scale evolution of thin liquid films bounded by a viscous phase with diffusing charged surfactants, J. Coll. Int. Sci., 244 (2001), pp. 303-312.
23. J. N. ISRAELACHVILI, Intermolecular and Surface Forces with Applications to Colloidal and Biological Systems, Academic Press, London, 1985.
24. J. J. RILEY, M. G. EL HAK, AND R. W. METCALFE, Compliant coatings, Ann. Rev. Fluid Mech., 20 (1988), pp. 393-420.
25. J. B. GROTBERG, Pulmonary flow and transport phenomena, Ann. Rev. Fluid Mech., 26 (1994), pp. 529-571.
26. S. A. BERGER AND L.-D. JOU, Flows in stenotic vessels, Ann. Rev. Fluid Mech., 32 (2000), pp. 347-382.
27. M. S. CARVALHO AND L. E. SCRIVEN, Deformable roll coating flows: Steady state and linear perturbation analysis, J. Fluid Mech., 339 (1997), pp. 143-172.
28. V. KUMARAN AND R. MURALIKRISHNAN, Spontaneous growth of fluctuations in the viscous flow of a fluid past a soft interface, Phys. Rev. Lett., 84 (2000), pp. 3310-3313.
29. D. HALPERN AND J. B. GROTBERG, Fluid-elastic instabilities of liquid-lined flexible tubes, J. Fluid Mech., 244 (1992), pp. 615-632.
30. D. HALPERN AND J. B. GROTBERG, Surfactant effects on fluid-elastic instabilities of liquid-lined flexible tubes: A model of airway closure, J. Biomech. Engrg., 115 (1993), pp. 271-277.
31. D. A. EDWARDS, H. BRENNER, AND D. T. WASAN, Interfacial Transport Processes and Rheology, Butterworth-Heinemann, New York, 1991.
32. H. A. STONE, A simple derivation of the time-dependent convective-diffusion equation for surfactant transport along a deforming interface, Phys. Fluids A, 2 (1990), pp. 111-112.
33. H. B. ATABEK AND S. H. LEW, Wave propagation through a viscous incompressible fluid contained in an initially stressed elastic tube, Biophys. J., 6 (1966), pp. 481-503.
34. L. D. LANDAU AND E. M. LIFSHITZ, Theory of Elasticity, 3rd ed., Butterworth-Heinemann, New York, 1986.
35. A. C. GOLDENVEIZER, Theory of Elastic Thin Shells, Pergamon, New York, 1961.
36. M. R. E. WARNER, R. V. CRASTER, AND O. K. MATAR, Dewetting of surfactant covered ultra thin films, Phys. Fluids, 14 (2002), pp. 4040-4054.
37. M. B. WILLIAMS AND S. H. DAVIS, Nonlinear theory of film rupture, J. Coll. Int. Sci., 90 (1982), pp. 220-228.
38. R. F. SINCOVEC AND N. K. MADSEN, Algorithm 540 PDECOL, ACM Trans. Math. Software, 5 (1979), pp. 326-351.
39. P. KEAST AND P. H. MUIR, Algorithm 688 EPDCOL - A more efficient PDECOL code, ACM Trans. Math. Software, 17 (1991), pp. 153-166.
40. R. V. CRASTER, O. K. MATAR, AND D. T. PAPAGEORGIOU, Pinchoff and satellite formation in surfactant covered viscous threads, Phys. Fluids, 14 (2002), pp. 1364-1376.