The Dynamics of Thin Films I: General Theory

SIAM Journal on Applied Mathematics

Volumn 58, Issue 2, 1998, Pages 456-473

  Ida, M P ^a   Miksis, M J ^a  

^a NORTHWESTERN UNIVERSITY   (United States)

Author keywords

Lamella; Matched asymptotic expansion; Stability

Indexed keywords

DYNAMICS; LOADS (FORCES); MATHEMATICAL TECHNIQUES; STABILITY; SURFACE ACTIVE AGENTS; SURFACE TENSION;

MATCHED ASYMPTOTIC EXPANSION;

THIN FILMS;

EID: 0032048569     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0036139995289556     Document Type: Article

References (30)

1. R. ARIS, Vectors, Tensors, and the Basic Equations of Fluid Mechanics, Dover, New York, 1989. Original edition, Prentice-Hall, Englewood Cliffs, NJ, 1962.
2. J. P. BURELBACH, S. G. BANKOFF, AND S. H. DAVIS, Nonlinear stability of evaporating/condensing liquid films, J. Fluid Mech., 195 (1988), pp. 463-494.
3. J. P. BURELBACH, S. G. BANKOFF, AND S. H. DAVIS, Steady thermocapillary flows of thin liquid layers II. Experiment, Phys. Fluids A, 2 (1990), pp. 322-333.
4. L. F. CRABTREE, D. KÜCHEMANN, AND L. SOWERBY, Three dimensional boundary layers, in Laminar Boundary Layers, L. Rosenhead, ed., Dover, New York, 1988, pp. 409-491. Original edition, Clarendon Press, Oxford, 1963.
5. A. DE WITT, D. GALLEZ, AND C. I. CHRISTOV, Nonlinear evolution equations for thin liquid films with insoluble surfactants, Phys. Fluids, 6 (1994), pp. 3256-3266.
6. L. P. EISENHART, A Treatise on the Differential Geometry of Curves and Surfaces, Ginn & Co., Boston, 1909.
7. L. P. EISENHART, An Introduction to Differential Geometry with Use of the Tensor Calculus, Princeton Univ. Press, Princeton, NJ, 1947.
8. T. ERNEUX AND S. H. DAVIS, Nonlinear rupture of free films, Phys. Fluids A, 5 (1993), pp. 1117-1122.
9. R. FINN, Equilibrium Capillary Surfaces, Springer-Verlag, New York, 1986.
10. R. J. GUMERMAN AND G. M. HOMSY, The stability of radially bounded thin films, Chem. Engrg. Commun., 2 (1975), pp. 27-36.
11. L. M. HOCKING, The influence of intermolecular forces on thin fluid layers, Phys. Fluids A, 5 (1993), pp. 793-799.
12. M. P. IDA, The Dynamics of Thin Liquid Films, Ph.D. thesis, Northwestern University, Evanston, IL, 1995.
13. M. P. IDA AND M. J. MIKSIS, Dynamics of a lamella in a capillary tube, SIAM J. Appl. Math., 55 (1995), pp. 23-57.
14. M. P. IDA AND M. J. MIKSIS, The dynamics of thin films II: Applications, 58 (1998), pp. 474-500.
15. 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.
16. E. KREYSZIG, Differential Geometry, Dover, New York, 1991. Original edition, Univ. of Toronto Press, 1959 (Mathematical Expositions 11).
17. C. MALDARELLI, R. K. JAIN, I. B. IVANOV, AND E. RUCKENSTEIN, Stability of symmetric and unsymmetric thin liquid films to short and long wavelength perturbations, J. Colloid Interface Sci., 78 (1980), pp. 119-143.
18. J. F. PATZER, II AND G. M. HOMSY, Hydrodynamic stability of thin spherically concentric fluid shells, J. Colloid Interface Sci., 51 (1975), pp. 499-508.
19. M. PRÉVOST AND D. GALLEZ, Nonlinear rupture of thin free liquid films, J. Chem. Phys., 84 (1986), pp. 4043-4048.
20. E. RUCKENSTEIN AND R. K. JAIN, Spontaneous rupture of thin liquid films, J. Chem. Soc. Faraday Trans. II, 70 (1974), pp. 132-147.
21. L. E. SCRIVEN, Dynamics of a fluid interface equation of motion for Newtonian surface fluids, Chem. Engrg. Sci., 12 (1960), pp. 98-108.
22. A. SHARMA AND E. RUCKENSTEIN, Rupture of thin free films with insoluble surfactants: Non- linear aspects, AIChE Symp. Ser., 252 (1986), pp. 129-144.
23. C. V. STERNLING AND L. E. SCRIVEN, Interfacial turbulence: Hydrodynamic stability and the Marangoni effect, AIChE J., 5 (1959), pp. 514-523.
24. H. A. STONE, A simple derivation of the time-dependent convective-diffusive equation for surfactant transport along a deforming interface, Phys. Fluids A, 2 (1990), pp. 111-112.
25. M. J. TAN, S. G. BANKOFF, AND S. H. DAVIS, Steady thermocapulary flows of thin liquid layers I. Theory, Phys. Fluids A, 2 (1990), pp. 313-321.
26. 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), pp. 359-376.
27. A. VRIJ, Possible mechanism for the spontaneous rupture of thin, free liquid films, Discuss. Faraday Soc., 42 (1966), pp. 23-33.
28. A. M. WAXMAN, Dynamics of a couple-stress fluid membrane, Stud. Appl. Math., 70 (1984), pp. 63-86.
29. C. E. WEATHERBURN, Advanced Vector Analysis, Bell's Mathematical Series, Advanced Section, G. Bell and Sons, London, 1947. Reprinted, Open Court, LaSalle, IL, 1948.
30. M. B. WILLIAMS AND S. H. DAVIS, Nonlinear theory of film rupture, J. Colloid Interface Sci., 90 (1982), pp. 220-228.