A theory for the wave-induced motion of finite monomolecular films
Author:
B. D. Dore
Journal:
Quart. Appl. Math. 43 (1985), 37-55
MSC:
Primary 76T05; Secondary 76A10
DOI:
https://doi.org/10.1090/qam/782255
MathSciNet review:
782255
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Abstract: The fluctuating velocity field of monomolecular films of arbitrary configuration is investigated when gravity waves propagate on the air-water interface. The surface-active material is assumed to have visco-elastic properties and to be insoluble. Boundary-layer techniques are employed, and a Dirichlet boundary value problem, involving Helmholtz’ equation for the divergence of the velocity field, is obtained for the film. Circular and rectangular films are considered explicitly, whilst an approximate method is given for slender films of arbitrary orientation. Application is made to viscous wave-damping.
J. T. Davies and R. W. Vose, On the damping of capillary waves by surface films, Proc. Roy. Soc. (London) A286, 218–234 (1965)
R. Defay, I. Prigogine and A. Bellemans, Surface tension and adsorption, Longmans, Green & Co. Ltd., London, 1966, p. 10
B. D. Dore, Oscillatory response of a monomolecular slick to progressive waves, Arch. Met. Geoph. Biokl. A31, 385–397 (1982)
B. D. Dore and D. Porter, The edge effect of a surface film on gravity waves, J. Inst. Maths. Applics. 14, 119–129 (1974)
B. D. Dore, Some effects of the air-water interface on gravity waves, Geophys. Astrophys. Fluid Dyn. 10, 215–230 (1978)
- R. Dorrestein, General linearized theory of the effect of surface films on water ripples. I, II, Nederl. Akad. Wetensch. Proc. Ser. B. 54 (1951), 260–272, 350–356. MR 0044282
F. C. Goodrich, The mathematical theory of capillarity. II, Proc. Roy. Soc. (London) A260, 490–502 (1961)
H. Hühnerfuss, W. Alpers, W. L. Jones, P. A. Lange and K. Richter, The damping of ocean surface waves by a monomolecular film measured by wave staffs and microwave radars, J. Geophys. Res. 86, 429–438 (1981)
- Horace Lamb, Hydrodynamics, 6th ed., Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1993. With a foreword by R. A. Caflisch [Russel E. Caflisch]. MR 1317348
V. G. Levich, Physicochemical hydrodynamics, Prentice-Hall, Inc., New Jersey, 1962
E. H. Lucassen-Reynders and J. Lucassen, Properties of capillary waves, Advan. Colloid Interface Sci. 2, 347–395 (1969)
W. D. Mallinger and T. P. Mickelson, Experiments with monomolecular films on the surface of the open sea, J. Phys. Oceanogr. 3, 328–336 (1973)
J. W. Miles, Surface-wave damping in closed basins, Proc. Roy. Soc. (London) A297, 459–475 (1967)
J. C. Slattery, Interfacial transport phenomena, Chem. Eng. Commun. 4, 149–166 (1980)
J. C. Slattery and R. W. Flumerfelt, Interfacial phenomena, ch. 1.4 of Handbook of Multiphase Systems (G. Hetsroni, ed.), Hemisphere Publishing Corporation, Washington, 1982, p. 1–224
- G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
J. T. Davies and R. W. Vose, On the damping of capillary waves by surface films, Proc. Roy. Soc. (London) A286, 218–234 (1965)
R. Defay, I. Prigogine and A. Bellemans, Surface tension and adsorption, Longmans, Green & Co. Ltd., London, 1966, p. 10
B. D. Dore, Oscillatory response of a monomolecular slick to progressive waves, Arch. Met. Geoph. Biokl. A31, 385–397 (1982)
B. D. Dore and D. Porter, The edge effect of a surface film on gravity waves, J. Inst. Maths. Applics. 14, 119–129 (1974)
B. D. Dore, Some effects of the air-water interface on gravity waves, Geophys. Astrophys. Fluid Dyn. 10, 215–230 (1978)
R. Dorrestein, General linearized theory of the effect of surface films on water ripples. I & II, Nederl. Aka. van Wetenschappen B54, 260–272; 350–356 (1951)
F. C. Goodrich, The mathematical theory of capillarity. II, Proc. Roy. Soc. (London) A260, 490–502 (1961)
H. Hühnerfuss, W. Alpers, W. L. Jones, P. A. Lange and K. Richter, The damping of ocean surface waves by a monomolecular film measured by wave staffs and microwave radars, J. Geophys. Res. 86, 429–438 (1981)
H. Lamb, Hydrodynamics, Cambridge University Press, Cambridge, 1932
V. G. Levich, Physicochemical hydrodynamics, Prentice-Hall, Inc., New Jersey, 1962
E. H. Lucassen-Reynders and J. Lucassen, Properties of capillary waves, Advan. Colloid Interface Sci. 2, 347–395 (1969)
W. D. Mallinger and T. P. Mickelson, Experiments with monomolecular films on the surface of the open sea, J. Phys. Oceanogr. 3, 328–336 (1973)
J. W. Miles, Surface-wave damping in closed basins, Proc. Roy. Soc. (London) A297, 459–475 (1967)
J. C. Slattery, Interfacial transport phenomena, Chem. Eng. Commun. 4, 149–166 (1980)
J. C. Slattery and R. W. Flumerfelt, Interfacial phenomena, ch. 1.4 of Handbook of Multiphase Systems (G. Hetsroni, ed.), Hemisphere Publishing Corporation, Washington, 1982, p. 1–224
G. N. Watson, Theory of Bessel functions, Cambridge University Press, Cambridge, 1944
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Article copyright:
© Copyright 1985
American Mathematical Society
