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.

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DOI:
https://doi.org/10.1090/qam/782255

Article copyright:
© Copyright 1985
American Mathematical Society