Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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

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