Free vibrations of a drop in partial contact with a solid support

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Abstract
Under the assumptions of zero gravity, of negligible viscous effects and of small surface deformations, the problem of the axisymmetric free vibrations of a liquid drop immersed in an outer fluid and in partial contact with a spherical bowl has been analysed. Using the Green function method and expanding the velocity potentials in series of Legendre polynomials, the problem has been reduced to the solution of a single integral equation whose kernel has been expressed in analytical form. It is found that, in comparison with an isolated drop, constrained drops have an additional vibration mode which reduces to a zero-frequency rigid motion as the support size tends to zero, while the remaining ones approach the modes predicted by Lamb for a free drop.The vibration modes have been numerically calculated for different sizes of the supported surface and compared with the experimental results of Bisch, Lasek & Rodot (1982).

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