Influence of the Properties of the Plate Surface on the Natural Oscillations of the Clamped Drop

Abstract

We consider free oscillations of a clamped liquid drop. An incompressible fluid of different density surrounds the drop. In equilibrium, the drop has the form of a circular cylinder bounded axially by the parallel solid planes, the contact angle is right. These plates have different surface (wetting etc.) properties. The solution is represented as a Fourier series in eigenfunctions of the Laplace operator. The resulting system of complex equations for unknown amplitudes was solved numerically. The fundamental frequency of free oscillations can vanish in a certain interval of values of the Hocking parameter. The length of this interval depends on the ratio of the drop dimensions. Frequencies of other drop eigenmodes decrease monotonically with increasing Hocking parameter.