Influence of the properties of the plate surface on the oscillations of the cramped drop

Abstract

We consider free and forced oscillations of a clamped liquid drop. The drop is surrounded by an incompressible fluid of a different density. In equilibrium, the drop has the form of a circular cylinder bounded axially by parallel solid planes, and the contact angle is right. These plates have different surface (chemical, mechanical, and geometrical) 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 aspect ratio of the drop. Frequencies of other eigenmodes of the drop decrease monotonically with increasing Hocking parameters.