The influence of the substrate surface heterogeneity on axisymmetric oscillations of a drop in a finite volume of liquid

Abstract

The article deals with the influence of substrate properties on drop dynamics in a vibration field. Natural and forced oscillations of a liquid drop surrounded by another liquid in a cylindrical vessel of a finite volume are investigated. In the equilibrium state, the drop has the shape of a cylinder and is limited in the axial direction by two parallel solid surfaces. The dynamics of the contact line of three media (drop–liquid–solid surface) is taken into account: the velocity of the contact line is proportional to the deviation of the contact angle from its equilibrium value. The proportionality coefficient (wetting parameter) is a function of the substrate surface coordinates, which allows us to consider this surface as inhomogeneous. The vessel is exposed to a vibration force directed along the symmetry axis of the vessel. Such vibrations excite only axisymmetric oscillations of the drop, but, due to the inhomogeneity, azimuthal modes will be excited, the spectrum of which is determined by the type of inhomogeneity. The dependence of frequencies and damping decrements of natural oscillations on the parameters of the problem is investigated. It is shown that heterogeneity qualitatively changes these dependences in comparison with the case of a homogeneous surface. The study of forced oscillations has revealed clearly noticeable resonance effects. It is shown that resonance frequencies of azimuthal modes are present.