Influence of substrate properties on a fluid drop’s free translational oscillations

Abstract

The liquid drop’s natural translational oscillations are considered. The equilibrium form of this drop is a circular cylinder. Its axis of symmetry is perpendicular to two parallel solid substrates. The properties (wetting, roughness etc.) of these surfaces differ from each other. The drop is in another liquid. The contact angles’s changes are linearly proportional to the velocities of both contact lines. The Fourier series form by Laplace’s operator eigenfunctions are used for the problem solution. A system of complex equations of eigenvalue problem is solved numerically. The main frequency of the translational mode becomes zero after a critical Hocking’s parameter in situation of identical plates. The branching point of a decrement curve agrees with the zero point of a fundamental frequency. This frequency may not be vanishing on nonidentical surfaces of plates.