The deformed oblate drop’s free translational oscillations

Abstract

Free translational oscillations of deformable liquid droplet are considered. It is placed into a vessel filled with another liquid. This droplet has an equilibrium revolution shape. The revolution axis of this form is perpendicular two parallel solid plates – floor and cover of vessel. The arbitrary equilibrium contact angle between the interface and the solid substrate can take arbitrary values in the range 0 and π. A contact line velocity is linearly proportional to contact angle deviation from its initial position. Proportionality coefficients (Hocking’s parameters) are individual for any substrate. They characterize individual dissipation coefficient, but whole system’s dissipation is proportional to a sum of all coefficients. There are three characteristic natural frequency intervals for the case of small aspect ratio. High frequencies are the capillary wave frequencies at the interface. The middle frequency is the fundamental or main one. Low frequencies correspond to the drop oscillations with a stationary contact angle. The cylindrical droplet has the highest frequency.