Behavior of a cylindrical bubble under vibrations

Eigen and forced vibrations of a cylindrical gas bubble surrounded by an incompressible fluid with a free non-deformable external interface are investigated. The bubble is bounded by two parallel solid planes. The system is subjected to an external vibration field. The contact line dynamics is taken into account by an effective boundary condition, and the contact line velocity is assumed to be proportional to deviation of the contact angle from the equilibrium value. The coefficient of proportionality, so-called wetting parameter (Hocking’s constant), characterizes the properties of the fluid and the substrate material. The equilibrium contact angle is right. An axially symmetric mode of eigen oscillations is studied; the dependence of frequencies and decrements on problem parameters is investigated. It has been found that for the main even mode of eigen oscillations (which describes the radial compression of the bubble) the frequency of eigen oscillations can vanish in some wetting parameter interval. The length of this interval increases with increasing ratio of the equilibrium bubble radius to the height. The eigen frequencies of other modes decrease with increasing Hocking’s constant. The lowest natural frequency is observed for the freely sliding bubble. The existence of «anti-resonance» frequencies is demonstrated, i.e. the values of external frequencies when the bubble interface does not deviate from the equilibrium value.