Azimuthal modes of eigen oscillations of a cylindrical bubble

The azimuthal modes of eigen oscillations of a cylindrical gas bubble surrounded by an incom­pressible fluid with a free non-deformable external interface are investigated in this article. A surface tension coefficient of external interface is small and negligible. Bubble is bounded by two parallel solid planes. Dynamics of contact line is taken into account by an effective boundary con­dition: velocity of the contact line is assumed to be proportional to deviation of the contact angle from the equilibrium value. The equilibrium contact angle is right. Depending on the frequency and damping rates of the parameters of the problem are investigated. It is shown that the funda­mental frequency of any mode may vanish at a certain range of wetting parameter values. Eigen frequency decreases with increasing radius of the outer liquid surface, increase with the geometri­cal parameter and do not depend on the gas pressure inside the bubble.