The translational oscillations of a cylindrical bubble in a bounded volume of a liquid with free deformable interface

Abstract

We consider the eigen and forced translation oscillations of a cylindrical gas bubble surrounded by an incompressible fluid with free deformable interface. The bubble has an equilibrium cylindrical shape and is bounded axially by two parallel solid surfaces. Dynamics of contact lines is taken into account by an effective boundary condition: velocity of the contact line is assumed to be proportional to contact angle deviation from the equilibrium value. The equilibrium contact angle is right. Eigen frequency decreases with liquid outer free surface radius decreasing and increases with the radius-to-height ratio increasing. We found that the main translational frequency of eigen oscillation vanishes at a certain value of the Hocking parameter (the so-called wetting parameter). The eigen frequencies of the bubble are higher than the eigen frequencies of fluid volume.