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

Abstract

The eigen axisymmetric oscillations of a cylindrical gas bubble surrounded by an incompressible fluid with free deformable interface are considered. 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. It’s found that the eigen frequency can vanish in some wetting parameter interval for the volume mode of natural oscillations (which describes the radial compression of the bubble). 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.