Effect of the contact-line dynamics on the natural oscillations of a cylindrical droplet

The natural oscillations of a cylindrical droplet of an inviscid liquid surrounded by a different liquid and bounded in the axial direction by solid planes are studied. The motion of the contact line is described using an effective boundary condition. The dependence of the frequency and damping ratio on the capillary parameter is found. It is shown that the fundamental frequency of the translation mode vanishes beginning from a certain value of the capillary parameter. Depending on the ratio of the radial and axial dimensions of the droplet, the fundamental frequency of the axisymmetric mode and modes higher than the translation mode can vanish in a certain range of the capillary parameter. This dependence of the natural oscillation frequencies on the problem parameters allows one to determine the capillary parameter.