Average Deformation of Sessile Drop Under High Frequency Vibrations

The behavior of a liquid drop placed on an oscillating solid substrate is studied. The vibrations are normal to the plane of the substrate. The amplitude of the vibrations is assumed to be small compared to the radius of the drop, and the vibration frequency is suppose to be much larger than the frequencies of the natural oscillations of the drop shape. The effect of vibrations on the drop shape is studied for a small values of the vibration parameter equal to the ratio of the vibration pressure to the capillary pressure. It is assumed that the drop surface in the absence of vibrations is hemispherical. Under the influence of vibrations, the drop height decreases and the base area increases. In this case, the surface deformation changes proportionally to the vibration parameter. At finite values of the vibration parameter, the quasi-equilibrium shape can differ significantly from spherical. In this case, the problem for pulsations is solved numerically using the boundary element method. To determine the average shape of a drop at finite values of the vibration parameter, the variational principle is used. The obtained results are in good agreement with the solution in the limit of small values of the vibration parameter. With an increase in the vibration parameter, the average contact angle decreases, the area of the base area increases, and the height decreases.