Influence of Viscosity on the Behavior of a Drop (Bubble) in Liquid Under the Influence of Vibrations

The paper studies the effect of viscosity on oscillations of a liquid or gaseous inclusion (a drop or a gas bubble) in a fluid of uniform density under the action of external vibrations. It is assumed that the vibration amplitude is small and the frequency is high, however, the vibration velocity and the thickness of the dynamic boundary layers are finite. Numerical modeling of the inclusion behavior in a non-averaged formulation using the liquid volume method is performed. The effect of viscous dissipation on the amplitude of inclusion oscillations and its averaged shape is studied. The fields of flows generated by vibrations near the inclusion for different vibration parameters are obtained. The numerical data are compared with known analytical results. Corrections are proposed that take into account viscous dissipation that occurs when the vibration frequency decreases.