Free surface oscillation driven by rotating stirrer

To gain insights into the mechanisms of free surface oscillation in a rotating mixing container, we observe the free surface deformation and measure the torque acting on the bar. The container was half-filled with liquids. Periodic surface oscillation occurs. At the rotational speed where the amplitude of the oscillation reaches its maximum, the time-averaged torque also takes the local maximum values. To account for the sloshing mechanism, an equation of motion is derived using the Lagrangian mechanics; we found that the sloshing occurs when the collision frequency of bar on the surface is consistent with the natural frequency of the system and the damping coefficient is sufficiently smaller than unity. The time-averaged torque increases when the sloshing becomes violent. We conclude that the hydrodynamics of oscillation is successfully modeled using point-mass mechanics, and thus we can reasonably capture the rotation speed at which violent oscillation occurs. Graphical Abstract Free surface deformation driven by the rotating arm in the cylindrical container which is half-filled with liquids