“…In contrast to the second stage, the pressure difference in and out the bubble is bigger, and the size of bubble, especially the thickness D bmax of ventilation bubble, increases faster, as can be seen in frame (a) of figure 18, when γ ⩽ 0.125. Besides, the free surface begins to exert a repulsive force to the upper side of ventilation bubble, similar to the Bjerknes force between surfaces bubbles (Vanhille and Campos Pozuelo 2014) or free surface and bubble (Li et al 2016, Cui et al 2018, which induces the center of the ventilation bubble to move downward, however this effect is relatively small based on the experiment data in frames (c) and (d), in which the declination trend of L bcenter L bmax and D bcenter D bmax have no obvious change. Which should be mentioned is that as the moving cylinder is nearly touching the freesurface, the ventilation bubble becomes 'fat', since D bmax has an apparent increase at this stage, as can be seen in frames (a) and (d).…”