Flow induced by the single-bubble chain depending on the bubble release frequency

In the present study, we experimentally investigated the flow induced by the in-chain bubbles (2.4–2.8 mm in size) while varying the bubble release frequency ([Formula: see text] Hz), using high-speed two-phase particle image velocimetry and shadowgraphy. Along the streamwise (vertical) direction, we identified the transition of in-chain bubble dynamics and associated liquid flow. That is, the released bubbles tend to follow the straight path initially but transition to the oscillating (zigzag or spiral) trajectories. In particular, in the developing regime (near the nozzle), the coherent behavior of bubble chain generates the rib-like oblique jet flow, deviating from the rise path, even after the onset of the path instability of each bubble. As the flow develops, the scattering of rising path along the lateral direction becomes significant, and the liquid flow shows the similarity to the typical single-phase jet flow, which becomes more obvious at f b > 8 Hz. In this regime, with increasing the f b , the oscillating motion of bubbles changes to the flattened spiral one, and the deviation (fluctuation) of the lateral amplitude increases resulting from the enhanced flow-induced wobbling of bubble shape. Finally, we developed an analytical model to predict the evolution of time-averaged vertical velocity profile of the liquid, which considers the contributions of (i) local void fraction and (ii) evolution of upstream flow, and validated successfully with the measurement.