Vortex pairing in the wake of an oscillating bubble rising in a thin-gap cell

We investigate experimentally the oscillatory motion and wake of a bubble rising in a counter flow in a thin gap cell (3 mm) by shadowgraphy and PIV. The equivalent diameter $d$ of the bubble in the plane of the cell is used to define the Archimedes number $Ar = \frac{\sqrt{g d^3}}{\nu}$ ($\nu$ is the kinematic viscosity and $g$ the gravitational acceleration). The counter flow is characterized by the Reynolds number $Re_{cf}$ based on the mean liquid velocity and the gap thickness. For $500 \leq Ar \leq 5500$ and $0 \leq Re_{cf} \leq 200$, the mean vertical velocity of the bubble relative to the counter flow, $V_{br}$, corresponds to the mean rising velocity in liquid at rest; and the frequency and the amplitude of the oscillatory motion superpose for all $Re_{cf}$ when normalized with $V_{br}$ and the timescale $d/V_{br}$. For a given size of the bubble ($d \approx 9.5$ mm and $Ar \approx 2800$) corresponding to a Reynolds number based on $V_{br}$ and $d$ of about $1900$, we then investigate in detail the wake associated to the bubble in several counter flows. As $Re_{cf}$ increases, the number of vortices released increases. Furthermore, the wake of the bubble undergoes vortex pairing for $0 \leq Re_{cf} \leq 110$), whereas no vortex pairing is observed for $Re_{cf} \geq 140$.