Interaction and coalescence of large bubbles rising in a thin gap

We present accurate measurements of the relative motion and deformation of two large bubbles released consecutively in a quiescent liquid confined in a thin-gap cell. Although the second injected bubble was smaller, we observed that, in all cases, it accelerated and caught up with the leading bubble. This acceleration is related to the wake of the leading bubble, which also induces significant changes in the width and curvature of the trailing bubble. On the contrary, the velocity of the leading bubble is unaltered during the whole interaction and coalescence process. Shape adaptation of the two bubbles is observed just prior to coalescence. After pinch-off, the liquid film is drained at a constant velocity.

Figure 1

Liquid velocity around an isolated large bubble obtained by particle image velocimetry ($\mathrm{Ar}=7000,V_{\infty }=0.16\mathrm{m}/\mathrm{s},d=1.5\mathrm{cm}$). Left, in the laboratory frame; right, focus on the recirculating wake in the bubble frame.

Figure 2

Overview of the trajectories of two coalescing bubbles (${\mathrm{Ar}}_1=16700$ and ${\mathrm{Ar}}_2=8600$). The trailing bubble is entrained in the wake of the leading bubble (1–5); the bubbles adapt their shapes (6) and coalesce forming a single bubble (7, 8).

Figure 3

Vertical velocity of the trailing bubble (top lines) and of the leading bubble (bottom lines) normalized by the terminal velocity of an isolated bubble of the same size as the leading bubble. $\langle \text{.}\rangle$ denotes averaging over multiple experiments. (Darker solid lines) Results averaged over 40 experiments and (darker dashed lines) data from a single experiment (${\mathrm{Ar}}_1=15450$ and ${\mathrm{Ar}}_2=8500$). The green (light gray) curves compare two sets of experiments, both for $7500<{\mathrm{Ar}}_2\le 9000(\langle {\mathrm{Ar}}_2\rangle =8437)$ and two different ranges of ${\mathrm{Ar}}_1$, the dashed line for $11010<{\mathrm{Ar}}_1<12800$ ($\langle {\mathrm{Ar}}_1\rangle =11806$), and the solid line for $15950<{\mathrm{Ar}}_1<17520(\langle {\mathrm{Ar}}_1\rangle =16685)$.

Figure 4

(a) Evolution of the normalized width of the bubbles during approach. Top and bottom lines correspond to the leading and trailing bubbles, respectively. (b) Curvature of the bubbles as a function of separation distance. Top, middle, and bottom lines correspond to the normalized curvature at the top of the trailing bubble, top of the leading bubble, and bottom of the leading bubble, respectively. (Solid lines) Results averaged over 40 experiments and (dashed lines) results from a single experiment (${\mathrm{Ar}}_1=15450$ and ${\mathrm{Ar}}_2=8500$).

Figure 5

Overview of different pairs of bubbles just prior to coalescence showing how the bubbles adapt their shapes to each other. Note that each pair of bubbles is shaped like a single big bubble (${\mathrm{Ar}}_1\approx 11000$ and ${\mathrm{Ar}}_2\approx 7000$).

Figure 6

Two sequences of film drainage. (Top three images) The liquid ligament is retracting at a constant velocity. (Bottom images) The film changes geometry halfway, and the fluid is collected in a rim. The scales on the right equal 1 cm.