Bubble collapse and jet formation in corner geometries

The collapse of a vapor bubble near a flat solid boundary results in the formation of a jet that is directed toward the boundary. In more complex geometries such as corners, predictions of the collapse cannot be made in a straightforward manner due to the loss of axial symmetry. We experimentally investigate the bubble collapse and jet formation in corners formed of two flat solid boundaries with different opening angles. Using potential flow analysis, we accurately predict the direction of the jet and bubble displacement. We further show that for a corner with an opening angle $\alpha$, there exist analytic solutions that predict the jet direction for all the cases $\alpha =\pi /n$, where $n$ is a natural number. These solutions cover, in discrete steps, the full range of corners from the limiting case of a bubble near a single wall $\left(n=1\right)$ up to a bubble in between parallel walls $\left(n\to \infty \right)$.

Figure 1

Schematic drawing of the experimental setup, excluding the camera, lens, and light source for imaging (a) and snapshots from high-speed recordings (b)–(g). Growth and collapse of a free bubble (b)–(d) and a bubble in a corner with opening angle $\alpha =\pi /3\mathrm{rad}$ (e)–(g). Both bubbles were created by a laser pulse at $t=0$. The free bubble shows an axisymmetric collapse and remains in its original position, while the bubble in the corner generates a jet and is displaced toward the direction of the jet. We define the jet direction ${\theta }_j$ with respect to the normal of one of the solid surfaces.

Figure 2

Schematic representation of a bubble at a position ${\vec{r}}_j=R{e}^{i{\theta }_b}$ in a corner with an opening angle $\alpha =\pi /2$. The walls (thick solid lines) are modeled using three image sinks $s_{1–3}$ which together induce a velocity ${\vec{u}}_j$ at the bubble position. The bubble center and the sink $s_1$ are at the same vertical distances from the horizontal wall. The same symmetrical condition is applied to the bubble center, sink $s_2$, and the vertical wall. Radial distance from the corner is $R$ for all sinks.

Figure 3

Comparison between experimentally determined jet angles (symbols) and model predictions (solid and dashed lines) without any adjustable parameters. Experiments 1–3 are performed at various distances from the $\pi /3\mathrm{rad}$ corner; experiments 4–7 are performed in a $\pi /2\mathrm{rad}$ corner at various distances as well as different bubble sizes [28]. The correlation found by Brujan et al. [21] is shown by the dotted line.

Figure 4

(a) Normalized model results for $n=2$ (blue), $n=3$ (orange), $n=8$ (green), $n=20$ (red), $n=100$ (purple), and $n=1000$ (brown). The curve approaches a step function as $n\to \infty$. (b) Normalized experimental data (symbols) and model (lines) for $n=2$ (blue) and $n=3$ (orange).