Nonspherical laser-induced cavitation bubbles

The generation of arbitrarily shaped nonspherical laser-induced cavitation bubbles is demonstrated with a optical technique. The nonspherical bubbles are formed using laser intensity patterns shaped by a spatial light modulator using linear absorption inside a liquid gap with a thickness of $40\mu \text{m}$. In particular we demonstrate the dynamics of elliptic, toroidal, square, and V-shaped bubbles. The bubble dynamics is recorded with a high-speed camera at framing rates of up to $300000$ frames per second. The observed bubble evolution is compared to predictions from an axisymmetric boundary element simulation which provides good qualitative agreement. Interesting dynamic features that are observed in both the experiment and simulation include the inversion of the major and minor axis for elliptical bubbles, the rotation of the shape for square bubbles, and the formation of a unidirectional jet for V-shaped bubbles. Further we demonstrate that specific bubble shapes can either be formed directly through the intensity distribution of a single laser focus, or indirectly using secondary bubbles that either confine the central bubble or coalesce with the main bubble. The former approach provides the ability to generate in principle any complex bubble geometry.

Figure 1

(Color online) Experimental setup. Cavitation bubbles are generated with a pulsed laser reflected from a digital spatial light modulator (SLM) which is focused after passing through several optics into a thin liquid film with a $20\times$ microscope objective. The liquid film is contained in a chamber of $40\mu \text{m}$ height which is filled with a light absorbing aqueous yellow ink. The fast bubble dynamics is studied with a high-speed camera.

Figure 2

Geometry of the axisymmetric bubble simulations and the resulting planes used to compare with the high-speed photography. The axis of symmetry is the $z$ axis. For the elliptic (a), the v-shaped (b), and the square bubble (d) we compare the bubble dynamics to the projection in the $rz$ plane of an ellipsoidal, hollow cone, and double cone, respectively. The toroidal bubble (c) in the experiments is compared to its projection in the $r\phi$ plane and the $rz$ plane.

Figure 3

Experimental observation of an elliptical bubble with eccentricity inversion. The bubble is generated with a longer horizontal shape but during the collapse phase the vertical dimension becomes larger. First frame represents the image used to shape the laser focus (frame rate $300000\text{fps}$, exposure time $1.76\mu \text{s}$, laser energy $22\mu \text{J}$). The top right corner shows the time after the laser pulse in microseconds and the black bar denotes $100\mu \text{m}$ and the time stamps in the upper right are given in microseconds.

Figure 4

Numerical simulation of an elliptic bubble, with an initial pressure of $P_0\left(t=0\right)=50\text{bar}$. When compared to Fig. 3 similar phenomena can be observed: an initially elliptic bubble with longer horizontal axis turns into an almost spherical bubble during its maximum size and then collapses with a longer vertical axis. The breakup of the bubble as shown in the last frame could not be observed in the experiment, likely due to a lack of temporal resolution.

Figure 5

This graph shows the eccentricity $\left(a/b\right)$, where $a$ is the horizontal axis and $b$ the vertical axis of the bubble. The squares correspond to the experiment shown in Fig. 3 and the solid line is the BEM simulations.

Figure 6

Experimental observation of a more complex bubble dynamics emerging from a V-shaped focus. The recording shows selected frames taken at $300000\text{fps}$ with an exposure time of $2.2\mu \text{s}$, laser energy of $58\mu \text{J}$. The dots in the frames are from $3\mu \text{m}$ diameter polystyrene particles used for flow visualization. The black bar denotes a length of $100\mu \text{m}$ and the time stamps in the upper right are given in microseconds.

Figure 7

Simulation of a V-shaped bubble: the initially V-shaped bubble quickly turns into a more rounded shape. The “hollow” part of the V shape remains visible for quite some time, but finally disappears at $t^{\prime }\sim 0.4$. It then overshoots and becomes a bulge clearly visible at the right-hand side of the bubble. This bulge develops into a jet from $t^{\prime }=0.94$ onward. A ring jet is formed in the left central section of the bubble. Once this jet impacts the simulations are being stopped. The jet from the right hand side has not yet fully penetrated the bubble at this instant. The axis of symmetry is the $z$ axis.

Figure 8

Toroidal bubble created from a circular focus depicted in the first frame. The bubble expands initially with a rough surface likely due to separate bubbles which only coalesce in a later stage. Please note that the bubble retains its toroidal shape during the expansion and collapse cycle. The recording is taken at a frame rate of $250000\text{fps}$ with an exposure time of $1.8\mu \text{s}$ and laser energy of $51.8\mu \text{J}$. The black bar denotes a length of $100\mu \text{m}$ and the time stamps in the upper right are given in microseconds.

Figure 9

Two cross sections of the toroidal bubble simulation results for (a) the $r\phi$ plane (to be compared with Fig. 8), (b) the $rz$ plane.

Figure 10

Coalescence method to create a square bubble. The laser is focused onto five distinct but near by spots as depicted in the first frame. All five bubbles quickly expand and are already merged into one bubble at $t=5.9\mu \text{s}$. Please note the diamond shape of the bubble during collapse. The frames are selected from a recording taken at $300000\text{fps}$ with an exposure time of $1.8\mu \text{s}$. The laser energy to all five spots is $20\mu \text{J}$. The black bar denotes a length of $100\mu \text{m}$ and the time stamps in the upper right are given in microseconds.

Figure 11

Simulation of the square bubble dynamics without the bubble-bubble coalescence. The bubble starts with a diamond shape resembling the shape of the focus, see first frame of Fig. 10. The last frame shows distinct differences compared to the experiment which we contribute to residual gas pressure.

Figure 12

Creation of a rotated square bubble by confining the expansion of a central bubble with four helper bubbles. The larger distance between the laser foci (first frame) suppressed the coalescence although as similar laser energy of $26\mu \text{J}$ is used. Selected frames taken at $300000\text{fps}$ with an exposure time of $1.8\mu \text{s}$. The black bar denotes a length of $100\mu \text{m}$.