Laser-induced cavitation bubbles and shock waves in water near a concave surface

Abstract

The interplay among the cavitation structures and the shock waves following a nanosecond laser breakdown in water in the vicinity of a concave surface was visualized with high-speed shadowgraphy and schlieren cinematography. Unlike the generation of the main cavitation bubble near a flat or a convex surface, the concave surface refocuses the emitted shock waves and causes secondary cavitation near the acoustic focus which is most pronounced when triggered by the shock wave released during the first main bubble collapse. The shock wave propagation, reflection from the concave surface and its scattering on the dominant cavity is clearly resolvable on the shadowgraphs. The schlieren approach revealed the pressure build up in the last stage of the collapse and the first stage of the rebound. A persistent low-density watermark is left behind the first collapse. The observed effects are important wherever cavities collapse near indented surfaces, such as in cavitation peening, cavitation erosion and ophthalmology.

Keywords: Acoustic focusing; Cavitation bubble; Laser breakdown; Secondary cavitation; Shock wave.

Graphical abstract

Fig. 1

Schematics of the experimental setup. The central part of the experiment in shown in the top view (the x-y plane including the optical axis), while the excitation beam profile of the illumination pulse and the image on the detector are presented in the side view (the x-z plane). The magenta-colored area represents the path of the excitation pulse, while the green-colored area gives the path of the illumination pulse. The CB (the black disk), the BSW (the blue circle) and the ophthalmic lens deflect the illumination pulse and form the shadow image. For comparison, the approximate dimensions of the human eye in contact with the ophthalmic lens are shown by the yellow colored area. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 2

Field of view (FoV) of two high-speed visualization techniques superimposed on the area of interest behind the ophthalmic lens. Red rectangle: FoV of high-speed camera schlieren technique with a frame rate of 210 kHz, full field pulsed illumination, 61.4-kpx resolution, pixel size of 20 μm and magnification of 0.66. Yellow square: FoV of still camera shadowgraphy, pulsed illumination spot of 24.8-mm diameter, 1.44-Mpx resolution, pixel size of 5.86 μm and magnification of 0.27. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3

Theoretical estimates of the positions of the BSW fronts (the orange, green, red and blue lines) and the size of the CB (the black disk) are superimposed on the reduced, cylindrical geometry of the lens-water system (a) before SW reflection from the acoustic mirror (4.21 μs after the breakdown; actual spatial dimensions) and (b) after SW reflection (9.46 μs after the breakdown; spatial dimensions normalized to the radius of the concave mirror R). The BSW is emitted at a distance a. An arbitrary ray declined by an angle ϕ < ϕ_max is reflected by the acoustic mirror at the point P₁ and crosses the axis at the point P₂. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4

Representative multiple-event shadowgraphs 1M-12M revealing the shock wave propagation, reflection, mode-conversion, focusing and scattering, taken soon after the optical breakdown at a breakdown distance a = 10.13 mm (γ = 5.7) from the apex of the concave surface at twelve time instants. Each measurement is accompanied by the shock wave propagation model 1T-12T repeating the main features observed in the measurements. The red dashed rectangles in shadowgraphs (2M, 6M and 10M) are also presented in the schlieren frames (Fig. 5: A1-A3). Yellow arrows guide the eye to interesting features. Vertical yellow dotted lines mark the distance between two selected wavefronts. The dimensions of the model are normalized to the radius of the concave lens surface R = 8.1 mm. Lines: see the legend, black disk: bubble, white dot: breakdown site, red dot with a tail: acoustic focus for paraxial rays (dot) and the focal interval (tail), gray-shaded area: invisible part of the lens. Additionally, frame 6T shows a few rays originating at the breakdown site and being reflected by the lens toward the focal interval. The inset in 1T shows the superposition of the shadowgraph captured at 335 ns after the breakdown and the luminescent 0.4-mm-long plasma. White bar: 5 mm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5

Sixteen selected schlieren snapshots A1-D4 of the cavitation and shock wave dynamics extracted from the single event fast camera movie at a breakdown distance a = 10.13 mm (γ = 5.7). Yellow arrows indicate important features on the snapshot. Full white arrowheads designate the x-position of the breakdown, while open white arrowheads indicate the x-position of the center of the dominating cavity, moving towards the ophthalmic lens with time. The vertical dashed white line marks the edge of the ophthalmic lens. The red, green, yellow and blue dots with tails designate the acoustic focus for paraxial rays (dot) and the focal interval (tail) for the BSW, the first, second and third CSW, respectively. The first three frames (A1-A3) are also visualized within the red dashed rectangles (Fig: 4: 2M, 6M and 10M) by the shadowgraphic technique. White bar: 1 mm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)