Comprehensive analysis of spherical bubble oscillations and shock wave emission in laser-induced cavitation

Abstract

The dynamics of spherical laser-induced cavitation bubbles in water is investigated by plasma photography, time-resolved shadowgraphs and sensitive single-shot probe beam scattering that portrays the transition from initial nonlinear to late linear oscillations. The frequency of late oscillations yields the bubble's gas content. Numerical simulations with an extended Gilmore model using plasma size as input and oscillation times as fit parameter provide insights into experimentally not accessible bubble parameters and shock wave emission. Model extensions include a term covering the initial shock-driven acceleration of the bubble wall, an automated method determining shock front position and pressure decay and a complete energy balance for the partitioning of absorbed laser energy into vaporization, bubble and shock wave energy and dissipation through viscosity and condensation. These tools are used for analysing a scattering signal covering 102 oscillation cycles from a bubble with 36 μm maximum radius produced by a plasma with 1550 K average temperature. Predicted bubble wall velocities during expansion agree well with experimental data. Upon first collapse, most energy was stored in the compressed liquid around the bubble and radiated away acoustically. The collapsed bubble contained more vapour than gas and had a pressure of 13.5 GPa. The decay of the rebound shock wave pressure with radius r was initially $\mathrm{\ \propto }{r^{ - 1.8}}$ , and energy dissipation at the shock front heated the liquid near the bubble wall to temperatures above the superheat limit. The shock-induced temperature rise reduces damping during late bubble oscillations. Damping in first collapse increases significantly for small bubbles with less than 10 μm radius.

Interferometric Fiber Optic Probe for Measurements of Cavitation Bubble Expansion Velocity and Bubble Oscillation Time

“…It finally collapses in the time interval t ≈ 220–230 µs. The complete time sequence of the dynamics shown in Figure 3 a is common to many other phenomena of laser-induced cavitation in water [ 16 , 18 , 25 ]. As a result of the collapse, the energy is converted into a shock wave that propagates through the water medium at supersonic speed until it reaches the speed of sound (~1500 m/s), typically after 0.6 mm of travel [ 7 ].…”

“…In laser-induced phenomena, bubble dynamics plays a crucial role as it determines the characteristics of the generated shockwave waveform [ 14 ]. Many experiments and models have been implemented to explain or predict the dynamics, the maximum bubble expansion ratio, or multiple bubble rebounds [ 15 , 16 , 17 , 18 ]. Often, a very expensive high-speed camera [ 19 , 20 , 21 ] and other complex techniques such as shadow photography, high-speed imaging, laser transmission probes, and laser deflection probes have been used to observe bubble evolution in water or a tissue phantom [ 22 , 23 , 24 , 25 , 26 , 27 , 28 ] and consequently validate models that predict bubble dynamics and/or pressure shock wave formation.…”

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“…In the presence of a transient pressure, the pre-existing gas bubble can pulsate and grow, or microbubbles start to form on gas nuclei [43] , [44] . During their life cycle cavitation bubbles undergo expansions and shrinkages via rectified diffusion and it ends with the emission of multiple shock waves that lead to a severe secondary pressure gradient [45] , [46] (see Fig. 5 f bottom panel).…”

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“…In the literature, similar oscillations but with by far shorter duration and thus a higher frequency, were also measured and attributed to the different states of the cavitation bubble, such as bubble initialization, compression, expansion, oscillations, or rebounds and collapse. [31, 44, 51, 52]…”

“…In the literature, similar oscillations but with by far shorter duration and thus a higher frequency, were also measured and attributed to the different states of the cavitation bubble, such as bubble initialization, compression, expansion, oscillations, or rebounds and collapse. [31,44,51,52] The time difference between the measurements of the initial pressure wave and the first reflection is approx. 50 μs (Figure 3A, inset) and changes with a different hydrophone-to-focus-distance.…”