Effect of the Rayleigh-Taylor instability on maximum reachable temperatures in laser-induced bubbles

Laser-induced bubbles provide an effective vehicle to achieve high-energy concentrations and maximum temperatures in bubble luminescence phenomena. One limitation to the temperatures that can be achieved is the development of the Rayleigh-Taylor instability (RTI) during the instants previous to the bubble maximum compression. For a given fluid, the control parameters of the experiment are: the bubble maximum radius, the bubble ambient radius, the initial perturbations of the bubble, and the liquid pressure at infinity. In this work, experiments using laser-induced bubbles in a highly viscous phosphoric acid were performed in order to determine the achievable parameters values in the phase space. The effect of $R_{\max }$, $R_0$, $a_2^i$, $a_3^i$, and $p_{\infty }$ on the maximum temperature achieved by the gas contents inside the bubble were numerically determined. The results show for each static pressure an optimum region for maximum temperatures of the gas contents bounded by the RTI.

Figure 1

Experimental setup. (a) Measurement of the temporal evolution of the radius of a LIB bubble using Mie scattering technique. L1, L2, and L3 are the pulse conforming lens set. L4 and L5 are the collecting light lens. (b) Imaging of the bubble at maximum radius and ambient radius using backlighting technique. The CCD camera is used with a $f=50$ mm imaging lens.

Figure 2

Normalized Mie scattering data of a LIB in PA99 at $T_0=23{}^{\circ }$C. The static pressure on the bubble is $p_{\infty }=(800\pm 50)$ Pa (2 mbar air pressure on the cuvette liquid-gas interphase). The time of Rayleigh collapse is $t_C=(1.58\pm 0.02)$ ms. The calculated maximum radius from Eq. (1) is $R_{\max }=(1140\pm 40)$ $\mu$m. (Dotted black line) The theoretical evolution of Rayleigh collapse.

Figure 3

Picture of a LIB taken with a backlighting technique showing the maximum radius. A postprocessing of this image allows the determination of the bubble perturbation at bubble maximum radius $a_2^i$, maximum bubble radius $R_{\max }$, and ambient radius $R_0$. Using mode $n=2$ for the spherical harmonics decomposition, the maximum radius is $R_{\max }=(820\pm 20)$ $\mu$m while the amplitude of the perturbation of mode 2 is $a_2^i=8$ $\mu$m. The static pressure was $p_{\infty }=(700\pm 50)$ Pa (3 mbar air pressure on the cuvette liquid-gas interphase). The ambient radius is $R_0=(30\pm 2)$ $\mu$m.

Figure 4

Phase diagrams in ($R_0$,$R_{\max }$) for argon bubbles in PA99. The colorplot indicates the maximum temperature of the gas contents inside a cavitating bubble. The solid black line is the Rayleigh-Taylor boundary for the second mode calculated from Ref. [13]. The upper part of the boundary indicates that the bubble will break at the main collapse. The lower part indicates that the bubble is RT stable during the main collapse. In all cases the initial perturbation of mode 2 is $a_2^i=$1$\%$$R_{\max }$. If the bubble breaks, the temperature at the breakage time is reported. (a) $p_{\infty }=800$ Pa. (b) $p_{\infty }=1000$ Pa. (c) $p_{\infty }=10000$ Pa. (d) $p_{\infty }=50000$ Pa. (e) $p_{\infty }=100000$ Pa. (f) $p_{\infty }=500000$ Pa. In the subplot (f) in dotted black line the RT boundary of the third mode is shown. The predicted temperatures at rupture time corresponding to the third mode are lower than in the second mode.