Viscosity Destabilizes Sonoluminescing Bubbles

In single-bubble sonoluminescence (SBSL) microbubbles are trapped in a standing sound wave, typically in water or water-glycerol mixtures. However, in viscous liquids such as glycol, methylformamide, or sulphuric acid it is not possible to trap the bubble in a stable position. This is very peculiar as larger viscosity normally stabilizes the dynamics. Suslick and co-workers call this new mysterious state of SBSL “moving-SBSL.” We identify the history force (a force nonlocal in time) as the origin of this destabilization and show that the instability is parametric. A force balance model quantitatively accounts for the observed quasiperiodic bubble trajectories.

Figure 1

Phase diagrams in the ambient radius $R_0$ vs driving pressure $P_a$ phase space for the bubbles in water ($\nu ={10}^{-6}{\mathrm{m}}^2/\mathrm{s}$, upper) and glycol ($\nu =20\times {10}^{-6}{\mathrm{m}}^2/\mathrm{s}$, lower) for a driving frequency of $f=23\mathrm{kHz}$ and a liquid temperature of $T=18°\mathrm{C}$. In the lower left area (blue online) the bubbles are shape and path stable. In the medium gray area (green online) the bubbles are shape unstable and path stable. In the light gray area (yellow online) they are both shape and path unstable. Hence, in the medium and light gray area bubbles cannot exist. In the glycol case there is a new and additional phase (dark gray, red online) of shape stable, but path unstable bubble which we identify with the observed m-SBSL. Here the bubbles spiral out of the center of the flask, as demonstrated through the three-dimensional bubble trace in the physical ($x,y,z$) space (lower right) and its projection $y(t)$: dark (blue online) curves correspond to our experimental observations, lighter (red online) curves to the result of our model. The corresponding curves for the water case show very different behavior, namely, only a bubble moving to the center of the cell (upper right). In the phase diagram for glycol additional symbols are plotted. They mark our experimental data points. Dark (blue online) circles denote moving bubbles, the single white square a bubble where additional shape oscillation could be observed and the single white circle a still bubble. The agreement with the predictions from the theoretical phase diagram is very good; i.e., the blue circles are all inside or close to the dark (red online) area. Note that we have found various nonspiralling bubbles (white circles) in the blue area (where they belong), but as simultaneously shape- and path-stable bubbles are well understood, for clarity we did not include these points in the diagrams. Only one nonspiralling shape stable bubble is slightly off the blue regime (white circle at 0.95 bar and $40\mu \mathrm{m}$ in the lower figure). The reason may be that the Mathieu tongue around $40\mu \mathrm{m}$ is less pronounced in our model as compared to the experiments.

Figure 2

$y$ position and 3D trajectory of a m-SBSL bubble in $N$-methylformamide [3] from our numerical simulations. The employed parameters are $\sigma =0.038\mathrm{N}{\mathrm{m}}^{-1}$, $\nu =1.65{\mathrm{m}}^2{\mathrm{s}}^{-1}$, $\rho =1000\mathrm{kg}{\mathrm{m}}^{-3}$, $c=1660\mathrm{m}{\mathrm{s}}^{-1}$, $f=30\mathrm{kHz}$, $R_0=9\mu \mathrm{m}$, $P_a=1.65\mathrm{bar}$ and we took thermal damping into account along the model of Ref. 21. Just as in experiment, we observe translational motion. The bubble velocity, in order of magnitude, matches the value of $v=3\mathrm{mm}{\mathrm{s}}^{-1}$ reported in the experimental work [3].