Stability of a sonoluminescing nitrogen bubble in chilled water

Bubbles are levitated in a resonator driven by an ultrasound wave. Their highly nonlinear oscillations feature a strong collapse, where fluidlike densities and temperatures of several thousand degrees Kelvin are reached, resulting in the emission of ultrashort light pulses. Previous experiments and theories explained the observed stable bubble dynamic and emission on long time scales with the requirement of a noble gas. Recent experiments reveal stable sonoluminescent emission of nitrogen bubbles in chilled water without the presence of a noble gas. Numerical calculations show that a diffusive and dissociative equilibrium can be reached when the temperature within a nitrogen bubble is limited due to the presence of water vapor. Calculated stability lines agree with published experimental results. The results show that noble-gas-free stable single bubble sonoluminescence of nitrogen bubbles is possible.

Figure 1

Stability lines of nitrogen-vapor bubbles in water at different ambient gas concentrations and $20°\text{C}$. Shown is the ambient radius as a function of driving pressure at a hydrostatic pressure overhead of 3 cm water column and 21.930 kHz. The lower three lines show diffusive stability. The upper three lines show stability of diffusion and chemical dissociation. Attached to the $18\%$ ambient concentration lines are arrows denoting the direction of bubble growth.

Figure 2

Radius-time curve from experiment (dots) and numerical fit of a nitrogen bubble at $9°\text{C}$. The ambient radius has been determined to be $6\mu \text{m}$, the driving pressure 1.387 bars.

Figure 3

Experimental data (dot connected circles) and numerical simulations (lines) of stable nitrogen-vapor bubbles in water at $18\%$ ambient gas concentration and $9°\text{C}$. Top: Shown is the ambient radius (filled circles, straight lines) and maximal radius (hollow circles, dashed lines) as a function of driving pressure. Bottom: Temperature (filled circles, straight lines) and relative content of water vapor at bubble collapse minimum (hollow circles, dashed lines). The different numerical lines denote values obtained at diffusion-dissociation equilibrium, calculated with two different approaches: (a) evaporation coefficient $\alpha =0.14$ and (b) $\alpha =0.22$ including Lindemann/Hinschelwood correction. The thin dotted line shows values of ambient radius at the threshold of parametric instability, calculated according to approach “a”.

Figure 4

Diffusion and dissociation rate of nitrogen at equilibrium (dashed lines) and the number of molecules of nitrogen (straight lines) in the bubble for the two different numerical approaches. The curves are labeled according to Fig. 3.

Figure 5

Measured spectrum of light emission from a stable nitrogen bubble (dots) and calculated blackbody spectrum of 8500 K.