Computational investigation of Tb(III) ion line intensities in single-bubble sonoluminescence

We perform a computational fluid dynamics simulation of trivalent terbium [Tb(III)] ion line emissions from single-bubble sonoluminescence (SBSL). Our simulation includes dynamic boundary conditions as well as the effects of gas properties and quenching by species, such as nitrite ion (${\mathrm{NO}}_2^{-}$). Simulation results demonstrate that when the maximum temperature inside a dimly luminescing bubble is relatively low, emission peaks from excited Tb(III) ions are prominent within the emission spectra. As the maximum temperature of the bubble increases, emission peaks of Tb(III) ions fade away relative to the continuum background emission. These calculations match observations of Tb(III) line emissions from SBSL occurring in aqueous solutions of terbium nitrate $\left[\mathrm{Tb}{\left({\mathrm{NO}}_3\right)}_3\right]$ under an argon gas atmosphere. The evolution of the radiation energy spectrum over time for sonoluminescing bubbles provides a clear mechanism explaining Tb(III) emission peaks gradually merging into the continuous background emission as the radiation power increases.

Figure 1

SBSL spectra from $\mathrm{Tb}{\left({\mathrm{NO}}_3\right)}_3$ aqueous solutions under 100 Torr of argon (Ar) gas. The vertical dashed lines show three central wavelengths of spectral peaks.

Figure 2

An Ar bubble in $\mathrm{Tb}{\left({\mathrm{NO}}_3\right)}_3$ aqueous solutions at $15{}^{\circ }\mathrm{C}$ driven at eight different pressures, $p_a=1.13$, 1.15, 1.18, 1.20, 1.23, 1.26, 1.28, and 1.31 atm are labeled as $p_{ai}(i=1,2,...,8,\mathrm{respectively})$. (a) Energy spectra, (b) temperature when the bubble reaches its minimum size, and (c) corresponding pressure.

Figure 3

Calculation of maximum temperature and $\beta$ versus the amplitude of acoustic pressure ($p_a$), respectively. We only select the intensity of spectral line at $\lambda =540\mathrm{nm}$ and its continuum background obtained by the interpolation method.

Figure 4

Simulation results for an Ar bubble in a $\mathrm{Tb}{\left({\mathrm{NO}}_3\right)}_3$ aqueous solution at $15{}^{\circ }\mathrm{C}$ driven by an acoustical pressure of 1.31 atm $[p_{a8}$ in Fig. 2]. (a) Radiation power of the bubble versus time, (b) energy spectra, (c) temperature, and (d) pressure.

Figure 5

Simulation results for an Ar bubble in a $\mathrm{Tb}{\left({\mathrm{NO}}_3\right)}_3$ aqueous solution at $15{}^{\circ }\mathrm{C}$ driven by an acoustic pressure of $p_a=1.26\mathrm{atm}$ $[p_{a6}$ in Fig. 2]. (a) Total radiation power versus time, (b) energy spectra, (c) temperature, and (d) pressure.

Figure 6

Simulation results for an Ar bubble in a $\mathrm{Tb}{\left({\mathrm{NO}}_3\right)}_3$ aqueous solution at $15{}^{\circ }\mathrm{C}$ driven by an acoustic pressure of $p_a=1.31\mathrm{atm}$. (a), (c), and (e) Total radiation power versus time. (b), (d), and (f) Energy spectra.

Figure 7

Distributions of (a) $E_i$, (b) $\alpha$, and (c) ${\kappa }_{\lambda }R$ at $\lambda =540\mathrm{nm}$ along the radius of a simulated bubble, corresponding to the moments (i.e., $\mathrm{A},\mathrm{B},...,\mathrm{H}$) marked in Fig. 4.

Figure 8

Variations of (a) $E_i$, (b) $\alpha$, and (c) ${\kappa }_{\lambda }R$ at $\lambda =540\mathrm{nm}$ with $r$ inside a bubble, corresponding to the moments (i.e., $\mathrm{A},\mathrm{B},...,\mathrm{H}$) marked in Fig. 5.