Bubble Dynamics and Sonoluminescence Phenomena
Understanding of the behavior of evolving bubble inside liquid is not a simple problem. The full hydrodynamic problem for the bubble motion involves solving 3-D Navier-Stokes equations inside and outside the bubble, coupled with equations of heat and mass transfers at the bubble wall. We have solved this problem without massive computational work! A breakthrough came by finding a set of homologous solutions of the mass and momentum equations in spherical symmetry [SL-1]. With uniform density and pressure approximation, the violent oscillation of the bubble formed from the evaporated droplet at the superheat limit cannot be accounted [SL-2]. The bubble behavior of a nonsonoluminescencing gas bubble can be described correctly by the solutions with uniform pressure approximation [SL-1]. However, the gas pressure inside bubble is no longer uniform if the bubble wall acceleration exceeds 1012 m/s2 [SL-3]. The solutions for 3-D Navier-Stokes equations in spherical symmetry show that sonoluminescence occurs due to the rapid increase and subsequent decrease in the bubble wall acceleration which induces a thermal spike [SL-3, SL-4]. The temperature profile obtained by the solutions suggests that the light pulse duration is less than 300 ps [SL-5]. Also the solutions have revealed that the Guderley’s similarity solution is not valid just prior to the collapse [SL-4]. In addition correct spectral behavior of sonoluminescence was obtained by assuming that the source for the sonoluminescence is bremsstrahlung in partially ionized gases [SL-3, SL-4]. The shock pulse emanating form a sonoluminescing gas bubble were calculated [SL-5] and measured [SL-6] and the propagation of a pressure wave inside bubble near the bubble collapse [SL-7, SL-8] have also been calculated by using the solutions.
It has been found that there always exists a mismatch between the natural frequency of an oscillator (bubble) and the characteristic frequency of the applied ultrasound, so that a proper choice of time scale of the driving force is crucial for the calculation of the bubble behavier under ultrasound [SL-8, SL-9]. It has also been found experimentally that the upscaling of SBSL cannot be achieved at low frequencies of ultrasound due to such mismatch [SL-10]. An artificial resonance may occur in the course of numerical evaluation of the equation for bubble motion under ultrasound if the bubble motion is forced to be in phase with the characteristic frequency of the driving force [SL-8]. Two time normalization method [SL-8] was introduced to avoid the artificial resonance. Of course the two time normalization method introduced by us is a physical approximation which represents lagging behavior of bubble motion under ultrasound. Such relaxational motion of bubble, which is typical for nonlinear oscillators [SL-11], turns out to be due to the combined effect of surface tension and viscosity of liquid. This method enables to explain why a sonoluminescing air bubble can be maintained at partial pressure of about 0.03~0.14 atm [SL-12] and why the sonoluminescing air bubble can be stable at the driving pressure of 1.45 atm [SL-13].
Our theory predicts that extremely high temperature above million degree might be achieved from a submicron sonoluminescing gas bubble driven at 1 MHz [SL-13]. This happens because the submicron bubble driven at MHz frequency can be stable even at higher driving pressure above 10 atm [SL-14]. Even our theoretical model predicts correctly the nonlinear behavior of bubble in sulfuric acid solutions, which shows two states of bubble motion [SL-15] and the characteristics of a sonoluminescing gas bubble such as the peak pressure and temperature and the flash width [SL-16] in those solutions. Our theory will be used as a tool for optimum design of sonochemical reactors. [SL-17].
Exact solution of the cosmological fluid equations for Newtonian stars, which yields many fruitful results such as stellar stability, spherical oscillation and gravitational collapse [SL-18] was obtained by using our homologous solution for the mass and momentum equations. The linear velocity profile obtained shows homologous character of the gases inside the sphere: every mass point during the collapse or expansion may be traced back to a single point. Furthermore, the exact solution yields to calculate central densities, pressures and temperatures of the Newtonian stars such as the Sun, Jupiter and the Saturn [SL-19]. Our calculation results may be applicable to the formation of protostars. Using these exact solution of the cosmological fluid equations without mass term, fire-ball expansion and subsequent shock wave propagation by detonation of explosives were studied [SL-20]. Recently, core-collapse supernova explosion and the subsequent supernova explosion due to core bounce were studied analytically [SL-21]. Our study reveals that the heat transfer across the system boundary determines the evolution of the ideal gas systems and vice versa.
Experimental works on the single bubble sonoluminescence(SBSL) have also been done at PCL. It has been found that a selective bifurcation instead of period doubling occurs when the driving pressure is increased and the bubble gains extreme stability (SL state) after the cascade occurrence of such bifurcation [SL-22]. Accurate measurement of the radius of a sonoluminescing gas bubble by light scattering method and direct imaging technique was tried [SL-23] by using the remarkable stability of sonoluminescing gas bubble having the same shape variation sequence in every oscillation cycle and having only 50 ps jitter in the time flashes. Such SBSL characteristics enable to measure the bubble radius by the light scattering method and direct imaging tenique sequentially. The spectrum from SBSL was measured and the observed results were compared with the results by the theory proposed [SL-3, SL-4]. Calculated and experimental results yield common spectral behavior in the visible region : the spectral radiance shows power-law dependence on wavelength with an exponent of -2.5 [SL-24]. We have succeded in measuring the pulse width from the sonoluminescing gas bubble in sulfuric acid solutions [SL-25] and glycerin-water mixtures [SL-26], where the SL bubble is extremly unstable. The measured values of the pulse widht were found to be in the range of 150 ps to several ns [SL-25, SL-26]. No appreciable difference in the measured pulse width [SL-27] and the bubble behavior [SL-28] for the sonoluminescing air bubble in various solutions was found. The measured results for the pulse width of sonoluminescence in various solutions whose density varied from 1000 kg/m3 to 1800 kg/m3 suggest that light is emitted from the core region where the temperature is almost uniform [SL-26].
Application of sonoluminescence phenomena such as possibility of bubble fusion and the chemical reaction enhanced by multibubble sonoluminescence are underway. For example, degradation of Methylene blue, a typical textile dyestuffs in aqueous solution was examined for the first time at the multibubble sonoluminescence (MBSL) condition [SL-29]. At the optimum condition of MBSL, the solution was degradated completely. Recently, uniform coating on CdS particles on TiO2 nanoparticles[SL-30] was succeeded through a one pot reaction under MBSL condition. Zinc oxide(ZnO) and ZnO-coated tintanium nanoparticles were synthesized in various alcohol solution[SL-31] at the MBSL condition. Furthermore, Li4Ti5O12(LTO), a powerful anode material for all kids of rechargeable lithium batteries was systhesized by heating the LiOH coated TiO2nanoparticles prepared at the MBSL condition[SL-32]. We also synthesized the nanoparticles with core/shell structure such as ZnS coating on to TiO2 nanoparticles [SL-33] and PbS coating on TiO2 nanoparticles [SL-34] at the MBSL condition. Recently lithium iron phosphates (LiFePO4), which has been considered as promising cathode materials was synthesized at the MBSL condition [SL-35]. Specially we prepared the supported Ni catalysts with core/shell structure at the MBSL condition and found that 10% Ni Ni/Al2O3 catalysts of core/shell structure produced good conversion efficient of CH4, which is about 96% at reaction temperature of 800℃ and showed good thermal stability [SL-36]. With the supported Ni catalysts Ni/Al2O3and Ni/MgO-Al2O3 synthesized at the MBSL conditions, the methane conversion of 97% in steam reforming reation at 750 ℃ [SL-37] and 95% in dry (CO2) reforming reaction at 800℃ [SL-38] were achieved for the first 150h. A test for the mixed reforming of methane with these catalysts was also done [SL-39]. Recently, the pulse width from a bubble cloud under MBSL conditions was measured for the first time [SL-40]. The observed pulse width which appears to be comparable to that of the single bubble sonolunimescence indicates that the cloud of bubbles collapse simultaneously to emitting a light that is synchronized with th applied ultrasound. Based on this observation, MBSL is studied hydro-dynamically to obtain the velocity profile and radiation pressure field by solving the continuity and momentum equations for a spherical cluster containing numerous microbubbles[SL-41]. Molecular dynamics simulation for the sonoluminescing gas bubble [SL-42] with ten million molecules is in progress with supercomputer facility at KISTI (Korea Institute of Science and Technology Information), Daejon, Korea. An appropriate boundary condition at the bubble wall was found to be one of important factor to simulate the sonoluminescing bubble by molecular dynamics [SL-43].
[SL-1] Ho-Young Kwak and Hyup Yang, “An aspect of sonoluminescence from hydrodynamic theory,” Journal of Physical Society of Japan, Vol. 64, pp. 1980-1992, 1995.
[SL-2] Ho-Young Kwak, Si-Doek Oh and Cheon-Ho Park, “Bubble dynamics for the evolving bubble formed from the droplet at the superheat limit,” International Journal of Heat Mass Transfer, Vol. 38, pp. 1709-1718, 1995.
[SL-3] Ho-Young Kwak and Jung Hee Na, “Hydrodynamic solutions for a sonoluminescing gas bubble,” Physical Review Letters, Vol. 77, pp. 4454-4475, 1996.
[SL-4] Ho-Young Kwak and Jung Hee Na, Physical process for single bubble sonoluminescence,” Journal of Physical Society of Japan, Vol. 66, pp. 1101-1110, 1997.
[SL-5] Yoon-Pyo Lee, Sarng-Woo Karng, Jin-Seok Jeon and Ho-Young Kwak, “Shock pulse from a sonoluminesceing gas bubble,” Journal of Physical Society of Japan, Vol. 66, pp. 2537-2540, 1997.
[SL-6] Sarng Woo Karng, Yoon Pyo Lee, Ki Young Kim, and Ho-Young Kwak, “Implosion mechanism for a sonoluminescing gas bubble,” Journal of the Korean Physical Society, Vol. 43, pp. 135-144, 2003.
[SL-7] Ho-Young Kwak, Yoon-Pyo Lee and Sarng-Woo Karng, Pressure wave propagation inside a sonoluminescing gas bubble,” Journal of Physical Society of Japan, Vol. 68, pp. 705-708, 1999.
[SL-8] Ho-Young Kwak, Joong-Yeob Lee and Sarng Woo Karng, “Bubble dynamics for single bubble sonoluminescence,” Journal of Physical Society of Japan, Vol.70, pp.2909-2917, 2001.
[SL-9] Sarng Woo Karng and Ho-Young Kwak, “Relaxation behavior of microbubbles in ultrasonic field,” Japanese Journal of Applied Physics, Vol. 45, pp. 317-322, 2006.
[SL-10] Jin-Seok Jeon, Joong-Yeob Lee and Ho-Young Kwak, “Possibility of upscaling for single bubble sonoluminescence at a low driving frequency”, Journal of Physical Society of Japan, Vol.72, pp. 509-515, 2003.
[SL-11] Sarng Woo Karng, Ki Young Kim, and Ho-Young Kwak, “Lagging motion of forced nonlinear oscillators,” Journal of Sound and Vibration, Vol. 287, pp. 117-128, 2005.
[SL-12] Jung-Hee Na, Gi-Taek Byun, and Ho-Young Kwak, ‘Diffusive stability for a sonoluminescing gas bubble,” Journal of the Korean Physical Society, Vol. 42, pp. 143-152, 2003.
[SL-13] Ho-Young Kwak, Sarng-Woo Karng and Yoo-Pyo Lee, “Rayleigh-Taylor instability on sonoluminescing gas bubble,” Journal of the Korean Physical Society, Vol. 46, pp. 951-962, 2005.
[SL-14] Ki-Taek Byun, Sarng Woo Karng, Ki Young Kim and Ho-Young Kwak, “Sonoluminescence characteristics from micron and submicron size bubbles,” Journal of the Korean Physical Society, Vol. 47, No. 6, 2005.
[SL-15] Ki Young Kim and Ho-Young Kwak, “Prediction of bubble behavior in sulfuric acid solutions by a set of solutions of Navier-Stokes equations,” Chemical Engineering Science, Vol. 62, pp. 2880-2889, 2007.
[SL-16] Ki Young Kim, Ki-Taek Byun and Ho-Young Kwak, “Characteristics of sonolunescing bubbles in aqueous solutions of sulfuric acid,” Journal of Physical Society of Japan, Vol. 75, No. 11, 2006.
[SL-17] Ki Young Kim, Ki-Taek Byun, and Ho-Young Kwak, “Temperature and pressure fields due to collapsing bubble under ultrasound,” Chemical Engineering Journal, Vol. 131/132, pp. 125-135, 2007.
[SL-18] Jung Whan Jun and Ho-Young Kwak, “Gravitational collapse of Newtonian stars”, International Journal of Modern Physics D, Vol. 9, pp. 35-42, 2000.
[SL-19] Ho-Young Kwak and Jung Whan Jun, “Hydrodynamics and thermodynamics of Newtonian stars,” Geophys. Astrophys. Fluid Dynamics, pp. 1-14. 2003.
[SL-20] Ho-Young Kwak, Ilgon Ko and Ki-Moon Kang, “Expanding of fire-ball and subsequent shock wave propagation by detonation of explosives,” International Journal of Thermal Sciences, Vol. 59, pp. 9-16, 2012.
[SL-21] Ho-Young Kwak, “Core-collapse supernova explosions: An analytical one-dimensional analysis,” Far East Journal of Applied Mathematics, vol. 93, pp. 247-268, 2015.
[SL-22] Byung-Rock Kim, Jin Seok Jeon and Ho-Young Kwak, “Stability and selective bifurcation for a gas bubble oscillating under ultrasound”, Journal of Physical Society of Japan, Vol. 68, pp. 1197-1204, 1999.
[Sl-23] Jin-Seok Jeon, Ik-Jun Yang, Sarng Woo Karng and Ho-Young Kwak, “Radius measurement of a microbubble oscilliating under ultrasound”, Japanese Journal of Applied Physics, Vol.39, pp. 1124-1127, 2000
[SL-24] Jin-Seok Jeon, Ik-Jun Yang, Jung Hee Na and Ho-Young Kwak, “Radiation mechanism for a single bubble sonoluminescence,” Journal of Physical Society of Japan, Vol. 69, pp. 112-119, 2000.
[SL-25] Jin-Seok Jeon, Chansoo Lim and Ho-Young Kwak, “Measurement of pulse width of sonoluminescing gas bubble in sulfuric acid solution,” Journal of the Physical Society of Japan, Vol. 77, Paper # 033703, 2008.
[Sl-26] Chansoo Lim, Jin-Seok Jeon and Ho-Young Kwak, ” Pulse width measurements for sonoluminescing gas bubble in various solution,” Europhysics Letters, Vol. 86, Paper # 17002, 2009.
[SL-27] Jin-Seok Jeon, Chansoo Lim, Ilgon Ko and Ho-Young Kwak, ” Pulse width measurement of sonoluminescing air bubble in various solution using a time-correlated single photon counting technique,” Submitted for publication, 2009.
[SL-28] Chansoo Lim, Jeong Eun Kim, Jae Young Lee and Ho-Young Kwak, ” Nonlinear behavior of micro bubble under ultrasound due to heat transfer,” Journal of Mechnical Science and Technology, in press, 2009.
[SL-29] Ki-Taek Byun and Ho-Young Kwak, “Degradation of Methylene blue under multibubble sonoluminescence,” Journal of Photochemistry and Photobiology, Vol. 175, pp. 45-50, 2005.
[SL-30] Seong Soo Lee, Kook Won Seo, Seok Hwan Yoon, Il-Wun Shim, Ki-Taek Byun and Ho-Young Kwak, “CdS coating on TiO2 nanoparticles under multibubble sonoluminescence condition,” Bulletin of the Korean Chemical Society, Vol. 26, pp. 1579-1581, 2005.
[SL-31] Ki-Taek Byun, Kook Won Seo, Il-Wun Shim, and Ho-Young Kwak,” Syntheses of ZnO and ZnO-coated nanoparticles in various alcohol solutions at multibubble sonoluminescence (MBSL) condition, Chemical Engineering Journal, Vol. 132, pp. 125-135, 2007.
[SL-32] Seung Soo Lee, Ki-Taek Byun, Jong Pil Park, Sin Kyu Kim, Ho-Young Kwak, and Il-Wun Shim, “Preparation of Li4Ti5O12 nanoparticles by a simple sonochemical method,” Dalton Transations, Vol. 37, pp. 4182-4184, 2007.
[SL-33] Seung Soo Lee, Ki-Tack Byun, Jong Pil Park, Sin Kyu Kim, Joung Chan Lee, Suk-Kyu Chang, Ho-Young Kwak and Il-Wun Shim, ” Homogeneous ZnS coating onto TiO2nanoparticles by a simple one pot sonochmical method,” Chemical Engineering Journal, Vol. 139, pp. 194-197, 2008.
[SL-34] Sin Kyu Kim, Seung Soo Lee, Jong Pil Park, Jae Young Park, kang Min Ok, Ho-Young Kwak and Il-Won Shim,” Coating of TiO2 nanoparticles with PbS- thin films and preparation of PbS nanoparticles using a one-pot sonochemical reaction,” Thin Solid Films, Vol. 517, pp. 6663-6665, 2009.
[SL-35] Ki-Moon Kang, Hyo-Won Kim, Ho-Young Kwak, Characteristics of LiFePO4/C composite prepared by sonochemical method under conditions of multibubble sonoluminescence” Korean Journal of Chemical Engineering, vol.33, pp. 688-696, 2016.
[SL-36] Hyo Won Kim, Ki Moon Kang and Ho-Young Kwak, ” Preparation of supported Ni catalysts with a core/shell structure and their catalytic tests of partial oxidation of methane,” International Journal of Hydrogen Energy, Vol. 34, pp. 3351-3359, 2009.
[SL-37] Hyo-Won Kim, Ki-Moon Kang, Ho-Young Kwak and Jong Hyun Kim, “Preparation of supported Ni catalysts on various metal oxides with core/shell structures and their tests for steam reforming of methane,” Chemical Engineering Journal, Vol. 168, pp. 775-783, 2011.
[SL-38] Ki-Moon Kang, Hyo-Won Kim, Il-Wun Shim and Ho-Young Kwak, “Catalytic test of supported Ni catalysts with core/shell structure for dry reforming of methane,” Fuel Processing Technology, Vol. 92, pp. 1236-1243, 2011.
[SL-39] Ki-Moon Kang, Il-Wun Shim and Ho-Young Kwak, “Mixed and autothermal reforming of methane with supported Ni catalysts with a core/shell structure,” Fuel Processing Technology, Vol. 93, pp. 105-114, 2012.
[SL-40] Ilgon Ko and Ho-Young Kwak, “Measurement of pulse width from a bubble cloud under multibubble sonoluminescence conditions,” Journal of the Physica Society of Japan, Vol. 79, Paper No. 124401, 2010.
[SL-41] Shahid Mahmood, Yungpil Yoo, Jaekyoon Oh, Ho-Young Kwak, “Hydrodynamic approach to multibubble sonoluminescence,” Ultrasonics Sonochemistry, Vol. 21, pp. 1512-1518, 2014.
[SL-42] Ki Young Kim and Ho-Young Kwak, and Jong Hyun Kim, “Molecular dynamics simulation of collapsing phase for asonoluminescing gas bubble in sulfuric acid solutions : A comparative study with theoretical results”, Journal of Physical Society of Japan, Vol. 76, Paper #024301, 2007.
[SL-43] Ki Young Kim, Chansoo Im, Ho-Young Kwak, and Jong Hyun Kim, “Validation of molecular dynamics simulation for a collapsing gas bubble,” Molecular Physics, Vol. 106, pp. 967-975, 2008.