Simulation. Lizhu Tong 1 Co., Ltd Numerical. Model. 1. Introduction. flows. discussed. kinds. the maximum. plasma model.

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1 Simulation of the Plasma Generated a Gas Bubble Lizhu Tong 1 1 Keisoku Engeerg System Co., Ltd Uchikanda, Chiyoda-ku, Tokyo , Japan, tong@kesco.co.jp Abstract: The plasmas generated water volve various physical phenomena such as flows agitated by bubbles, high electric fields for breakdown, discharges bubbles with the size variation, and so on. In this paper, studies have been made on the simulation of plasmas generated bubbles with the size variation. The species taken account clude electrons, three kds of ions, and ten kds of neutral (molecule, radical, excited) species. 43 chemical reactions are considered. The time evolution of bubble size is simulated usg the movg mesh method provided COMSOL Multiphysics. The plasma properties durg the variation bubble size are obtaed. The effect of the duration for the variation bubble size and the maximum bubble size on discharge properties is examed. Keywords: Gas Bubble, Atmospheric Pressure Plasma, Movg Boundary. 1. Introduction Electrical discharges gas-liquid environ- ments and liquids (primarily water, but some cases also organic liquids) have been studied for a number of years for applications electrical transmission, chemical destruction pollution control, chemical synthesis, polymer surface treatment, biological activation, biomedical treatment, material and nanoparticle synthesis, and chemical analysis of liquid solutions [1]. Discharges directly side bubbles have presented an terestg case for fundamental studies and potential applications because of large surface areas and the presence of the gas phase for ease of discharge itiation [2-5]. Some model simulationss for discharges with humid air or jected gas bubbles have been reported [6-9]. Sce the bubble size varies durg discharge, the plasma simulation bubbles becomes complicated. Until now the studies are performed only for either bubble dynamics [6,7] or plasma properties ignorg the variation bubble size [8,9]. In this work, bubble dynamics and plasma properties are coupled to a one-dimensional ( 1-D) bubble plasma model. The plasma module and the movg mesh technique provided COMSOL Multiphysics are used. The plasma properties with bubbles are presented and discussed. 2. Numerical Model Figure 1. Schematic of 1-D bubble plasma model. The simulations are performed usg 1-D plasma model a 0% %H 2 O gas bubble at atmospheric pressure. The bubble radius is varied from 1 to 8.5 mm, which is taken from the previous research on bubble dynamics [ 7]. The study is made for the first period of the variation bubble radius [6,7]. The duration for the variation bubble radius is chosen = 0.8, 1.6, or 2.4 ms. The plasma species taken account clude the ions: H 2 O +, O H 2 O, H, OH, H 2, O( 1 2 +, H + 2, the neutrals: D), O, O 2, O 3, HO 2 2, H 2 O 2, as well as electrons. The reactions of electron impact collision and those of ions and neutral species are listed Table 1. The detailed formation for plasma modelg can be found our previous work [13,14]. 1-D bubble plasma model for the plasmas generated bubbles is shown Fig. 1. A dc power supplied voltage V and a ballast resistor R b are used. V dc is discharge voltage and j is discharge current density. V dc is solved by, (1) where V= - 1 kv, R b = k. A is set 0.03 cm 2 this work. The movg mesh technique, named as Arbitrary Langrangian Eulerian (ALE) method, Excerpt from the Proceedgs of the 2013 COMSOL Conference Boston

2 is used to trace the variation solved doma. Table 1: The chemical reactions cluded the model. No Reaction e +H 2 O e + H 2 O e +H 2 O e + H+ OH e +H 2 O e + H 2 + O( 1 D) e +H 2 O 2e + H 2 O + e +H 2 e + H 2 e +H 2 e + H + H e +H 2 2e + + H 2 e +O 2 e + O 2 e +O 2 e + O + O e +O 2 e + O + O( 1 D) e +O 2 2e + + O 2 e +O e + O( 1 D) O( 1 D) O 2O + O 2 O 3 +O O + 2O 2 O 3 +O 2 H +O + H 2 OH +H 2 H +O + H 2 O OH +H 2 O H +O 2 + H 2 HO 2 +H 2 H +O 2 + O 2 HO 2 +O 2 H +O 2 + H 2 O HO 2 +H 2 O H +OH+ H 2 H 2 O +H 2 H +OH+ O 2 H 2 O +O 2 H +O 3 OH +O 2 H +O 3 O + HO 2 H +HO 2 H 2 2O +O H +HO 2 O 2 +H 2 H +HO 2 2OH O +O( 1 D) 2O O( 1 D) +H 2 OH +H O( 1 D) +O 2 O+ O 2 O( 1 D) +O 3 2O 2 O( 1 D) +O 3 2O + O 2 O( 1 D) +OH H+ O 2 O +HO 2 OHH +O 2 O( 1 D) +HO 2 OH +O 2 O( 1 D) +H 2 O 2 2 H 2 O +O 2 O( 1 D) +H 2 O O +H 2 O O( 1 D) +H 2 O H 2 +O 2 OH +O 3 HOO 2 +O 2 2OH H 2 O 2 OH +HO 2 OO 2 +H 2 O OH +H 2 O 2 H 2 O +HO 2 2HO 2 H 2 O2+ O 2 Ref. The method enjoys the advantages of both Eulerand can capture the greater deformation with the higher ian and Langrangian frames of reference resolution [15]. ALE method comprises of two frames: a reference frame with X coordate for a 1-D formulation and a spatial frame with x coordate. The reference frame has fixed co- ordates while the spatial frame has coordates movg with time, subject to boundary conditions. The mesh displacement is obtaed by solvg the followg equation Results (2) Figure 2. Electron density, electron temperature, and electric potential at the different times for = 1.6 ms. Excerpt from the Proceedgs of the 2013 COMSOL Conference Boston

3 H 2 O + OH O 2 O 3 H 2 H 2 O 2 Figure 3. Densities of chemical speciess at the different times for = 1.6 ms. Figure 2 shows the electron density, electron temperature, and electric potential at the different times for = 1.6 ms. As the bubble size is enlarged, the electron density extends from the surface of cathode to anode grounded. At t = 0.8 ms, the largest bubble size reaches, which the electron density the neighborhood of cathode appears a large reduction. The highest electron temperature is located the region close to the cathode durg the whole discharge, which sustas the behavior of DC discharge. The density of H 2 O + ion is shown Fig. 3. The densities of H + 2 and O + 2 ions are found to be two orders lower than H 2 O +, so that both are not presented here. As shown Fig. 3, the distributions of neutral species have a common aspect, i.e., the high densities appear the neighborhood of cathode, but as the crease bubble size, the densities the region depart from cathode are dramatically reduced over two orders. After t = 0.8 ms, due to the reduction of solved doma, the densitiess start to rise up. The production efficiency of H 2 O 2 for discharge side gas bubble has been reported [2,4]. It is noted that OH radicals play some important roles, such as oxidation, decomposition of organic pollutants, and so on. The densities of H 2 2O 2 and OH obtaed this work are possessed of a high Excerpt from the Proceedgs of the 2013 COMSOL Conference Boston

4 = 0.8 ms = 2.4 ms Figure 4. Electron density at the different times for = 0.8 and 2.4 ms. Radius: 1~ ~4.8 mm level values, as shown Fig. 3. The density of O 3 is found to be five orders lower than other neutral species, which is similar to some previous researches, e.g., the density of O 3 has been reported to be dramatically reducedd as the crease of H 2 O concentration and the density of O 3 presents a very low value when H 2 O concentration rises up to only 6% [9]. Figure 4 shows the results for the duration for the variation bubble size of 0.8 and 2.4 ms. The electron density at = 0.8 ms is distctly lower than that at = 2.4 ms, especially for the time of small bubble size. This could be deduced that longer discharge times cause more ionizations so that the electron density is creased at = 2.4 ms. The results for different variations bubble radius are given Fig. 5. The bubble radius varies with 1~4.8 and 1~6.7 mm. As the reduction of maximum bubble radius, the electron density becomes relative uniform the bulk of discharge. The dampg phenomenon the region far from cathode is remitted. 4. Conclusions The simulation of the plasma generated a gas bubble is performed usg COMSOL Multiphysics 4.3a. The movg mesh technique is coupled for the first time with plasma simulation. The obtaed densities of chemical species, such as OH, H 2 O 2, and so on, would be beneficial to many further researches on environ- mental applications. The present research provides an efficient method to study plasmas generated bubbles, especially water. 5. References Radius: 1~ ~6.7 mm Figure 5. Electron density at the different times for the variations of bubble radius: 1~4.8 and 1~6.7 mmm at = 1..6 ms. 1. V.I. Parvulescu, M. Magureanu, P. Lukes, Plasma Chemistry and Catalysis Gases and Liquids, Wiley-VCH Verlag & Co. KGaA, Weheim, Germany (20). 2. K.Y. Shih, B.R. Locke, Effects of electrode protrusion length, pre-existg bubbles, solution conductivity and temperature, on liquid phase pulsed electrical discharge, Plasma Process. Polym., 6 (), (2009). 3. K. Yasuoka, K. Sato, Development of repeti- tive pulsed plasmas gas bubbles for water treatment, Int. J. Plasma Environ. Sci. Technol., 3 (1), (2009). Excerpt from the Proceedgs of the 2013 COMSOL Conference Boston

5 4. L. Němcová, A. Nikiforov, C. Leys, F. Krcma, Chemical efficiency of H 2 O 2 production and decomposition of organic compounds under action of DC underwater discharge gas bubbles, IEEE Trans. Plasma Sci., 39 (3), (20). 5. M. Kurahashi, S. Katsura, A. Mizuno, Radical formation due to discharge side bubble liquid, J. Electrostatics, 42, 93-5, (1997). 6. J.A. Cook, A.M. Gleeson, R.M. Roberts, A spark-generated bubble model with semiempirical mass transport, J. Acoust. Soc. Am., 1 (4), (1997). 7. X.P. Lu, One-dimensional bubble model of pulsed discharge water, J. Appl. Phys., 2, (4pp) (2007). 8. N.Y. Babaeva, M.J. Kushner, Structure of positive streamers side gaseous bubbles immersed liquids, J. Phys. D: Appl. Phys., 42, (5pp) (2009). 9. N. Takeuchi, Y. Ishii, K. Yasuoka, Modellg chemical reactions dc plasma side oxygen bubbles water, Plasma Sources Sci. Technol., 21, (8pp) (20).. LXcat, COMSOL Multiphysics 4.3a- Model library for Plasma Module.. D.X. Liu, P. Bruggeman, F. Iza, M.Z. Rong, M.G. Kong, Global model of low-temperature atmospheric-pressure He+H 2 O plasmas, Plasma Sources Sci. Technol. 19 (2), (20). 13. L.Z. Tong, Effect of gas flow rate and gas composition Ar/CH 4 ductively coupled plasmas, COMSOL Conference 20 Boston, USA (20). 14. L.Z. Tong, Numerical study of the effect of gas flow low pressure ductively coupled Ar/N 2 plasmas, Central European Journal of Physics (4), (20). 15. K.B. Deshpande, Validated numerical modellg of galvanic corrosion for couples: Magnesium alloy (AE44) mild steel and AE44 alumium alloy (AA6063) bre solution, Corrosion Sci. 52, (20). Excerpt from the Proceedgs of the 2013 COMSOL Conference Boston