behaviour of oh radicals in an atmospheric-pressure streamer discharge studied by two-dimensional...
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Behaviour of OH radicals in an atmospheric-pressure streamer discharge studied by two-
dimensional numerical simulation
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2013 J. Phys. D: Appl. Phys. 46 175206
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IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 46 (2013) 175206 (13pp) doi:10.1088/0022-3727/46/17/175206
Behaviour of OH radicals in anatmospheric-pressure streamer dischargestudied by two-dimensional numericalsimulationAtsushi Komuro1, Ryo Ono1 and Tetsuji Oda2
1 Department of Advanced Energy, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba227-8568, Japan2 Department of Electrical Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo113-8656, Japan
E-mail: [email protected] and [email protected]
Received 20 December 2012, in final form 28 February 2013Published 11 April 2013Online at stacks.iop.org/JPhysD/46/175206
AbstractThe production process of OH radicals in an atmospheric-pressure streamer discharge isstudied. A streamer discharge model is developed to analyse the characteristics of a pulsedpositive streamer discharge in point-to-plane electrodes filled with humid air at atmosphericpressure. The results indicate that the behaviour of OH radicals in and after the discharge pulseis characterized by three reaction processes: ‘OH-production’, ‘OH-cycle’ and‘OH-recombination’. The first process of OH-production includes dissociation reactions ofH2O with O(1D) and N2(a′ 1�−
u ), which are the main production processes of OH in thedischarge. Immediately after the OH-production process, the OH radicals are destroyed by areaction with O(3P) to form O2 and H. Then the subsequent reactions produce OH againthrough the reaction of H + HO2, which is the OH-cycle process. Finally, the OH radicals areconsumed by the OH-recombination process.
(Some figures may appear in colour only in the online journal)
1. Introduction
Non-thermal plasmas generated in air at atmospheric pressurehave attracted considerable interest because of their non-thermal property and high reactivity [1]. A streamer discharge(e.g. a corona discharge and a dielectric barrier discharge)is one such non-thermal plasma. In a streamer discharge,chemically active species such as O, N and OH are produced,which play important roles in many applications such as thedecomposition of gaseous pollutants [2], water treatment [3],ozone production [4, 5], plasma-assisted ignition [6], surfacetreatment [7, 8] and medical applications [9]. However, theunderstanding of radical production in a streamer discharge isstill poor. The above applications need to be optimized in ahighly scientific way to both improve the energy efficiencyand confirm their safety. The authors previously clarified
the production mechanism of O and N radicals in a streamerdischarge in dry air by comparison between experimentaland simulated results [10]. For the increased practical useof atmospheric-pressure plasmas, a discharge model underhumid-air conditions needs to be developed.
The OH radical has been considered one of the importantreactants in the removal of gaseous pollutants since OHhas a higher oxidation potential than other oxidative speciessuch as O, HO2, H2O2 and O3. For example, Lowkeand Morrow [11] theoretically showed that OH plays amajor role in removing SO2 in a pulsed corona discharge.Magne et al [12] reported that the OH radical reacts withmore volatile organic compounds (VOCs) than the O radicalat ambient temperatures. However, the behaviour of the OHradical is not yet well understood because of its complexreaction processes [13]. For example, in many previous
0022-3727/13/175206+13$33.00 1 © 2013 IOP Publishing Ltd Printed in the UK & the USA
J. Phys. D: Appl. Phys. 46 (2013) 175206 A Komuro et al
Figure 1. Dependence of reaction rates (kδ) with mean electronenergy under humid-air (H2O = 2.0%) conditions where k is thereaction rate constant by electron impact and δ is the fraction ofnitrogen, oxygen or water in the mixture.
studies, OH has been considered to be mainly produced bythe following reactions [2, 11]:
H2O + e → H + OH + e, (1)
H2O + e → H− + OH, (2)
O(1D) + H2O → OH + OH. (3)
Figure 1 shows the reaction rates of (1), (2) and the productionof O(1D). These rates are calculated from the Boltzmannequation with the set of cross sections for humid-air conditions.The reaction rate of O(1D) production, and as a result thereaction rate of (3), is much faster than those of (1) and(2). Therefore, as figure 1 indicates, OH radicals are mainlyproduced by (3). However, this conclusion cannot explainour previous experimental results, which show that almost thesame amount of OH is produced in humid-air and humid-nitrogen discharges [14]. The following reaction has beensuggested as a major production channel of OH radicals inhumid nitrogen [15, 16]:
N2(A3�+
u ) + H2O → N2 + OH + H. (4)
The production rate of N2(A3�+
u ) by electron impact isalso shown in figure 1. It is over an order of magnitudeslower than the production rate of O(1D) and four orders ofmagnitude slower than that of (3) [16]. Therefore, (4) cannot besubstituted for (3) as a major OH-production reaction channelin humid nitrogen.
The discharge propagation kinetics in humid air is alsocomplicated. Even a small amount of humidity in air stronglyaffects the electron transport coefficients, such as drift velocityand mean electron energy, because H2O molecules have alarge cross section at low energies (<1 eV) owing to their highdipole moment [17]. In addition, the humidity acceleratesvibrational relaxation rates and therefore increases the gastemperature after the discharge [18, 19]. Moreover, somedischarge products derived from H2O such as H, HO2 and H2O2
are also reactive and have been reported to have important rolesin the discharge kinetics [12, 15]. However, these effects havenot been sufficiently confirmed.
In this paper, the streamer discharge kinetics inH2O/O2/N2 is analysed using our previously developed two-dimensional streamer discharge model. In particular, thebehaviour of OH radicals is discussed by comparison betweenexperimental and simulated data. Then, the mechanism of OHradical production is discussed.
2. Kinetic model
2.1. Discharge model
The simulations are performed in a 13 mm-gap point-to-planeelectrode configuration according to our experimental setup.Streamer dynamics are described by the following system ofequations:
∂ns
∂t+ div(nsvs(E/N)) = Ss(E/N), s = e, p, n, (5)
neve(E/N) = neµe(E/N)E − De(E/N)grad(ne), (6)
npvp(E/N) = npµp(E/N)E, (7)
nnvn(E/N) = nnµn(E/N)E, (8)
divE = e
ε0(np − ne − nn), (9)
where ns , vs(E/N), Ss(E/N), µs(E/N) and Ds(E/N) arethe charged particle density, charged particle velocity, particlechemical source term, mobility and diffusion coefficient,respectively. The subscript ‘s’ denotes electrons (e) orpositive (p) or negative (n) ions. E is the electric field,ε0 is the permittivity of free space, and e is the absolutevalue of the electronic charge. The transport and sourceparameters involving electrons (such as ve, De, and the reactioncoefficients in Ss) are calculated using Bolsig+ software [20]with previously published e-V cross sections [21]. A detaileddescription of the chemical reaction model is given in thefollowing section. In (7) and (8), all ion mobilities areassumed to be 2.2 × 10−4 m2 V−1 s−1 [22]. This assumptionis a rough estimation because ion mobilities are a function ofreduced electric field E/N . However, since it is commonlyaccepted that the ion mobilities are significantly slower thanthe electron mobility due to a much larger mass, the ions hardlymove (remain relatively static) within several nanoseconds.A similar value of ion mobility is used by Morrow andLowke [23]. Ion diffusion is neglected for the same reason.Photoionization is taken into account through the three-exponential Helmholtz models [24, 25]. Equations (5) and (9)are solved using a general personal computer in an attemptto reduce the computational cost. Some numerical techniquessuch as the method of solving (5) and (9) are given in ourprevious paper [10].
Figure 2(a) shows the configuration of the electrodes andthe computation domain. To simulate the development of adischarge, we chose a cylindrical domain of 18 mm height and8 mm radius. The total number of grid points is Nz × Nr =1792 × 256 with spatial steps from δz = 1 µm (near thepoint anode and plane cathode) to 10 µm (at the interelectrode
2
J. Phys. D: Appl. Phys. 46 (2013) 175206 A Komuro et al
z-a
xis
[m
m]
r-axis [mm]8
0
2
4
6
10
8
12
13
1
3
5
7
9
11
0
5
10
15
20
25
0 200 400 600 800 1000
Vo
lta
ge
[kV
]
Time [ns]
0
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0.1
0.15
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0 50 100 150 200
Vo
lta
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[k
V]
Cu
rre
nt
[A]
Time [ns]
Point
anode
(a)
(b)
(c)
0 1 ~ ~ ~
. . .
-5
-4
Figure 2. (a) Schematic view of the calculation domain and mesh, (b) waveform of the applied pulsed voltage and (c) enlarged view of theapplied voltage and calculated discharge current. The applied voltage is 24 kV.
gap) [26] in the z-direction and from δr = 2.5 to 200 µm in ther-direction. The spatial resolution is derived from Eichwaldet al [27]. The point electrode has the form of a hyperboloidof revolution with a radius of 40 µm, corresponding to thatused in our experiment. At the conducting anode, the positiveion fluxes are fixed to zero, while the negative ion andelectron fluxes are estimated using the Neumann boundarycondition [27]. At the conducting cathode, the Neumannboundary condition is applied to all positively and negativelycharged fluxes [27]. All radial derivatives of the densities areset to zero at the open boundaries [28]. Figure 2(b) showsthe waveform of the applied pulsed voltage and figure 2(c)shows an enlarged view of figure 2(b) and the discharge currentcalculated by an extension of Morrow and Sato’s formula [29].In this simulation, the actual pulsed voltage, which is measuredfrom our experiments, is applied to the conduction anode tip.The discharge voltage V , which is set to 24 kV in figure 2(b),is defined by the peak voltage of the pulse. The rate of voltageincrease is about 0.52 kV ns−1.
In our simulation, the neutral particles are assumed to bestatic. Much work remains to be done on the questions ofgas heating and the decrease in gas density, which affect theelectron distribution function through the variation of reduced
electric field, E/N , and the Arrhenius constant through thegas temperature [30]. Actually, it has been suggested that thedecrease in density due to gas heating is responsible for theformation of sparks, initiated by a discharge [31]. However,Popov [32] estimated that the gas heating is equal to 22–26 Kat 3 µs under the same conditions as this paper, and themain heating occurred after the discharge (time t > 200 ns).Therefore, it is estimated that the gas heating does not affectthe electron distribution function through E/N variations inthe single discharge. At t > 3 µs, the V–T relaxation throughH2O molecules [18] can cause gas heating, which may affectArrhenius constants through the gas temperature. Therefore,we compare the simulated data with the experimental dataup to a time 3 µs after the discharge, which is considered tocorrespond to the pre-diffusion phase of neutral species in thedischarge of a single-pulse streamer [33, 34].
2.2. Chemical reaction model
We used a reduced reaction model including electron impactreactions (excitation, ionization, dissociation, recombination,attachment and detachment), ion recombination and thereactions of neutrals as shown in tables 1–3. For N2 andO2 molecules, the excited species correspond to effective
3
J. Phys. D: Appl. Phys. 46 (2013) 175206 A Komuro et al
Table 1. Considered reactions involving electrons.
Reaction Rate constant (cm3 s−1)
(R1) N2 + e → N2(v) + e f1(E/N)(R2) N2 + e → N2(A1) + e f2(E/N)(R3) N2 + e → N2(A2) + e f3(E/N)(R4) N2 + e → N2(B) + e f4(E/N)(R5) N2 + e → N2(a) + e f5(E/N)(R6) N2 + e → N2(C) + e f6(E/N)(R7) N2 + e → N2(E) + e f7(E/N)
(R8) N2 + e → N(4S) + N(2D) + e f8(E/N)(R9) N2 + e → N+
2 + 2e f9(E/N)(R10) N2 + e → N+
2 (B) + e f10(E/N)(R11) O2 + e → O2(v) + e f11(E/N)(R12) O2 + e → O2(a) + e f12(E/N)(R13) O2 + e → O2(b) + e f13(E/N)(R14) O2 + e → O2(A) + e f14(E/N)
(R15) O2 + e → O(3P) + O(3P) + e f15(E/N)
(R16) O2 + e → O(1D) + O(3P) + e f16(E/N)
(R17) O2 + e → O(1S) + O(3P) + e f17(E/N)(R18) O2 + e → O+
2 + 2e f18(E/N)
(R19) O2 + e → O−(2P) + O(3P) f19(E/N)
(R20) O2 + O2 + e → O−2 + O2 f20(E/N)
(R21) H2O + e → H2O(ν2) + e f21(E/N)(R22) H2O + e → H2O(ν1) + e f22(E/N)(R23) H2O + e → H2O(ν3) + e f23(E/N)(R24) H2O + e → H + OH + e f24(E/N)(R25) H2O + e → O(P) + H2 + e f25(E/N)(R26) H2O + e → H2O+ + 2e f26(E/N)(R27) H2O + e → OH− + H f27(E/N)(R28) H2O + e → H− + OH f28(E/N)(R29) H2O + e → H2 + O− f29(E/N)
states clustered around actual molecular levels as describedin table 4, in accordance with the method proposed byFresnet et al [35]. The rate constants of the electron impactreactions are calculated by an analysis of the Boltzmannequation. The effects of superelastic collisions induced byhighly vibrationally excited molecules on the electron energydistributions (EEDF) are not considered in this simulationbecause the densities of vibrationally excited molecules arerelatively small and have little effect in a single atmospheric-pressure pulse discharge [10, 36]. However, superelasticcollisions are expected to have an effect under low-pressuredischarge or repetitive discharge conditions [37, 38]. In thecharged-particle kinetics, three positive ions: N+
2, O+2 and
H2O+, four negative ions: O−2 , O−, OH− and H−, and electrons
are considered. Complex ions such as O+4, N+
4 and O+2N2,
and the charge transfer reactions are not considered in thissimulation. Reaction kinetics and rate coefficients of complexions have been studied in many papers [39–42]. However,the effects of complex ions on radical production have onlybeen investigated in simulated cases [43], and corroborationmust be made through actual experiments. Even withoutsuch complex ions, the development of primary and secondarystreamers was well reproduced in our reduced model, whosevalidity was confirmed by comparison between experimentaland simulated streak photographs [10]. In addition, thesimulated production of O and N radicals was also in goodqualitative agreement with experimental results [10]. Thus,these effects are ignored in our simulation.
There are a large number of reaction pathways and rateconstants that have been proposed to explain the relaxationkinetics from non-equilibrium conditions triggered by adischarge [45–44]; however, most of the rate constants areunknown or have only been estimated theoretically becauseof the difficulty of measuring such fast reactions. Therefore,we use only reliable reactions whose rate constants havebeen validated by direct measurements or indirect methodsinvolving theoretical estimations and experimental results.For example, the quenching rate constant of N2(A 3�+
u ) byO2 is reliable since it has been directly measured and itsvalidity has been confirmed in other papers [47, 48]. Therates of the recombination reactions of N2(A 3�+
u ) are alsoreliable because the reaction kinetics of the N2 discharge,including some impurities, have been well modelled withthe theoretically estimated recombination rates even thoughthe rates were not fully measured [35, 37]. On the otherhand, some detachment processes from negative ions that playimportant roles in discharge relaxation phenomena [62, 63, 65]are not well defined. The detachments induced by excitedmolecules of nitrogen, such as N2(A 3�+
u ) and N2(B 3�g),have not been clearly shown because the rate constants usedin some studies on discharge modelling were taken from onlyone reference. Therefore, we use detachment reactions thathave been investigated in more than one paper. For theother chemical reactions, we also attempted to find as manypapers as possible with the help of the NIST database [49],and we chose the rate constants carefully. The vibration tovibration (VV) transitions and vibration to translation (VT)transitions are considered using our previously developedvibrational relaxation model [18]. However, they have nomajor effects in this simulation because the VV and VTtransitions mainly occur several µs after the discharge [18].
Admittedly, the simplified reaction model does notdescribe all the kinetics triggered by the discharge. However, itis valid under limited conditions from the start of the dischargeuntil 3 µs after the discharge pulse, as considered in this paper.
3. Results
3.1. Streamer discharge kinetics under humid-air conditions
Figure 3 shows the spatial distribution of discharge lightemission obtained from the optical emission of the secondpositive system (SPS) of N2: C 3�u → B 3�g, whoseintensity is proportional to the N2(C
3�u) density. Thenumerically calculated SPS emission in the space r = (r, z)
is spatially integrated along the line of sight. In addition, it istemporally integrated over 2 ns. Therefore, we calculate thetime-integrated space-averaged optical emission [50, 51]. Theprimary streamer is formed near the anode tip and starts topropagate towards the plane cathode, as shown in figure 3.When the streamer head arrives at the plane cathode, thesecondary streamer starts to extend. These characteristics of anatmospheric-pressure streamer discharge have been confirmedelsewhere in both experiments and simulations [10, 27, 52].The light emission in humid air is similar to that in dryair. It is known that the changes in the spatial distribution
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J. Phys. D: Appl. Phys. 46 (2013) 175206 A Komuro et al
Table 2. Considered reactions involving charged particles.
RateReaction constant (cm3 s−1) Ref
(R30) N+2 + e → N(4S) + N(4S) 1.80 × 10−7
(300
Te
)0.39
[60]
(R31) N+2 + e → N2 4.00 × 10−12 [30]
(R32) N+2 + O− → N2 + O(3P) 4.00 × 10−7 [30]
(R33) N+2 + O−
2 → N2 + O2 1.60 × 10−7 [30]
(R34) O+2 + e → O(3P) + O(3P) 1.95 × 10−7
(300
Te
)0.7
[61]
(R35) O+2 + e → O2 4.00 × 10−12 [30]
(R36) O+2 + O− → O2 + O(3P) 9.60 × 10−8 [30]
(R37) O+2 + O−
2 → 2O2 4.20 × 10−7 [30](R38) H2O+ + e → OH + H 3.80 × 10−7 [30](R39) H2O+ + e → H2 + O(3P) 1.40 × 10−7 [30](R40) H2O+ + e → H + H + O(3P) 1.73 × 10−7 [30](R41) H2O+ + O− → H2O + O(3P) 4.00 × 10−7 [30](R42) H2O+ + O−
2 → H2O + O2 4.00 × 10−7 [30](R43) O−
2 + H → HO2 + e 1.20 × 10−9 [62](R44) O−
2 + H → OH− + O(P) 1.50 × 10−9 [62](R45) O−
2 + O2(a) → 2O2 + e 2.00 × 10−10 [63](R46) O−
2 + O(P) → O3 + e 3.00 × 10−10 [63](R47) O− + O2(a) → O3 + e 3.00 × 10−10 [63](R48) O− + O(P) → O2 + e 2.00 × 10−10 [63](R49) H− + H2O → OH− + H2 3.80 × 10−9 [46](R50) H− + H → H2 + e 2.00 × 10−9 [64](R51) H− + O2 → HO2 + e 1.20 × 10−9 [65](R52) OH− + H → H2O + e 1.40 × 10−9 [62](R53) OH− + O(P) → HO2 + e 2.00 × 10−9 [65]
Table 3. Considered reactions for neutral species.
Reaction A (cm3 s−1) β Ea (K) Ref
(R54) N2(A1) + O2 → N2 + O(3P) + O(3P) 1.70 × 10−12 0 0 [32](R55) N2(A1) + O2 → N2 + O2(b) 7.50 × 10−13 0 0 [32](R56) N2(A1) + O2 → N2O + O2(P) 7.80 × 10−12 0 0 [66](R57) N2(A1) + N2(A1) → N2 + N2(E) 1.00 × 10−11 0 0 [35](R58) N2(A1) + N2(A1) → N2 + N2(B) 7.70 × 10−11 0 0 [32](R59) N2(A1) + N2(A1) → N2 + N2(C) 1.60 × 10−10 0 0 [32](R60) N2(A1) + O(3P) → N2 + O(1S) 3.00 × 10−11 0 0 [46](R61) N2(A1) + O(3P) → NO + N(2D) 7.00 × 10−12 0 0 [35](R62) N2(A1) + O(3P) → N2 + O(P) 2.00 × 10−11 0 0 [35](R63) N2(A1) + H → N2 + H 2.10 × 10−10 0 0 [35](R64) N2(A1) + OH → N2 + OH 1.00 × 10−10 0 0 [35](R65) N2(A1) + H2O → N2 + H + OH 5.00 × 10−14 0 0 [35](R66) N2(A1) + NO → N2 + NO(A) 6.90 × 10−11 0 0 [35](R67) N2(A2) + N2 → N2(A1) + N2 1.00 × 10−11 0 0 [35](R68) N2(A2) + O(P) → N2 + O(P) 2.00 × 10−11 0 0 [35](R69) N2(A2) + H → N2 + H 2.10 × 10−10 0 0 [35](R70) N2(A2) + OH → N2 + OH 1.00 × 10−10 0 0 [35](R71) N2(A2) + H2O → N2 + H + OH 5.00 × 10−14 0 0 [35](R72) N2(A2) + NO → N2 + NO(A) 6.90 × 10−11 0 0 [35](R73) N2(A2) + O(P) → NO + N(S) 7.00 × 10−12 0 0 [32](R74) N2(B) + O2 → N2 + O(3P) + O(3P) 3.00 × 10−10 0 0 [32](R75) N2(B) + N2 → N2(A1) + N2 1.00 × 10−11 0 0 [35](R76) N2(B) → N2(A1) + hν 1.50 × 105 (s−1) 0 0 [32](R77) N2(a) + O2 → N2 + O(3P) + O(3D) 2.80 × 10−11 0 0 [32](R78) N2(a) + N2 → N2(B) + N2 2.00 × 10−13 0 0 [66](R79) N2(a) + N2 → N2 + N2 2.00 × 10−13 0 0 [35](R80) N2(a) + H2 → N2 + H + H 2.60 × 10−10 0 0 [35](R81) N2(a) + H2O → N2 + OH + H 3.00 × 10−10 0 0 [58](R82) N2(a) + NO → N2 + N(4S) + O(3P) 3.60 × 10−10 0 0 [66](R83) N2(C) + O2 → N2 + O(3P) + O(3P) 2.50 × 10−10 0 0 [32]
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J. Phys. D: Appl. Phys. 46 (2013) 175206 A Komuro et al
Table 3. (Continued.)
Reaction A (cm3 s−1) β Ea (K) Ref
(R84) N2(C) + N2 → N2(B) + N2 1.00 × 10−11 0 0 [32](R85) N2(C) + N2 → N2(a) + N2 1.00 × 10−11 0 0 [35](R86) N2(C) → N2(B) + hν 2.80 × 107 (s−1) 0 0 [35](R87) N2(E) + N2 → N2(C) + N2 1.00 × 10−10 0 0 [35](R88) N+
2 (B) → N+2 + hν 1.40 × 107 (s−1) 0 0 [67]
(R89) NO(A) → NO + hν 5.10 × 106 (s−1) 0 0 [35](R90) N(2D) + O2 → NO + O(1D) 9.70 × 10−12 0 −185 [16](R91) N(2D) + O2 → NO + O(3P) 1.50 × 10−12 0.5 0 [66](R92) N(2D) + NO → N2 + O(3P) 1.80 × 10−10 0 0 [68](R93) N(2D) + N2 → N(4S) + N2 1.70 × 10−14 0 0 [16](R94) N(2D) + O(3P) → N(4S) + O(3P) 3.30 × 10−12 0 −260 [16](R95) N(2D) + H2O → OH + NH 4.00 × 10−11 0 0 [16](R96) N(4S) + HO2 → NO + OH 2.19 × 10−11 0 0 [69](R97) N(4S) + NO → N2 + O(3P) 3.51 × 10−11 0 49.84 [46](R98) N(4S) + N(4S) + N2 → N2 + N2 1.38 × 10−33 0 502.9 [70](R99) N(4S) + NO2 → NO + NO 2.30 × 10−12 0 0 [46](R100) N(4S) + NO2 → O(3P) + N2O 5.80 × 10−12 0 220 [71](R101) N(4S) + O2 → NO + O(P) 4.47 × 10−12 1 3270.2 [72](R102) O2(a) + N(S) → O(P) + NO 2.00 × 10−14 0 0 [71](R103) O2(a) + O(P) → O(P) + O2 7.00 × 10−16 0 0 [66](R104) O2(a) + O2 → O2 + O2 2.20 × 10−18 0.8 0 [73](R105) O2(a) + N2 → O2 + N2 1.4 × 10−19 0 0 [74](R106) O2(a) + NO → O(P) + NO2 3.49 × 10−17 0 0 [75](R107) O2(a) + NO → NO + O2 2.50 × 10−11 0 0 [76](R108) O2(b) + N2 → O2(a) + N2 2.10 × 10−15 0 0 [77](R109) O2(b) + O2 → O2(a) + O2 4.10 × 10−17 0 0 [77](R110) O2(b) + O(P) → O2 + O(P) 8.00 × 10−14 0 0 [77](R111) O2(b) + H2O → O2 + H2O 4.60 × 10−12 0 0 [77](R112) O2(b) + O3 → O2(a) + O2(a) + O(P) 1.80 × 10−11 0 0 [66](R113) O2(b) + NO → O2(a) + NO 4.00 × 10−14 0 0 [66](R114) O2(A) + O2 → O2(b) + O2(b) 2.90 × 10−13 0 0 [66](R115) O2(A) + N2 → O2(b) + N2 3.00 × 10−13 0 0 [66](R116) O2(A) + O(P) → O2(b) + O(D) 9.00 × 10−12 0 0 [66](R117) O(3P) + O2 + N2 → O3 + N2 5.51 × 10−34 −2.6 0 [77](R118) O(3P) + O2 + O2 → O3 + O2 6.01 × 10−34 −2.6 0 [77](R119) O(3P) + O(3P) + N2 → O2 + N2 9.46 × 10−34 0 −484.7 [78](R120) O(3P) + O(3P) + O2 → O2 + O2 3.81 × 10−33 −0.63 0 [79](R121) O(3P) + N(4S) + N2 → NO + N2 6.89 × 10−33 0 −134.7 [78](R122) O(3P) + NO + N2 → NO2 + N2 1.03 × 10−30 −2.87 −780.5 [80](R123) O(3P) + HO2 → OH + O2 2.70 × 10−11 0 −224 [77](R124) O(3P) + NO2 → O2 + NO 5.50 × 10−12 0 187.9 [77](R125) O(1D) + O2 → O(3P) + O2 3.12 × 10−11 0 −70 [81](R126) O(1D) + N2 → O(3P) + N2 2.10 × 10−11 0 −115 [81](R127) O(1D) + H2 → OH + H 1.10 × 10−10 0 0 [77](R128) O(1D) + H2O → OH + OH 2.2 × 10−10 0 0 [77](R129) O(1D) + H2O → H2 + O2 3.57 × 10−10 0 0 [82](R130) O(1D) + H2O2 → H2O + O2 5.20 × 10−10 0 0 [77](R131) O(1S) + H2O → O(P) + H2O 3.00 × 10−10 0 0 [83](R132) O(1S) + H2O → OH + OH 5.00 × 10−10 0 0 [83](R133) O(1S) + H2O → H2 + O2 5.00 × 10−10 0 0 [83](R134) O3 + H → OH + O2 1.40 × 10−10 0 480 [74](R135) O3 + NO → NO2 + O2 3.16 × 10−12 0 −1563 [46](R136) O3 + O(P) → O2 + O2 8.00 × 10−12 0 2060 [77](R137) O3 + O(D) → O2 + O(P) + O(P) 1.20 × 10−10 0 0 [74](R138) O3 + OH → HO2 + O2 1.70 × 10−12 0 940 [77](R139) O3 + O3 → O2 + O(3P) + O3 7.16 × 10−10 0 11200 [84](R140) OH + OH + N2 → H2O2 + N2 6.90 × 10−31 −0.8 0 [77](R141) OH + OH + O2 → H2O2 + O2 6.05 × 10−31 −3 0 [74](R142) OH + OH + H2O → H2O2 + H2O 1.54 × 10−31 −2 −183.6 [86](R143) OH + OH → H2O2 2.6 × 10−11 0 0 [77](R144) OH + OH → H2O + O(3P) 6.2 × 10−14 2.6 −945 [77](R145) OH + H + N2 → H2O + N2 6.87 × 10−31 −2 0 [86](R146) OH + H + H2O → H2O + H2O 4.38 × 10−31 −2 0 [86](R147) OH + HO2 → H2O + O2 4.8 × 10−11 0 −250 [77](R148) OH + N(4S) → NO + H 3.80 × 10−11 0 −85.39 [72]
6
J. Phys. D: Appl. Phys. 46 (2013) 175206 A Komuro et al
(R149) OH + O(3P) → O2 + H 2.40 × 10−11 0 −110 [77](R150) OH + NO + N2 → HNO2 + N2 7.40 × 10−31 −2.4 0 [74](R151) OH + NO + O2 → HNO2 + O2 7.40 × 10−31 −2.4 0 [74](R152) OH + NO2 + N2 → HNO3 + N2 2.60 × 10−30 −2.9 0 [74](R153) OH + NO2 + O2 → HNO3 + O2 2.20 × 10−30 −2.9 0 [74](R154) HO2 + HO2 → H2O2 + O2 2.20 × 10−19 0 −600.2 [77](R155) HO2 + NO → OH + NO2 3.60 × 10−12 0 −269.4 [77](R156) HO2 + HO2 + N2 → H2O2 + O2 + N2 1.90 × 10−33 0 −980 [74](R157) HO2 + HO2 + O2 → H2O2 + O2 + O2 1.90 × 10−33 0 −980 [74](R158) HO2 + NO2 → HNO2 + O2 1.20 × 10−13 0 0 [85](R159) H + HO2 → H2 + O2 1.75 × 10−10 0 1030 [86](R160) H + HO2 → H2O + O(3P) 5.00 × 10−11 0 866 [87](R161) H + HO2 → OH + OH 7.40 × 10−10 0 700.0 [86](R162) H + O2 + O2 → HO2 + O2 5.94 × 10−32 −1.0 0 [46](R163) H + O2 + N2 → HO2 + N2 5.94 × 10−32 −1.0 0 [46]
and the time variation of the discharge emission depend onthe gas composition and the shape of the applied pulsedvoltage [52, 53]. Although the dependence of humidity on thedischarge emission has not been clearly shown experimentally,the effect is estimated to be small from our simulated results.Figure 4(a) shows the axial distribution of the reduced electricfield at several different times. The reduced electric field,E/N , is approximately 800 Td (1 Td = 10−17 V cm2) at thestreamer head and it is almost constant when the streamerpropagates to the plane cathode. However, the velocity ofthe streamer head and the reduced electric field in the streamerchannel increase during its propagation through the gap. Inour simulation, we confirmed that the propagation velocity ofthe streamer head and the reduced electric field in the streamerchannel depend on the rate of increase in the applied pulsedvoltage. The development of a reduced electric field in theprimary streamer in humid air is not significantly different fromthat in dry air, obtained in our previous paper [10], becausethe ionization and photoionization rate coefficients are notchanged for an admixture containing a few per cent of H2Oin atmospheric-pressure air. However, the axial distribution ofthe reduced electric field in the secondary streamer is slightlydifferent in dry and humid air, as shown in figure 4(b). Thereduced electric field in the secondary streamer, which isknown to be determined by the balance between the ratesof ionization and attachment [10, 54], slightly increases withhumidity. This slight increase is caused by the electronegativecharacter of H2O. Figure 5 shows the total ionization andattachment rates in dry and humid air. The electron attachmentreaction H2O + e → H− + OH causes the slight shift of theequilibrium point between the total ionization and attachmentrates.
3.2. Comparison with experimental data
Figure 6 shows the simulated axial distribution of the OHradical density at t = 3 µs after the discharge pulse haselapsed. This result indicates that a large number of OHradicals as well as O and N radicals are produced near theanode tip [10]. Compared with our previous experimentalresults [19, 55], the simulated axial distribution of OH infigure 6 is in good qualitative agreement. However, thesimulated axial distribution of OH radicals has a stepwise
Table 4. Effective electronic states of N2 and O2 considered in thissimulation.
Electronic Excitation Effectivestate energy (eV) state
N2(X, v = 0) 0 N2(X)N2(A
3�+u , v = 0 . . . 4) 6.17 N2(A1)
N2(A3�+
u , v = 5 . . . 9) 7.00 N2(A2)
N2(B3�g) 7.35 N2(B)
N2(W3�u) 7.36 N2(B)
N2(A3�+
u , v > 10) 7.80 N2(B)N2(B
′ 3�−u ) 8.16 N2(B)
N2(a′ 1�−u ) 8.40 N2(a)
N2(a 1�g) 8.55 N2(a)N2(w
1�u) 8.89 N2(a)N2(C
3�u) 11.03 N2(C)N2(E
3�+g ) 11.88 N2(E)
N2(a′′ 1�+
g ) 12.25 N2(E)O2(a 1�g) 0.977 O2(a)O2(b 1�+
g ) 1.627 O2(b)O2(c 1�u) 4.05 O2(A)
z-a
xis
[m
m]
r-axis [mm]0 1-1
0
2
4
6
10
8
12
13
1
3
5
7
9
11
V
Emission
Intensity
[a.u.]
0
14 9 14 19 21 40
Time [ns]
Figure 3. Calculated spatial distribution of discharge light emissionat each time in H2O(2%)/air mixtures. The applied voltage is 28 kV.
change in density around the edge of the secondary streamerhead, whereas the experimentally measured OH radical densitydecreases exponentially from the point anode to the planecathode along the discharge axis. This is because the
7
J. Phys. D: Appl. Phys. 46 (2013) 175206 A Komuro et al
10
100
1000
0 2 4 6 8 10 12z - axis [mm]
Red
uce
del
ectr
icfi
eld
[T
d]
7.5 10.0 12.5 15.0 17.5
19.1
H2O (2%) / Air
5.0 ns
(a)
0
50
100
150
0 2 4 6 8 10 12
H2O = 2.0%H2O = 0.1%
z - axis [mm]
Red
uce
del
ectr
icfi
eld
[T
d]
Time = 50 ns
(b)
Figure 4. Axial distributions of reduced electric field (a) at varioustimes during primary streamer propagation and (b) that at t = 50 nswhen the secondary streamer appears. The applied voltage is 28 kV.
0
2
4
6
8
10
100 105 110 115 120 125 130 135 140
IonizationAttachment(Humid Air)Attachment(Dry Air)
k δδ δδ[
10-1
2 cm3 s-1
]
Reduced electric field [Td]
H2O (2%) / Air
Figure 5. Dependence on the reduced electric field, E/N , of therates of the ionization and attachment reactions in dry and humid air.k is the sum of rates of ionization and attachment reactions and δ isthe fraction of nitrogen, oxygen or water in the mixture.
0
0.5
1
1.5
2
2.5
3
3.5
4
0 2 4 6 8 10 12
OH
den
sity
[1015
cm-3
]
z-axis [mm]
H2O = 2%
H2O = 0.1%
Vp = 28 kV
Figure 6. Axial distribution of OH radical density at t = 3 µs. Theapplied voltage is 28 kV.
Figure 7. Total number of OH radicals at t = 3 µs as a function ofH2O concentration. Experimental values were measured in ourprevious work [19].
simulated axial distribution of the reduced electric field inthe secondary streamer changes in a stepwise manner at thesecondary streamer tip, as shown in figure 4(b). This stepwisedistribution has also been reported in a previous paper [27]and is theoretically well defined [31]. However, our previousexperimental results indicate different characteristics. Wepreviously measured the axial distributions of O [56], N [57],and OH [19, 55] radical densities and showed that these radicaldensities decrease exponentially from the point anode to theplane cathode. For these experiments, the limitations of thelaser-induced fluorescence method used make measuring astepwise shape around the edge of the secondary streamerhead, as shown in figure 6, difficult because of experimentalinaccuracies. Therefore, it is difficult to distinguish whetherthe difference is merely an error caused by the experimentitself, or an error caused by a physical phenomenon notconsidered in our simulation.
The number of OH radicals produced in a single dischargepulse is simulated as shown in figure 7. Then, the effect of
8
J. Phys. D: Appl. Phys. 46 (2013) 175206 A Komuro et alz-a
xis
[m
m]
O radical density
[cm-3] (t = 200 ns)
0
1017
r-axis [mm]0 1-1
0
2
4
6
10
8
12
13
1
3
5
7
9
11
Primary
Streamer
Secondary
Streamer
(a)
(b)
(c)
0
200
400
600
800
1 10 100
Red
uce
d E
lectr
ic F
ield
[T
d]
Time [ns]
0
0.5
1
1.5
2
1 10 100
Ele
ctr
on
den
sit
y [
101
5cm
-3]
Time [ns]
Figure 8. (a) Spatial distribution of O radical density at timet = 200 ns in H2O(2%)/O2/N2. Time evolution of (b) reducedelectric field and (c) electron density at z = 3 mm. The appliedvoltage is 28 kV.
humidity on the number of OH radicals generated is comparedwith the experimental results [19]. Figure 7 indicates thatthe number of OH radicals produced by the discharge issaturated with increasing water vapour, and the simulationresult is qualitatively consistent with the experiments exceptfor a difference in the total number of OH radicals withina factor of 2. The mechanism of OH radical production isdiscussed in detail in the following section.
3.3. Mechanism of OH radical production
The temporal behaviour of OH density in the rectangularsection indicated in figure 8(a) is plotted in figure 9. Theobservation volume is set at z = 3 mm below the pointanode, where the reactivity is high in the secondary streamerchannel. Figures 8(b) and (c), respectively, show the temporalvariation of the reduced electric field and electron densityat the observation volume for z = 3 mm. These figuresshow how electrons are produced in large numbers in theprimary streamer and that the number of electrons decreasesin the secondary streamer, concomitant with a significantdecrease in the reduced electric field, E/N , as explained inour previous paper [10]. Figure 9 shows the time variation ofthe OH radical density with H2O concentration at z = 3 mm,which is compared with the time variation in figures 8(b)and (c). From the comparison among figure 8(b) (E/N ),figure 8(c) (electrons) and figure 9 (OH radicals), it isconfirmed that the OH radicals are mainly produced in thesecondary streamer and decrease in number after the dischargein two phases, labelled (i) and (ii). In particular, the rate ofdecrease in the second phase is accelerated with increasinghumidity. This strong dependence of the decrease in OH
0
0.5
1
1.5
2
2.5
3
3.5
1 10 100 1000
H2O = 2.5%H2O = 2.0%H2O = 1.5%H2O = 1.0%H2O = 0.5%H2O = 0.1%
OH
den
sity
[1016
cm-3
]
Time [ns]
z = 3 mm, Vp = 28 kV, H2O / Air
( i )
( ii )
Figure 9. Temporal variation of OH density at z = 3 mm.(i) denotes the first decay caused by processes of ‘OH cycle’ and(ii) denotes the second decay caused by processes of ‘OHrecombination’.
radical density on humidity can explain the saturation of thenumber of OH radicals shown in figure 7. The detailedbehaviour of OH radicals is explained in figure 10(a), whichshows the time variation of the production and loss rates foreach of the reactions leading to the formation of OH radicalsas follows.
Firstly, the mechanism of OH radical production isdiscussed. From the results in figure 10(a), OH radicals aremainly produced by the dissociation reactions of O(1D) +H2O and N2(a) + H2O in the secondary streamer. Electrondissociation reactions such as e + H2O contribute less to OHradical production because the cross sections of these directdissociation processes are low in the energy range of thesecondary streamer compared with those of O(1D) and N2(a),as shown in figure 1. Although the dissociation of the reactionof O(1D) + H2O has been considered as one of the majorpathways for OH radical production, the contribution of N2(a)to OH-production has not been discussed before. Therefore,its validity should be discussed here. Fresnet et al [35] firstsuggested the importance of the reaction of N2(a) + H2O.They concluded that the decrease in the decomposition rateof NO with the increase in humidity in an atmospheric-pressure photo-triggered discharge is caused by the quenchingreaction of N2(a) by H2O because N2(a) plays the main partin the NO removal process. In addition, they measured therate coefficient of the reaction of N2(a) + H2O indirectlyfrom the temporal change in N2(a) and NO densities underseveral humid-air conditions. However, branching ratio ofthe reaction of N2(a) + H2O is unknown. Magne et al [58]and Aleksandrov et al [59] assumed that the branchingratio of N2(a) + H2O → N2 + O + OH is 1.0 in theirplasma chemical reaction model and obtained good agreementbetween experimental and simulation results, although theydid not pay sufficient attention to the branching reactions ofN2(a) + H2O. In this work, we used the rate coefficients ofN2(a) + H2O measured by Fresnet et al [35] and assumed the
9
J. Phys. D: Appl. Phys. 46 (2013) 175206 A Komuro et al
-2
0
2
4
6
8
10
10 100 10000
R24: e => H + OHR81: N2(a) + H2O
R123: O(3P) + HO2
R128: O(1D) + H2O
R149: OH + O(3P)
Time [ns]
OH
pro
du
ctio
nra
te[
1023
cm-3
s-1]
Vp = 28 kV, z = 3 mm, Humid Air (H2O = 2%)
(a)
-4
-3
-2
-1
0
1
2
0 0.5 1 1.5 2 2.5 3
OH
pro
du
ctio
nra
te[1
022cm
-3s-1
]
OH - production(R81) N2(a) + H2O
OH - cycle
OH - recombination(R140 - 144) OH + OH (+M)(R145, 146) OH + H (+M)(R147) OH + HO2
(b)
Time [ µµµµs ]
Vp = 28 kV, z = 3 mm, Humid Air (H2O = 2%)
(R123) O(3P) + HO2
(R148) OH+ N(4S)(R149) OH + O(3P)
(R128) O(1D) + H2O
Figure 10. (a) Production rates for OH at z = 3 mm inH2O(2%)/O2/N2 mixture and (b) roles of each reaction inOH-production and loss processes.
branching ratio to be 1.0, similarly to Magne et al [58] andAleksandrov et al [59].
Next, the decrease in the number of OH radicals isdiscussed. The number of OH radicals produced in thesecondary streamer rapidly decreases in two phases. Thefirst decay (see (i) in figure 9) is caused by the reactionwith O(3P), as shown in figure 10(a). The rate of OH-production by O(1D) and the rate of OH loss by O(3P) aresimilar in the discharge phase since similar amounts of O(1D)and O(3P) are produced by the direct dissociation process ordissociations by N2(A, B, C). However, the produced O(1D) arerapidly quenched by several species such as O2, N2 and H2O.Therefore, OH radicals are destroyed just after the dischargeby the reaction with O(3P), producing H + O2. In figure 9,we can observe a temporal plateau of the OH radical densityafter the first decay and the subsequent second decay (see (ii)in figure 9). This phenomenon can be explained as followsusing figure 10(b).
Figure 10(b) shows the time variation of the ratesof reactions in three reaction processes: ‘OH-production’,
Table 5. Group of reactions arranged for the role of OH behaviour.
OH-production(R81) N2(a) + H2O → N2 + H + OH(R128) O(1D) + H2O → 2OHOH-cycle(R123) O(3P) + HO2 → OH + O2
(R148) OH + N(4S) → NO + H(R149) OH + O(3P) → O2 + H(R161) H + HO2 → 2OH(R162) H + O2 + O2 → HO2 + O2
(R163) H + O2 + N2 → HO2 + N2
OH-recombination(R140) OH + OH + N2 → H2O2 + N2
(R141) OH + OH + O2 → H2O2 + O2
(R142) OH + OH + H2O → H2O2 + H2O(R143) OH + OH → H2O2
(R144) OH + OH → H2O + O(3P)(R145) OH + H + N2 → H2O + N2
(R146) OH + H + H2O → 2H2O(R147) OH + HO2 → H2O + O2
‘OH-cycle’ and ‘OH-recombination’, as shown in table 5. Therates of reactions in the OH-cycle change considerably fromnegative to positive at approximately 0.2–0.3 µs because theOH-cycle includes the OH-production reaction (R123) and(R161), and the OH loss reactions (R148) and (R149). The firstnegative rate in the OH-cycle is caused by the loss reactions(R148) and (R149) and the effect of the production reactions(R123) and (R161) emerges with increasing HO2, which ismainly produced by the reactions (R162) and (R163) throughH radicals formed by the reactions (R148) and (R149). This iswhy we call this process the OH-cycle. The OH-cycle results inthe first decrease in OH density (i) and the subsequent plateauphase between (i) and (ii), as shown in figure 9.
The second decrease in OH density (ii) is explainedas follows. From the results in figure 10(b), the decayof (ii) is caused by an OH-recombination process. TheOH-recombination includes a number of OH loss processesinvolving the recombination reactions (R140)–(R144) orreactions with water-related radicals such as HO2 and H(R145)–(R147). Therefore, the rate of OH-recombinationincreases with the square of the water concentration. TheOH-recombination allows us to interpret the decay of (ii) infigure 10(b) and the saturation of the experimentally obtainednumber of OH radicals in figure 7.
Figure 11 shows the flow of OH-production by theatmospheric-pressure streamer discharge. OH radicals aremainly produced by the reactions of N2(a) and O(1D) withH2O and are transformed into H2O or H2O2 via severalrecombination reactions with water-related radicals.
Under the present discharge conditions, we obtainedOH-production pathways similar to that in figure 11. However,the pathways might be different under different conditions.For example, under the repetitive discharge conditions with afrequency of over 1 kHz, the gas temperature in the dischargevolume might increase mainly by the vibrational relaxationphenomenon [18]. The recombination reactions in figure 11have negative temperature coefficients, and therefore the rateof decrease of OH density after the discharge might beslower than that considered in this paper. To simulate the
10
J. Phys. D: Appl. Phys. 46 (2013) 175206 A Komuro et al
H2O
2
H2O HO
2OH
H
O(3P), H
O(3P)N HO2
O2 (+M)
HO2
OH (+M)
N2(a), O(1D)
H, HO2
N2(a)
Figure 11. Schematic of OH radical production and loss processes.
increase in the gas temperature accurately, the fast gas heatingmodel [32] and the vibrational relaxation model [18] shouldbe coupled with the Navier–Stokes equations to consider theeffect of compressibility [30, 34]. In addition, the rate ofcurrent relaxation simulated by the extended Morrow and Satoequation [29], as shown in figure 2, is slightly faster thanthat observed experimentally [14]. The rates of the electronattachment and detachment reactions, which are consideredto be important for current relaxation, need to be examinedcarefully. Moreover, complex ions may also affect the rateof current relaxation. Complex ions were ignored in thissimulation because we were able to reproduce the primary andsecondary streamers well without them. It may be necessaryto evaluate the effect of complex ions on the production ofradicals for a more precise simulation.
4. Conclusion
In this paper, the mechanisms of OH radical formation inan atmospheric-pressure streamer discharge were discussed.The axial distribution of OH radical density and the effect ofhumidity on OH-production were qualitatively reproduced inour two-dimensional streamer discharge model. The followingconclusions were drawn from this study.
• The OH radicals are mainly produced in the secondarystreamer, and the dissociation of H2O by O(1D) and N2(a)is predominant in the production of OH. The density of OHradicals measured in humid nitrogen can be explained byconsidering the effect of OH-production processes relatedto excited nitrogen species, although the dissociationreaction via N2(a) needs further consideration.
• After the production of OH radicals, the OH radicaldensity is rapidly decreased by the reactions of OHwith O(3P). However, the H radicals resulting from theOH + O(3P) and OH + N(4S) reactions are transformedinto HO2, then the HO2 produces OH again by the reactionwith O(3P).
• Once the above ‘OH-cycle’ reactions reach quasi-equilibrium, the ‘OH-recombination’ reaction comes intoplay. As a result, the produced OH changes into
H2O or H2O2 by recombination reactions with water-related radicals. These simulation results provide a goodinterpretation of OH radical production in N2/O2/H2Omixtures.
Acknowledgment
This work was supported by Grant-in-Aid for Japan Societyfor the Promotion of Science (JSPS) Fellows.
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