Plasma-catalysis SO2 oxidation in an air stream by a relativistic electron beam and corona discharge

Rndiar. Phys. Chem. Vol. 40, No. 4, pp. 281-294, Int. J. Rodiat. Appl. In.wum., Part C Printed in Great Britain

0146-5724/92

1992

55.00 + 0.00

PergamonPress Ltd

PLASMA-CATALYSIS SO2 OXIDATION IN AN AIR STREAM BY A RELATIVISTIC ELECTRON BEAM AND CORONA DISCHARGES E. I. BARANCHICOV, G. S. BELENKY, M. A. DEMINSKY,V. P. DOROVSKY,E. M. ERASTOV, V. A. KOCHETOV,D. D. MASLENICOV, B. V. POTAPKIN,V. D. RUSANOV, V. V. SEVERNYand A. A. FRIDMAN* I.V. Kurchatov Institute of Atomic Energy, Kurchatov Square, 123182Moscow D-182, Russia Abstract-The results of theoretical and experimental investigations of SO1oxidation in an air flow by a high current pulse electron beam and impulse corona discharge are presented in this work. It was shown that in non-equilibrium plasma and in a certain range of current density and humidity the energy cost of oxidation is significantly reduced to a value corresponding to the chain character of the process. These results were explained by realization of the ion-molecule chain SO, oxidation mechanism and confirm the effect of non-equilibrium plasma catalytic activity in chemical reactions. It was shown that ion-molecular chain processes in droplet phase can also cause additional reduction of oxidation energy costs.

INTRODUCTION

with increasing electron affinity (0; > SO; > SO;). The end of the chain is a result of associative electron detachment (for example in the reaction SO; + H,O + H2S0, + e). If the chain length is long the plasma ions (practically without loss) can accelerate the oxidation process considerably since they are catalysts. In that work it was pointed out that the oxidation energy cost is proportional to the current density to the power of l/2, and there is a strong dependence of the efficiency of the process on humidity. The first circumstance is determined by termination of the chain carrier particle (ions in the process of ion-ion recombination). Experimental investigations of oxidation in air, induced by electron beam (EB) and impulse corona discharge, were made for confirmation of the catalytic activity effect of non-equilibrium plasma in exoergic chemical reactions. The results of these investigations are also presented in this work.

The electron beam and impulse corona discharge technology of air flow purification from SO* and NO, are now investigated in many countries (Leonhardt, 1984; Svedchikov and Belousova, 1988; Tokunaga and Suzuki, 1981; Baranchicov et al., 1990). One of the main problems which considerably influences the perspective of the practical usage of this method is the reduction of oxidation energy cost. In this work it was shown, that the energy cost feebly depends on current density, i, if j < 10m5A/cm2 and equals 10 eV/mol. In this case, for example, it is necessary to have 120 x 100 kW accelerators for gas stream (0.1% SO,) purification of a 300 MW electric power plant. This is why realization of this project is very difficult (because of the energy cost of purification). This paper is dedicated to a new gas-cluster chain oxidation mechanism, with theoretical investigation of this one realization. The results of the experiments realized for this mechanism’s verification are presented here. The role of the droplet-phase effect is also presented. In the work of Potapkin et al. (1989) it was proposed that oxidation energy cost can be significantly reduced by using the effect of SO2 plasmacatalytic oxidation. It was shown that in some ranges of current density an oxidation can be realized, with a low energy cost, as a result of a chain process with ion-molecule reactions of the chain propagation. In this case oxidation is realized in the fast conversion process of negative ions and the formation of ions

SO, OXIDATIONBY A RELATIVITIC

ELECTRONBEAM

#To avoid any delay in publication of this Special Issue, this

paper has been published without the authors’ corrections. *To whom correspondence should be addressed.

Experiments were carried out in two experimental set-ups with distinction in EB current density and a pulse generation regime. A scheme of the experimental set-up is shown in Fig. 2. The experiments were carried out in a gas mixture of the following composition: 1% SO,, 3.4% H,O, 19.6% 02, 76% N,. The total pressure of the mixture was 740 torr and the temperature of the mixture was 298 K. SO2 and the air-gas mixture were prepared in a special bottle with a storage pressure of about 5 atm. The mixture was introduced and irradiated into the reactor. The concentration of the water steam (corresponding to saturated steam pressure) was constant. The reactor

287

E. I. BARANCHKZOV el al.

288

v Baranchikov 1991 0 Tokunaga * Svedchikov

10-10

10-B

10-e

10”

10-2

1

102

Lg J A/sm* Fig. 1. Energy costs of oxidation A as a function of current density J. (1) Effect of liquid-phase a = 10e4 cm, 8 = 1; (2) effect of liquid-phase a = 10m5cm, 0 = 1.

volume was 800ml. The cylindrical reactor in the experiments with an impulse-period beam had a diameter of 80mm with stainless steel walls and a Plexiglass support. In the experiment with an impulse beam, the right parallel-piped reactor had walls made of Teflon. In both cases, an aluminum foil beam was made by an explosive-emission diode with a graphite cathode. The foil thickness was 50 nm. Current density (with electron energy of 300 keV) was changed from 1 to 10 A/cm2 in the experiment with the impulse-period generator. This is due to variation of the anode-cathode distance and cathode diameter [by analogy with the experiment of Golovanov and Elagin (1985)]. The pulsed frequency was equal to 100 G, and impulse duration was loons. In the experiment with the EB pulse, current density was changed from 1.5 + 0.5 x 10m2 to 10 + 2 A/cm2 by

virtue of the diode tension, which was changed from 180 to 200 keV. This corresponded to a variation of energy absorption by gas from 1Om~4 to 3 x lo-’ J/cm3 in experiments with a pulse beam. The number of pulses in every experiment was variable with the current density of the beam and was 100-500; rootmean-square deviation of the beam parameters in every experiment was less than +30%. The energy absorption by the gas was determined by the Hartec-Dondsa method (NO, dosimeter). The radiative yield of nitrogen was 12 molecules/l00 eV (Pikaev, 1985). Relative variations of concentration in the mixture after EB action were determined by monitoring the absorption of i.r.-radiation of the wavelength 725 nm. The spectra were recorded by an IRS-29 $ectrometer, the results were monitored by the iodine-titration method. Relative deviation of the results of the concentration measurements by these methods was less than + 15%. The energy cost of oxidation was determined from the following equation: A = Q/d[SO?] V eV/mol where Q is the energy absorbed by the gas, d[SO,] is the change in SO, concentration after irradiation and Vis the volume of the reactor. The SO, concentration decreases at the expense of liquid-phase absorption, without irradiation (dark oxidation), and was subtracted from the d[S02] value. The experimental dependence between the energy cost of oxidation and current density is shown in Fig. 1. In the frame of experimental errors the oxidation energy cost is proportional to the current density to the power of l/2 (A - (j)“‘). The minimum value of the energy cost of oxidation is 3.2 f 0.8 eV. Taking

Fig. 2. Scheme of set-up. I--Cathode; 2-foil; 3-reactor; 4--end-wall; 5-test clock; M2 ‘I-valve; 8, 9-electrode; l&reactor; 1l-generator; C+apacitor.

bottle;

Plasma-catalysis SO, oxidation

into account dark oxidation, the minimum energy cost reduces to 08eV/mol. This corresponds to a radiative yield of the chain processes of G = 125. In Fig. 1 are also the results of the experiments of Leonhardt (1984), Svedchicov and Belousoua (1989), Tokunaga and Suzuki (1981) and Washino et al. (1984) who used stationary sources of ionizing radiation with a smaller current density than in the above-mentioned experiment. SO, OXIDATION

IN CORONA

DISCHARGE

The reactor was similar to the one in the EB experiment. The corona discharge was aimed between the central cylindrical stainless electrodes. The central hexahedron electrode was made from brass. It was linked to the generator of the impulse voltage or the source of the constant current (20 kV) depending on the working regime (impulse or direct current for corona discharge). The relaxation generator of the impulse corona made negative or positive impulses with amplitudes of 30-70 kV and duration times of 50-200 ns. The pulsed frequency was 50 G. The outward electrode was grounded by capacity C (100 mkf). The current in the reactor volume was between the central and outward electrode charged capacity. The voltage U, was measured by a voltmeter with high resistance. The Q energy, which was absorbed in the gas mixture, was determined as: Q = KU, U, where iJ, is the amplitude of the voltage between the outward and central electrode and a is the form factor, which equals 1 for a constant voltage U, and equals 0.5 for an impulse voltage. The composition of the gas mixture, preparation method of the mixture and analysis method were the same as in the abovementioned experiments with EB. The mean current density of the corona discharge j,,, in the impulse was calculated as:

for comparison of the results of the experiments with corona discharge and REB, where f is the pulsed frequency; t is the time of exposition; U, the change of the voltage in capacity C at the time of the exposition; S,,, is the mean area between central and outward cylinder. The experimental data, as a function of current density, are shown on Fig. 1. The minimum value of energy costs of SO* oxidation was 5 f 2.7 eV/mol in the impulse corona, 10 f 2eV/mol in the corona with a direct current and 3.2 + 0.8 eV/mol in experiments with REB. From the obtained results we can make the following conclusions. The comparison of the minimum value of energy cost obtained in these experiments with calcualtions of Person and Ham (1988), Gentry et al. (1988) and experimental data of Leonhardt (1984) and Washino et al. (1984) (10 eV/mol) for the

289

gas-phase non-chain mechanism of SO, oxidation points to a chain character of the process in the experimental conditions. The directly proportional dependence of the energy cost of SO, oxidation to j1j2 can be explained by suggesting that the chain carrier particles’ termination is proportional to the concentration to the power of 2 and to the steady state of their concentration during the pulse. This marked circumstance indicates that radicals cannot be the active centres of chain reactions in the experimental conditions, because the characteristic time taken for recombination in this case is lo-lo4 times longer than the period of irradiation. Further, the comparison of the results obtained in this investigation with results of Baranchicov et al. (1990), Leonhardt (1984) Svedchicov and Belousoua (1989) and Tokunaga and Suzuki (1981) indicate that the resonance character of the energy cost of oxidation is a function of the current density. POSSIBLE

MECHANISMS

OF SO, CHAIN

OXIDATION

To explain the results of this experiment let us consider the two chain mechanisms of SO2 oxidation which can, in principle, significantly reduce the energy costs of SO2 removal in a heterophaseous air stream. Firstly a well-known liquid-phase chain mechanism and secondly a specially proposed ionic chain oxidation mechanism in a cluster. Liquid-phase oxidation

It is known that because of its long-length the SO, chain oxidation can effectively be realized in the liquid phase. Taking into account that a liquid phase is formed in the experimental conditions, because of the condensation of water vapor on H, S04, the chain liquid-phase oxidation can, in principle, considerably reduce the energy costs. The mechanism of the SO2 chain oxidation in liquid phase has been investigated in numerous works (Calvet, 1985; Penkett and Jones, 1979; Daniel and Jacob, 1986). As a result of this analysis work the liquid-phase SO2 chain oxidation mechanism was proposed (Deminsky et al., 1990). Depending on the solution acidity there are two types of liquid-phase SO2 oxidation mechanisms. In a high acidity range (pH < 6.5) the main ion formed from SO2 dissolution in water is HSO; and the oxidation mechanism can be presented as follows: Chain initiation

M+HSO;+MH+SO;

k,

(I)

Reactions of chain propagation SO; + 0,

-+ SO?

k, = 2.5 x lo-l2 cm’/s

(2)

SO; + HSO; -+ SO,- + HSO,k 3 = 1.7 x lo-‘6&/s

so;

+ so;

+ 2so;

(3)

+ 02 k4 = 1 x lo-i2 cm3/s

(4)

E. 1.

290

BARANCHICOVet

SO,-+HSO,+HSO,+SO, k, = 3.3 x IO-‘* cm’/s

(5)

SO;+HSO;-+HSO;+SO, k, = 4.2 x IO-” cm’/s HSO;

+ HSO;

-+ 2S0,

(6)

+ 2H+

k , = 2 x 10-‘4cm3/s

(7)

k, = 1.7 x lO~‘*cm’/s

(8)

k, = 3.3 x IO-” cm’/s

(9)

Termination so;

+ so,

+ s,o;-

al.

The initiation of SO, chain oxidation in liquid phase can be caused by light (Calvet, 1985) and by reactions with strong oxidizers (Daniels 1986). The broad spectrum of the oxidizers: positive ions, OH, HO,, H,O,, O,, 0, are formed in liquid and gas phases by outward radiation. The investigations made in the works by Penket and Jones (1979) and Saxena et al. (1987) show that SO2 oxidation, in liquid phase, by HO,, 0, and 0 has a non-chain polarization mechanism. The OH radical, on the other hand, can initiate chain oxidation in reactions with HSO, and SO:-: OH + HSO,

-+ H,O + SO,

so;+so,~s20~-

k, = 1.6 x IO-” cm’js

SO; + N -+ destruction;

x = 3,4. 5

where M is the active particle (in particular the OH radical) and N is an admixture. Inversely, the main ion formed from SO* dissolution in water in a low acidity range (pH > 6.5) is SO: and the mechanism is: Chain initiation : M+SO:-+SO,+M-

k,,

(13)

Reactions of chain propagation so;

+ 0, + so, k,, = 2.5 x IO ” cm’/s

(14)

, so; + so:- + so; + so;k,, = 5 x lO-‘4 cm’js so,-

+ so:-

so;

+ so:-

+ so:-

+ so:-

(16)

+ so, k,, = 1.7 x 10~‘4cm3/s

so:-

(15)

-+ so: - + so, k,, = 3.3 x 10~i2cm3/s

(17)

-+ 2so: k,, = 2 x IO- I4cm’is.

OH+SO:~-*OH-

(10-12)

+SO; k,, = 9.2 x IO-‘*cm3/s.

The role of the different types of active particle will be considered below. Simulation of the radiational yield of SO2 liquidphase oxidation as a function of current density and acidity was carried out by using the kinetic program ELENA. It was assume that the main particle, which initiates oxidation, was the OH radical with a radiation yield of 2.88 (Pikaev, 1985). The results of the simulation are shown in Fig. 3. It can be seen that there is a strong dependence of the chain length and radiation yield of the SO, oxidation mechanism in the liquid phase on the solution acidity. This is connected with the following: (i) that the concentrations of the SO:- and HSO, ion radicals depend on the solution acidity (pH) and (2) SOi- and HSO, oxidation rates differ considerably. Therefore, the liquid-phase process in the low pH range, when the ion concentrations are small, has a short chain length. It is necessary also to note the strong dependence of chain length and radiation yield on current density, which determined chain carrier particle termination. The particle termination is proportional to the concentration to the power of two [equations (8)-(12)] in the range of

(18)

The reactions of chain termination are identical to reactions (8)-( 12). One can see that the main chain carrier particle in the liquid phase in both cases is the SO; ion radical, which, in excess of 02, forms the SO, ion radical in reactions (2) and (14). Further, SO, chain oxidation has two paths in both ranges of acidity. The first path with a higher rate [reactions (3)-(5) and (15))( 16)] is realized when HSO; and SOi- are the most easily oxidized components. In another case, SO; reacts with the admixture molecules and has a slower rate of oxidation [reactions (16), (17) and (18)]. The reactions of chain termination are the result of the recombinations for the high concentration of the chain carrier particle, and the reaction with the admixture, for small concentrations, in both cases.

1’ 1o-9

I

I

1o-5

0.1

Log J A/cm* Fig. 3. Radiation yield of liquid-phase oxidation function of current density and acidity.

as a

Plasma-catalysis So, oxidation strong current density. Therefore this mechanism is more effective in the range of small current density and this is confirmed by the results of Backstrom (1934) (photo-initiation, chain length, y w 10’). From this analysis of liquid-phase oxidation mechanisms the following conclusions can be made: the mechanism effectivity in the conditions of our experiments, where there is high current density j > 10m3A/cm* and high acidity (pH < 2) (because of processes of natural condensation acid drops) is very small y N l-3 and the radiation yield G N 10. Thus it is impossible to explain the results of our experiments by realization of the liquid-phase chain oxidation mechanism. Moreover, additional arguments which confirmed this conclusion will be presented below. Plasma-catalysis

oxidation in gas and clusters

The results of the SO2 oxidation experiments can be explained by proposing realization of the ion-molecular chain SO2 oxidation mechanism. Moreover, besides ions the excitation (e.g. vibrationally) of particles also takes part in the chain propagation reaction. Indeed, the chain character of the process is a cause of the low energy cost of oxidation. At the same time the concentrations of ions, contrary to the concentrations of radicals, for the pulse duration in all the investigated ranges of current density have already achieved steady state values. This permits the explanation that oxidation energy cost is proportional to current density to the power of l/2 (A _ (j)‘/*) in conditions of the abovementioned experiments. The participation of excited particles, besides ions, in chain oxidation permits the explanation of the resonance character of energy cost dependence on current density. Indeed, the decreasing energy cost with decreasing current density (Fig. 1) can be explained by the competition of the recombination and ion-molecular chain propagation processes. But increasing energy cost with decreasing current density is due to competition of the chain propagation reaction with the excited particles’ quenching process of excited particles and ionmolecule reactions of chain propagation. Taking into account literature data (Fehsenfeld, 1974; Virin and Karachevcev, 1979; Laudavala and Morussi, 1985) the mechanism of ion-molecule chain SO2 oxidation can be represented in following

291

way. Electrons, which were generated by a relativistic electron beam or corona discharge, attach to molecular oxygen: e+O,+M+O;+M

Reaction e+so,rso, e + (H,O), + M+(H,O), + hfn > 6 O;+HzO+M-rO+(H1O)+M 02 + so,+so, + 0, so, +0*+M+S0~(02)+M so,- + so, + M+SO,(SO,) + M 0,+o*+M+O,-+M O,(H,O)+H,O+M-rO,-(H,O)+ M 0, (H,O) + SOpO,- (SO,) + H,O

(19a)

In the conditions of the experiments the rate of this reaction is about ten times greater than other possible attachment reactions (see Table 1): e+SO,+M+SO;

+M; e+(H20),.5+(H20),5.

After creation of negative 0; ions the most rapid process is water cluster formation in step by step reactions of water molecular attachment: 0; (H,O), + H,O + A4 --) 0; (H,O),+ , + M. Further, the result of SO2 penetration in the cluster is from the formation of a most thermodynamically stable cluster core (Keesee et al., 1980): 0, (H, 0)” + SO, + 0; (Hz O), SO2 -0;

x S02(H20)n+SO;

x 02(H20),.

(19b)

The core ion of this cluster has a peroxide structure and is a good oxidation agent (Fehsenfeld, 1974). For example, the NO, oxidation by this ion is well known (Viggiano et al., 1989): NO2 + SO; -, NO; + SO1. Moreover, the investiations of Mutrabecov (1986) on SO, chain oxidation in acidic solution (pH < 1) for high SO2 concentration are also confirmed by the presence of the active peroxide structure of SO; in liquid: [O, so2]-+so2+so;+so,. For this reason, after penetration the next SO2 molecular in the boundary layer of the cluster ion oxidation reaction and electron detachment process can occur: SO; x O2 x S02(H20), +(2H2S04(H20),_2

x e)* + Q.

The estimation of the enthalpy of this reaction, AH”, of 2 eV show the possibility of free electron formation. This means realization of the chain oxidation processes. The role of the excited molecules in this mechanism is to promote 0, penetration in the

Table 1. The rate of reactions of cluster fomtion. 3% H,O, 1% SO,, 16% O,, 80% N, (conditions as in Baranchicov er al. 1990)

e+O,+M-rO,+M

/Cam.

Rate constant

I/r Is-‘)

3.2 x IO-” c&/s _ lo-” cm’/s
5.8 x 10’ 3 x 106 13 x 106 2.9 x 10” l&12 x 108 2x 109 7.8 x IO9 7.2-9 x 10’ IA-I.6 x 10” 5.4 x 10%

E. I. BARANCHICOV et

292

core of the cluster ion [see process (19a)] as a possibility of activating the SO; ion which has two forms: (1) a high energy chemically-active peroxide isomer and (2) a low energy non-active cyclic isomer (Fehsenfeld, 1974; Viggiano et al., 1989). Since cluster formation time is very short in the conditions of our experiment (5 - lo-” s) the reactions of cluster formation do not limit the oxidation process. The main qualitative peculiarity of the proposed mechanism can be established by use of the following simplified scheme. As was earlier described, the first step of the oxidation mechanism is the reaction of electron attachment to molecular oxygen: e+O,+M+O;

+M

k,,.

(1%)

The process of SO2 oxidation is a result of a fast conversion which leads to formation of ions with increasing electron affinity, where excited molecules stimulate the process: 0;

+ SO, + SO; + 0, SO, + 0; + SO;

k,, k,,

SO4 + 0; -+ SO, + 0,

(20) (21)

k,,

(22)

Electrons are regenerated in reactions of associative detachment and this leads to oxidation: 0;

+ SO, -+ SO; + 0,

SO; +H,O+H,SO,+e

kIg k,,.

(23) (24)

In the frame of the described mechanism (19)-(24) in steady-state conditions and suggesting that, in excess water, reactions (22) and (24) are the limiting stage of the oxidation mechanism, we can get the following expression for oxidation energy cost: A = (4G,/(G,P) B =[l

+ 6))‘W,

+n,/n,+ni/n,]

x [l +(1 -4n,/n, X {l +n,/n,+ni/n,}-2)-..‘]

where n, is the steady-state

(2.5)

ion concentration:

n, = (K,$n,G,/K:‘ec)‘.‘2 n, and n2 are characteristic ion concentrations can be determined by the expressions:

(26) which

n2 = k,nso(K;G,/G,)m’.

(27)

Here Gi, G, are radiative yields of ions and vibrationally excited molecules; KIb, KF, K,, are rate constants of ionization by electron impact and ion-ion recombination and (VT) relaxation; j is the electron beam current density; n, is the concentration of gas; W, is energy costs of the ion. In formula (25) also taking into account the non-chain ion-molecular oxidation mechanisms:

=

and 6 may be presented (Potapkin, 1989):

H, SO,

H, SO0

by the degradation

method

s=(E;L)~‘[W-I-S0iEZ(E)dEIS:Z(E)dE] here Er g 4 eV, the radical energy cost of excitement; I = ionization potential; Z(E) = relativistic electron spectrum in gas, which, if E < I, equals: Z(E) = 2( I + E/Z)- ’ ln(2 + E/f) + (1 + E/I)- 2. As one can see from (25) if n, < n2, the energy costs of oxidation can be significantly lower than the energy cost of ions because of realization of the chain oxidation mechanism. The minimum value of energy cost in this case is A”‘” = G, W,/2G, = 100/2G,

(28)

which is achieved in n, = (n,n?)’ 2. As expected the participation in oxidation of the vibrationallyexcited molecules of oxygen leads to the dependence of energy costs of oxidation on the radiational yield of these molecules. The characteristic concentration of ions n2 is determined by the competition of ion-molecule reactions of chain propagation and ion-ion recombination (if n, < n, and n, = n, energy costs of oxidation is A = W,G,/G,). The value of the characteristic concentration n, corresponds to the equality of the oxidation reaction rate and the relaxation rate (if n, < n, and n, = n, the energy cost is also G, G,/ W,). Under the experimental conditions n, < n2 and the range of current density corresponds to the chain character of the observed process. We must note, as was shown by Potapkin et al. (1989) that the energy cost reduction with decreasing current density can be explained without using the proposal about the participation of vibrationally-excited molecules in the oxidation process. This proposal, as we have already mentioned, determines the existence of a minimum value of energy cost. Thus, the experiments demonstrate the possibility of oxidation energy cost reduction (without adding a basic substance) by realization of the ion-molecular chain oxidation mechanism in clusters. SIMULATION

n, = K,nOlkj

SO2 2 SO,=

al.

OF SO, OXIDATION

The results of SO, oxidation modeling in the frame of the proposed oxidation mechanism (l)-(18) and (19)-(24) give the possibility that not only qualitatively explain the main peculiarity observed in the experiments but quantitatively describe them. Theoretical investigation was produced by use of a specially elaborated code. This code takes into account the four oxidation mechanisms: the ion-molecular chain oxidation mechanism; the excited particle oxidation; the radical mechanism; and finally the SO, oxidation in droplet phase. In all more than 200 chemical and plasma-chemical reactions were taken into account. There are primary reactions by electron beam, ionmolecular reactions and reactions of basic ions,

Plasma-catalysis SO, oxidation electron-molecular and ion-molecular reactions of negative ions, recombination and reactions of neutral components. The rate constants were determined from the literature (Virin and Karachevcev, 1979) and with the help of the Dr Chemie program for determination of unknown chemical and plasma-chemical reaction rate constants (Nester and Fridman, 1991). The liquid-phase processes were taken into account in the balance equations for gas components as sink terms. The sink of the components (OH, for example) of the droplets was determined by analytical solution of the set of balance equations (29) and (30) for gas and liquid component concentrations with boundary conditions (31):

d

,nbH

-stream J8 = D,(&

in liquid on the boundary,

- @&))/a -stream

in gas on the boundary.

&(0)Horr

= n&n(u)

(31)

In the stationary case, solving these equations we have a gas sink of the droplet (Deminsky et al., 1981): J = D n(u)-‘A /k(l)

I

[xu cth(xu) - l]

(32)

U

where x = (k(‘)/D ‘)“*; A = k,(j/ec)n~,, G&; n ‘(a) = [D, A /k(‘){xu cth(xu) - 1) + D@(m)] / [O, {xu cth (xu) - l} + D,/H,,]. The validity of this approach is based on the following assumptions: the region of strong non-uniformity of the particle concentration profile, because of one skin of the droplet, is approximately droplet size and is significantly less than the distance between the droplets; the characteristic time of diffusion and chemical reaction is much less than the characteristic times of coagulation and nucleation processes in our conditions (r,,,, N 10-2-10-’ s, r_g N 10m2-1 s, Deminsky et al., 1981); the acidity is constant. The set of non-linear equations of first order was integrated by the Gear method (Gear, 1971), which allows a steady solution for this set to be obtained. We used a variant of the ELENA program. The results of these calculations are shown in Fig. 1 as a function of current density j. It is seen that the cluster oxidation mechanism describes the experimental data well in all ranges of current density. The minimum energy cost of 0.3 eV/mol is achieved at 10-j A/cm2 corresponding to realization of the chain

293

oxidation mechanism in clusters. This also shows the possibility of additional energy cost reduction by a liquid-phase mechanism for different droplet sizes. It is necessary to remark that the acidity (pH) of the liquid was held constant and equals 4-6.5 corresponding to addition in liquid phase of a basic component (for example NH.,). In this case only (see Fig. 2) the liquid-phase mechanism has an influence on the total radiation yield. Further, it is seen that the droplet-phase oxidation has an influence on energy costs in the j < 10m4A/cm2 region, when recombination processes are unimportant, and the strength depends on the parameters of the medium (acidity, humidity, droplets size etc.). The dependence of the radiation yield as a function of droplet size is shown in Fig. 4. This dependence can be explained by following the physical processes in the medium: diffusion of gas components to the droplets with chemical reactions in the gas; their dissolution and diffusion in the liquid with chemical reactions in the droplet; formation of active particles by outward radiation. As was shown earlier (Deminsky et al., 1991), the diffusion of a chain’s initiators is a limitation process of SO1 oxidation if the droplet size a 9 ug = (3D,8/k!))1’2. In this case the radiation yield G decreases with increasing size (due to radical-neutral and recombination reactions in the gas). The rate of chemical reaction in the liquid phase is a limitation process if a < u’ = [Q /k’fq’/2. In this case G does not depend on the droplet size. The value of u’ < a* < u* is determined in the range where the active particles of diffusion in the liauid are a limitation nrocess. It should be noted that the increasing relative humidity JI, will increase the radiation yield G and the range of droplet size. On the other hand, the increase in rp will lead to droplet coagulation and droplet size becomes more than the optimal size when SO, oxidation is effective (for example cp < 100% if j _ 10-6A/cm2, 1% SO,; Deminsky et al., 1990). Therefore, the conditions when the liquid-phase oxidation is most effective are: the liquid phase must enter the reactor volume as small droplets with a size of a c UK (a* * 10e5 cm for the OH radical) and the current 300

soy-1 % e=

1

J = 1 O4 A/cm’ 200 t s J 100

1

o-7

1 o-5 Ma

1o-3

W-4

Fig. 4. Radiation yield G as a function of drop size.

294

E. I. BARANCH~COVet al.

density j must be in the region of lo-’ < j < 10-3A/cm2. This provides a high rate of SO2 oxidation and a long chain length in the liquid. Thus, the results of this investigation confirm the possibility of the realization of the ion-molecule chain mechanism of SO, oxidation in gas and liquid (under certain conditions) phases, and, as a result lead to considerable reduction of energy costs of the removal of air streams.

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