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Interaction of solid particles with an ionized gas
Tenth Symposium (International) on Combustion,
pp. 699-707.
The Combustion Institute, 1965
INTERACTION OF SOLID PARTICLES W I T H AN IONIZED GAS S. L. SO0 AND R. C. DIMICK
Department of Mechanical Engineering, University of Illinois, Urbana, Illinois Consideration of equilibrium of ionization of a gas-solid suspension showed that the solid particles always became positively charged if the ionization of the gaseous atoms was negligible. However, the combination of high value of thermionic potential and low value of ionization potential of the gas may leave the solid particles negatively charged. Experiments with an arc flame of argon showed that addition of metals tended to increase the recombination rate while oxides tended to decrease the recombination rate of argon.
Introduction Attenuation of radio waves by the combustion product of a metallized propellant rocket has led to our studies of interaction of solid particles with an ionized gas, both as a source of free electrons and as a means of removing free electrons. I t was shown that a system of solid particles at temperatures of 2000 ~ to 3000~ constitutes a source of free electrons in a vacuum or in a gas when ionization of gaseous atoms can be neglected. This phenomenon, designated as thermal electrification, accounts for the charge on a solid particle given by exp ~ ~-~ (nc~e~/4~rEn~akT) exp (--r
(1)
where ~ = Ze2/4~EakT (assuming spherical particles of radius a), Z is the number of electron holes per particle, e the electronic charge, ~ the permittivity, k the Boltzmann constant, T the absolute temperature of the solid particle, r the thermionic potential, n~ is the number density of conduction electrons in the solid prior to emission, and np the number density of solid particles. The number of free electrons due to thermal electrification is thus to the order of Znp due to scattering b y the gaseous atoms and ions? I t was also shown that, with initially positively charged solid particles, free electrons could be removed from the ionized gas. Both of these effects were experimentally demonstrated in the decreasing electron concentration in a propane flame and quenching of a glow discharge by injecting thermally electrified particles of iron and silica into these media.: As a further step, interaction of solid particles with an ionized gas was considered in exploring the possibilities of both the thermal electrification and collection of electrons by solid particles as capacitors. ~ Simultaneous experimental study was
carried out by injecting solid particles of various metals and oxides into an arc heated jet of argon. Measurements with a rugged probe were made to determine the effect of solid particles on the recombination rate in argon.
Equilibrium Between Solid Particles and an Ionized Gas As a further step from our previous study, 1,2 we considered the case in which a substantial extent of ionization may occur among the gaseous atoms of a gas-solid suspension. At equilibrium, the condition of charge neutrality gives, for nonreactive solid particles in an inert gas
ne = n~ -~ Znp,
(2)
where ne and n~ are electron and positive ion concentration (per unit volume) in the gaseous phase, respectively. Ionization equilibrium in the gaseous phase gives1
n~n~ ~ n2/(PKp)
(3)
for low extent of ionization (say, less than 1%), where n is the concentration of neutral atoms, P is the pressure, and Kp the equilibrium constant; taking first degree ionization only for the present,
n ~ n ~ n (2gJg) (27rmkT/h2) 312exp ( - - I / k T ) , (4) where g, g~ are the statistical weights of the atom and ion respectively, h is the Planck constant, m is the electronic mass, I the ionization potential of first degree ionization. Equilibrium between the phases is reached when there is no net gain or loss of charge due to random motion. At the surface of the spherical solid particle, the number of ions di.ffusing toward the solid particle per unit time N~ is equal to 699
700
ELECTRICAL PROPERTIES O F FLAMES
that of electrons diffusing toward the particle (ATe) minus that of electrons leaving by thermionic emission, or 2V, -- (4ra2ATVe) exp ( - - r
= 2V~, (5)
where A is the coefficient of the RichardsonDushman equation for thermionic current density J, J = AT2exp ( - - r
(6)
a relation which is applicable even with the presence of the gaseous phase because: (a) at the temperature level of interest, surface adsorption of an inert gaseous phase is negligible, 4 and (b) the temperature level of interest is too low for secondary emission by collisions of electrons and ions to take place. 5 The gaseous phase present may consist of the vapor phase of a solid or its components; the modification to be made is in further details of Eqs. (3) and (4). For this reason the following experiments were carried out with argon for the gaseous phase, although the vapor phase of the solid is significant in some cases. The experimental coefficient 5 A is, in turn, related to the conduction electron concentration (for average reflectivity ~ of the surface for electrons) (7)
n~, = AT~/e(kT/2~'m)1]~(1 -- ~)
by equating the thermionic current density J to free electron current density; and, further, it can be shown that, for nonmetal or metal with a surface layer, Schottky's modification may be expressed as s A T 2 = e (2rib) ~/2(27rmkT/h2) TM ( k T / h ) (1 -- ~)
• exp (--Ae/2kT),
(8)
where nb is the total electron concentration in the solid, he is the energy gap from the conduction band. When Ae = 0 and nb -- 2 (2rrmkT/h2) ~12 from equating thermionic current density to that of emitted electrons, A reduces to its value for an ideal metal, 47reml~/h ~. For the Dehye length of the order of interparticle spacing, 1 the rates of free electrons Are, and ions N~, approaching a spherical solid particle based on a consistent approximation of the kinetic theory of scattering by a coulomb field is given by: N , = 2a~,(2~rkT/m) ~/2 exp o~, ~[~ = 2a~n~(2rkT/m~) ~/~ exp ( - - a ) ,
~ exp,~
(2m=ATVe) ( 2 . ~ k r ) -1~
-
X exp ( - - r
= (m/m,)ll~n~ exp ( - - a ) .
(12)
The equilibrium value of a is given, by eliminating n~ and n~ from Eqs. (2), (4), and (12), to be [B-
( m / m , ) m a e x p ( - - a ) ] [ ' B - - a expa-] = K, 4 (mime) 112sinh2[a -~- 88in (m~lm)]
(13) where the parameters B and K are given by B = 2~rmeA T 2
X exp (--d?/kT)/(2~rmkT)lf~47r~akTnp, -- (1 -- ~)(nr
exp ( - - r
g = ne 4 (2gJg) (2~rmkT/h2) 3/2
X exp ( - - I / k T ) / ( 4 w e a k T n ~ ) 2, = (ncse2/4~reakTnp) 2(n/nc,) 2 (2gJg)
• [(2~mkT/h2)~Vn] exp (--I/~T). The parameter B is the same as given by the right hand side of Eq. (1), and Eq. (13) reduces to Eq. (1) for K = 0, that is, negligible ionization in the gaseous phase. The parameter K relates the competition between thermionie emission and collection of electrons from thermal ionization of the gas by the electrostatic capacitance of the solid particles in the nature of a floating probe. ~ Equation (13), in general, gives a as a multivalued function for given B and K. However, the only values of a which are physically significant are those giving positive (or zero) values of n~ and hi, or a's are restricted to those giving n,=
(np41r~akT/e2)[B - (m/m~)I/2a exp ( - - a ) ~> 0 Eexp a-- ( m / m , ) 1/2 e x p ( - - a ) J
(14) and ( n p 4 ~ a k T / e ~ ) [ B -- ~ exp ~3 n~ ---- [ e x - - ~ - - ~ S e ~ - p - ~ - - ~ - ) ] > 0. (15)
Thus for given B and K, a is unique. Another asymptotic condition for ~ is that
(9)
sinh [~ + (1/4) In (mJm)3 > 0.
(10)
Therefore, the maximum negative charge that can be collected (besides the limits for electric breakdown s) by a solid particle is
(m~ being the mass of an ion); a < 0 for negatively charged solid particles. For small values of a, Eq. (10) reduces to that given by Rosen 3 JV~ = 2aZn~(2rrkT/m~)~12(1 -- a).
Eqs. (9) and (10) apply to all values of a. Substitution of these relations into Eq. (5) gives
(11)
> - - i In ( m J m ) ,
(16)
(17)
a condition limited by the rates of collision even
701
I N T E R A C T I O N OF S O L I D P A R T I C L E S W I T H I O N I Z E D GAS
B
/ J
f
f
~
~
AI20 3
)Cu [
-2
-I
0
I
2
{2
FIG. 1. Equilibrium of ionization of a gas (argon)-solid suspension. Circles show asymptotic states of experiments with various solids; dashed lines for each value of K gives the limit of m/m,~Ofor any gas. in the absence of thermionie emission. The relation between ~, B, and K for argon is shown in Fig. 1, which gives the trend for all gases. In this case, the value of rn~ for argon and m give :> --2.8 as the limit a for electron collection (the lowest is ~ > --0.94 for hydrogen atoms). Fig. 1 shows that for K = 0 the solid particles can only become positively charged, as dealt with earlier, 1 and this case gives the maximum value of a possible for given B. At higher values of K, depending on its relation to B, the solid particles can become positively charged or negatively charged (electrons are then effectively collected by solid particles). I t was seen that solid particles tended to become negatively charged with combination of low ionization potential of the gas and high thermionic potential of the solid. The circles in Fig. 1 are approximate asymptotic states of the experiments given below. The dashed lines for each value of K in Fig. 1 give the limit for any gas which gives heavy ions (m/m~~ 0). I t was seen that in the range of a near and above 0, the value of m/m, did not affect the relation between a, B, and K. Experimental Study The simplest model for ionization and recombination processes is an inert gas. However, measurable extent of equilibrium thermal ionization cannot be maintained in an inert gas at a temperature level of 3000~ and moderate pressures of tens of mm tIg. Therefore, our
experimental study was made with an arc flame of argon undergoing nonequilibrium recombination with or without addition of various solid particles. This was also a realistic model for recombination in the jet of a rocket after rapid expansion through a nozzle. Experiments were carried out with a subsonic arc-heated jet of argon (99.996% pure) with total temperatures ranging from 1000 ~ to 3000~ in a plenum chamber into which the arc-heated let and solid particles were delivered. The experimental system is shown in Fig. 2. When solid particles were not introduced, the conveyance gas (also argon) stream was maintained so that a total argon flow rate of 25.6 g/min was maintained in all tests. The power input to the arc ranged from 0.5 to 5.0 kw, 15 to 24 V at 30 to 210 amp. With the 88 sharp-pointed tungsten cathode, no erosion of the tip was noticeable over the test range. Feed rates of solid particles ranging from 0.08 to 4.5 g/min were metered using an S. S. White dental unit. Particle sizes were approximately 10 u for copper and alumina and 2 ~ for magnesia. A subsonic jet was produced by blowing down from the plenum chamber through a }-in.-diameter orifice into a vacuum duct (3-in. diameter, 12-in. long Vicor glass) at 40 to 90 mm Hg, connected to a vacuum tank and pump system. Measurements of charge density were made in terms of the saturation current to a rugged (to withstand the blast of solid particles and their coating action) double probe with water-cooled
702
ELECTRICAL PROPERTIES O F FLAMES
--~" III ~I++
III
I
I
TO 67 I/2 CU.FT. VACUUM
RESERVOIR
VlCOR GLASS [ l TEST SECTION " ~
/'
/PROBE
C.AM+
STILLING
I
L. .!
PLASMA
%
I
FIF. 2, S c h e m a t i c d i a g r a m of a p p a r a t u s .
copper electrodes of a__in, diam with 3 mm gap (potential difference was around 3 V). Measured current ranges from 0.001 to 1.0 ma were obtained with a Keithley electrometer. The probe faces were installed parallel to the direction of the jet to minimize coating by the solid material. The probe traverse in position was converted to the time of progression of the jet by measurement of the jet velocity (by a total head probe) and gas temperature (by a thermocouple probe). These probes (Fig. 3) were traversed along the axis of the jet. The temperature of the solid particles was measured with a pyrometer. Due to the necessary ruggedness of the probes,
only one of the probes (electric, pitot, and thermoeouple) can be accommodated during each run. Frequent cleaning of the experimental system was made necessary by the effective coating of the plasma sprayed solids, s Evaluation of D a t a Typical experimental results are shown in Figs. 4 and 5, with probe current vs time t (probe position in inches from the orifice of the jet is included in Fig. 4). Along this time scale, recombination took place in the ionized gas with or without addition of solid particles.
INTERACTIONOF SOLIDPARTICLESWITHIONIZEDGAS
TH E RMOCOU PLE
703
-~~ PITOTTUBE
PROB E
/ 0 - RING
GROOVES
\
SAUEREISEN
PORCELAIN
N ~ ~
Fro. 3. Probe construction. For the simple situation of an ionized gas without particles the recombination rate constant kr is defined according to 9 dnJdt
= - - krnen+ = - - krne 2.
(18)
The effect of ambipolar diffusivity is negligible for pressures above 10 mm Hg in the present investigation. 9 Integrating Eq. (18) gives kr =
(nJ -1-
ned-1)/(t-
to),
(19)
where subscript 0 denotes the initial time taken in the experiment. In terms of the probe current i which is proportional to n~ for the curves without solid particles such as in Figs. 4 and 5, taking ne ~ - nz and expressing d i / d t = - - a2i:,
(20)
where Ap is the area of the probe face and ~ is the average thermal velocity of the ions. Since ne ~ n~ between the probes, we have a2 ' ~ 4 k r / e A p y z
(23)
for ~, = ( S k T / T r m ~ ) 1/2, we get (for the experiments without solid particles) recombination coefficients as given in Table I. The data in Table I of kr for given P and ne compares favorably with data assembled by Loeb 9 and Bates. n When applied to the cases with solid particles (Cu, A1203, MgO), we postulate the variation of probe current i with time t in the form of a polynomial: di/dt = ao-
ali-
a2i:.
(24)
(21)
The physical meaning of this approximation is that:
which gives kr for a known relation between i and ne. With the approximation according to Talbot, ~o i,--~ A ~ n , e O , / 4 , (22)
1. a0 corresponds to the generation of current or charge carriers in the medium between the electrodes. This can arise due to thermionic emission from the solid particles,
we get a2 = (i- 1 -
i o - 1 ) / ( t - to),
704
ELECTRICAL
PROPERTIES
.OE
OF FLAMES
.0:2
~
.01
:---- "~ - W / O Alumina U .00~
d
.00
,002
k
0
LO Time (millisec)
Probe Position (inches f r o m orifice
~ol
.0ol ,.o,~o[, 0
,
I
45
4o
I
Time (milliseconds)
,
Fro. 5. Effect of alumina particles on the recombination of argon.
3
2
FIG. 4. Effect of copper particles on the recombination of argon. ionization of the vapor of the solid phase, or impurities on the solid particles. 2. al corresponds to a recombination with the solid particles by three-body collisions, i is first order here since the high electrical conductivity of a solid at high temperatures permits deionization through alternate collisions of the ions and electrons with the solids. 3. as has a similar meaning as before. It may include recombination of the ionized vapor of the solid phase and three-body recombination with the atoms or molecules of the solid phase when the concentration of the atoms or molecules of the solid phase is taken to be constant.
3.0
2.0
The above is necessarily a simplification of the real events. However, it serves to generalize the fact that copper particles increase in the over-all rate of recombination (Cases I and I I I ) , while AlcOa and MgO decrease the over-all rate of recombination (Cases IV, V, VI, and VII). The results of these computations are given in Table II. It was noted that for the curves with copper particles (Fig. 4), the increase of the recombination rate may be attributed to the vapor phase of the copper and the solid surfaces. For MgO and Al2Oa, kr decreases from the no-particle case by approximately an order of magnitude. This may be attributed to the scattering of the ions by positively charged solid particles. The coeiiicient a~ for MgO has a small negative value. Corresponding to al, we may
TABLE I Recombination of argon without solid particles Case
I
Ttot~l, ~ Ta, ~ P, mm Yig ~ho, g/rain Power input, kw ng/cm 3
n,0/cm3 v0, m/sec a2 k~, cmS/sec
2000 800 45 25.6 2.25 6.0 X 1017 3.0 X 10l~ 312 34.0* 1.4 X 10-~
* F o r all a2: i in m a ; t in reset.
III 3000 1300 60 25.6 4 4.9 X 1017 4.3 X 109 368 117 7.3 X 10-~
IV
V
2400 900 45 25.6 2.95 5.3 X 1017 5.4 X l0 s 330 370 2.3 X 10-6
1100 600 48 25.6 1 8.0 X 1017 3.2 X 109 250 3300 2.1 X 10-a
VI 2700 1200 93 33.1 3.4 7.5 X 1017 1.3 X 101Q 356 292 1.8 X 10-6
VII 2800 1200 130 33.1 3.7 1.05 • 10TM 2.5 X 109 360 850 5.3 X 10-6
705
INTERACTION OF SOLID PARTICLES WITH IONIZED GAS
TABLE II Recombination of argon with injection of various solid materials Case
III
I
Solid Size, tL dip, gm/min n.o ao al a2
Initial particle temperature, ~ Estimated: k~, cm3/sec % evaporated kl, 1/sec
IV
V
VI
VII
A1203 10 2 1.6 X 109 O. 0054 1.24 99
AI~O3 10 2 3.3 X 101~ O. 0027 0.67 160
MgO 2 0.08 1.3 X 101~ O. 0033
MgO 2 0.08 1.6 X 109 O. 0012
1000
1500
1500
1.3 X 10 -7 0.03
1.5 • 10-~ 0.03
1.7 • 10~ 0.86
1.3 X 10~ 0.65
Copper 10 4.52 5.6 X 101~ --0.48* --11.1" 25*
Copper 10 4.52 6.5 X 10g
1350
1500
1200
7.6 X 10-7 0.2
2.6 X 10-e 0.2
6.2 X 10-7 3.0 X 10-6 0.01 0.01 2.5 X 10-3 0.88 • 10-~ 1.5 )< 10s 2.4 • 103 0.47 0.76
416
n~/cm 3 4,ra2n~, m2/m3
4.4
29
* For all a0, a~, a:: i in ma, t in msec. denote the surface recombination coefficient as
kl
al X 10-3 - sec -1 47raZnp
(25)
for a total particle surface area 47ra2np (in me). Discussion
It was seen that for Z = O, ne - nz, ne >~ 0, Eq. (12) when substituted into Eq. (4) gives
(m/mz)l/2nz, and f ~
nz/n = (gz/g) exp E-- (I -- d?)/kT-],
(26)
the equation for surface ionization of an ideal metal given by Langmuir and Kingdon12 as a reduced form of Eq. (13). The same condition, when applied to Eq. (8), gives
nz/n = 2 (gJg ) ( 2=~k T/h~ ) ~' ( 2n, ) -'~ •
exp [ -
(I -- ~ --
89
(27)
showing that oxides, for instance, are more effective in producing surface ionization than metals. From the data given in Table II, estimated limiting values (based on the initial condition of the jet) of a, B, and K for various experiments are shown in Fig. 1. Cases I and I I I (copper) were computed from the ionization potential of their vapor, which is present in substantial
amounts (this changes the negative limit of in Fig. 1 to --2.9, but the modification of curves in Fig. 1 at the range of a of our interest is small). The copper particles, with a high thermionic potential of the solid (~b ---- 4.38 eV) and low ionization potential of their vapor (I = 7.68 eV), tends to become negatively charged or uncharged, thus enhancing recombination of argon ions (I -- 15.756 eV) at its surface. The oxides, due to negligible evaporation, become positively charged (r = 3.19 eV, r ---- 3.77 eV), and thus scatter the ions of argon and reduce its recombination rate. The increased rate at later times (Fig. 5) was due to cooling of solid particles. Therefore, if the solid particles were initially uncharged as in the above experiments (charging due to wall impact in the feeder is negligible), metals would be more effective in collecting free electrons. The really effective way of removing free electrons is by introducing significantly charged solid particles. 1 Conclusions
The nature of the basic interactions between an ionized gas and its entrained solid particles is seen clearly through the simplified model in the present study. Extension of the basic formulation to the case of a combustion product is a matter of further detail. When applied to the combustion product of a
706
ELECTRICAL PROPERTIES OF FLAMES
rocket motor, the problem of radio wave attenuation can be alleviated by keeping the electron concentration in the jet at a permissible magnitude through (i) proper selection of fuel components, such that the solid particles in the exhaust will be negatively charged; (it) addition of properly selected uncharged solid particles to the exhaust, such that electrons are efficiently collected; and (iii) addition of positively charged solid particles produced by intense corona charging. When applied to the case of a magnetohydrodynamic generator or accelerator, high electron concentration in the gas is desirable. The contribution of intentionally or unintentionally added solid particles in the ionized gas can be determined according to the above considerations. It is expected that ashes from combustion of a hydrocarbon fuel would increase the conductivity of the fluid medium, while metallic particles from erosion of a wall, if not oxidized, could decrease the conductivity of the fluid medium. ACKNOWLEDGEMENT
This work was sponsored by Project SQUID which is supported by the Office of Naval Research, Department of the Navy, under contract NONR 1858 (25) NR-098-038.
REFERENCES
1. See, S. L.: J. Appl. Phys. 34, 1689 (1963). 2. See, S. L. AND DIMICK, R. C.: "Experimental Study of Thermal Electrification of a Gas-Solid System," Multi-Phase Flow Symposium, Am. See. Mech. Engr., 1963. 3. Ros~N, G.: Phys. Fluids 5, 737 (1962). 4. ERLICH, G.: 1961 Trans. of 8th Vac. Symposium and 2nd International Congress, p. 126, Pergamon, 1962. 5. COSINE,J. D.: Gaseous Conductors, pp. 109-119, 173, Dover, 1958. 6. Tier HAAR, D. : Statistical Mechanics, p. 245, Reinhart, 1956. 7. BAROER, R. L.: Ionization and Deionization Processes in Low-Density Plasma Flows, p. 12, NASA TN ])-740, 1961. 8. G~ISAFF~bS. J. ANDSPrrziG, W. A. : Preliminary Investigation of Particle-Substrate Bonding of Plasma-Sprayed Materials, NASA TN D-1705, 1963. 9. LOEB, L. B.: Basis Processes of Gaseous Electronics, pp. 421, 479, 560, Ulfiv. of Calif. Press, 1955. 10. TALEOT, L.: Phys. Fluids 3, 289 (1960). 11. BATES, D. R.: Atomic and Molecular Processes, p. 267, Academic Press, 1962. 12. REIMANN, A. L.: Thermionic Emission, p. 298, Wiley, 1934.
COMMENTS Dr. S. C. Kurzius (AeroChem Research Laboralories, Inc.): A lack of consistency in the rate of recombination reported for argon plasma without solid t)articles, as shown, for example, by the data of Figs. 4 and 5 and Table I, is most evident. Is it not possible that the experimental set-up was subject to difficulties caused by contaminants, and that these difficulties are also reflected in the recombination results obtained with solids? Equations (9) and (10) imply that the current to a charged particle varies exponcntiaUy with the charge and, hence, the voltage of the particle. Experimental work with electrostatic probes demonstrate, however, that an exponential law is followed only in the region of the plasma potential. Prof. S. L. See: l)crivations of Eqs. (9) and (10) were presented in detail in a recent article f'DIMICK, R. C. XND See, S. L.: Phys. Fluids 7, 1638 (1964)]. The answer to the question on recombination rate is that the cases "without particles" do not reproduce easily from one case to the other, due to different contamination on the system after each "with-particle" measurement was made. Consistent comparison of "without-particle" run and "withparticle" run can only be made after each particular
"with-particle" run. This is because there is no real uncontaminated run, even with a new nozzle. However, the recombination rates from "withoutparticle" runs are, in general, consistent with temperatm'e.
Dr. G. N. Spokes (Stanford Research Institute): We have been doing some experiments on electronemission properties of alumina (unpublished). We find that the usually available high-purity alumina (Linde Corporation) contains several hundred parts per million of alkali-metal impurity. Is it possible that the author's alumina was similarly contaminated? If so, this could explain the change in apparent rate of electron loss. Ar2+ would, for example, disappear much faster than Na + or K +, due to the high recombination coefficient of the diatomic ion. ]n order to test the electron emission or absorption properties of alumina, a much purer grade of material would have to be used. Prof. S. L. See: We used alumina and magnesia of the Baker's reagent quality (Allied Chemical).
INTERACTION OF SOLID PARTICLES WITH IONIZED GAS These are known to contain up to 0.5% sodium and 0.005 % potassium. Although our paper included only results where the recombination rate was reduced by alumina and magnesia, recent experiments [DIMICK,R. C.: An Experimental Study of the Effects of Solid and Liquid Contaminants on the Deionization of a Gas, Ph.D. thesis, University of Illinois, October 19641 showed also cases where electrons were collected by the particles. The pres-
~07
ence of impurities is expected; the effects of the presence of particles, however, are consistent with particle temperature. We believe that, due to lower ionization potential of Na and 1K, depending on the temperature, their presence could enhance collection of electrons. This effect is substantiated in the case of cesium in the experiment of Balwanz (this Symposium p. 685). We agree t h a t spectrographic measurements of ion species will be worthwhile.
pp. 699-707.
The Combustion Institute, 1965
INTERACTION OF SOLID PARTICLES W I T H AN IONIZED GAS S. L. SO0 AND R. C. DIMICK
Department of Mechanical Engineering, University of Illinois, Urbana, Illinois Consideration of equilibrium of ionization of a gas-solid suspension showed that the solid particles always became positively charged if the ionization of the gaseous atoms was negligible. However, the combination of high value of thermionic potential and low value of ionization potential of the gas may leave the solid particles negatively charged. Experiments with an arc flame of argon showed that addition of metals tended to increase the recombination rate while oxides tended to decrease the recombination rate of argon.
Introduction Attenuation of radio waves by the combustion product of a metallized propellant rocket has led to our studies of interaction of solid particles with an ionized gas, both as a source of free electrons and as a means of removing free electrons. I t was shown that a system of solid particles at temperatures of 2000 ~ to 3000~ constitutes a source of free electrons in a vacuum or in a gas when ionization of gaseous atoms can be neglected. This phenomenon, designated as thermal electrification, accounts for the charge on a solid particle given by exp ~ ~-~ (nc~e~/4~rEn~akT) exp (--r
(1)
where ~ = Ze2/4~EakT (assuming spherical particles of radius a), Z is the number of electron holes per particle, e the electronic charge, ~ the permittivity, k the Boltzmann constant, T the absolute temperature of the solid particle, r the thermionic potential, n~ is the number density of conduction electrons in the solid prior to emission, and np the number density of solid particles. The number of free electrons due to thermal electrification is thus to the order of Znp due to scattering b y the gaseous atoms and ions? I t was also shown that, with initially positively charged solid particles, free electrons could be removed from the ionized gas. Both of these effects were experimentally demonstrated in the decreasing electron concentration in a propane flame and quenching of a glow discharge by injecting thermally electrified particles of iron and silica into these media.: As a further step, interaction of solid particles with an ionized gas was considered in exploring the possibilities of both the thermal electrification and collection of electrons by solid particles as capacitors. ~ Simultaneous experimental study was
carried out by injecting solid particles of various metals and oxides into an arc heated jet of argon. Measurements with a rugged probe were made to determine the effect of solid particles on the recombination rate in argon.
Equilibrium Between Solid Particles and an Ionized Gas As a further step from our previous study, 1,2 we considered the case in which a substantial extent of ionization may occur among the gaseous atoms of a gas-solid suspension. At equilibrium, the condition of charge neutrality gives, for nonreactive solid particles in an inert gas
ne = n~ -~ Znp,
(2)
where ne and n~ are electron and positive ion concentration (per unit volume) in the gaseous phase, respectively. Ionization equilibrium in the gaseous phase gives1
n~n~ ~ n2/(PKp)
(3)
for low extent of ionization (say, less than 1%), where n is the concentration of neutral atoms, P is the pressure, and Kp the equilibrium constant; taking first degree ionization only for the present,
n ~ n ~ n (2gJg) (27rmkT/h2) 312exp ( - - I / k T ) , (4) where g, g~ are the statistical weights of the atom and ion respectively, h is the Planck constant, m is the electronic mass, I the ionization potential of first degree ionization. Equilibrium between the phases is reached when there is no net gain or loss of charge due to random motion. At the surface of the spherical solid particle, the number of ions di.ffusing toward the solid particle per unit time N~ is equal to 699
700
ELECTRICAL PROPERTIES O F FLAMES
that of electrons diffusing toward the particle (ATe) minus that of electrons leaving by thermionic emission, or 2V, -- (4ra2ATVe) exp ( - - r
= 2V~, (5)
where A is the coefficient of the RichardsonDushman equation for thermionic current density J, J = AT2exp ( - - r
(6)
a relation which is applicable even with the presence of the gaseous phase because: (a) at the temperature level of interest, surface adsorption of an inert gaseous phase is negligible, 4 and (b) the temperature level of interest is too low for secondary emission by collisions of electrons and ions to take place. 5 The gaseous phase present may consist of the vapor phase of a solid or its components; the modification to be made is in further details of Eqs. (3) and (4). For this reason the following experiments were carried out with argon for the gaseous phase, although the vapor phase of the solid is significant in some cases. The experimental coefficient 5 A is, in turn, related to the conduction electron concentration (for average reflectivity ~ of the surface for electrons) (7)
n~, = AT~/e(kT/2~'m)1]~(1 -- ~)
by equating the thermionic current density J to free electron current density; and, further, it can be shown that, for nonmetal or metal with a surface layer, Schottky's modification may be expressed as s A T 2 = e (2rib) ~/2(27rmkT/h2) TM ( k T / h ) (1 -- ~)
• exp (--Ae/2kT),
(8)
where nb is the total electron concentration in the solid, he is the energy gap from the conduction band. When Ae = 0 and nb -- 2 (2rrmkT/h2) ~12 from equating thermionic current density to that of emitted electrons, A reduces to its value for an ideal metal, 47reml~/h ~. For the Dehye length of the order of interparticle spacing, 1 the rates of free electrons Are, and ions N~, approaching a spherical solid particle based on a consistent approximation of the kinetic theory of scattering by a coulomb field is given by: N , = 2a~,(2~rkT/m) ~/2 exp o~, ~[~ = 2a~n~(2rkT/m~) ~/~ exp ( - - a ) ,
~ exp,~
(2m=ATVe) ( 2 . ~ k r ) -1~
-
X exp ( - - r
= (m/m,)ll~n~ exp ( - - a ) .
(12)
The equilibrium value of a is given, by eliminating n~ and n~ from Eqs. (2), (4), and (12), to be [B-
( m / m , ) m a e x p ( - - a ) ] [ ' B - - a expa-] = K, 4 (mime) 112sinh2[a -~- 88in (m~lm)]
(13) where the parameters B and K are given by B = 2~rmeA T 2
X exp (--d?/kT)/(2~rmkT)lf~47r~akTnp, -- (1 -- ~)(nr
exp ( - - r
g = ne 4 (2gJg) (2~rmkT/h2) 3/2
X exp ( - - I / k T ) / ( 4 w e a k T n ~ ) 2, = (ncse2/4~reakTnp) 2(n/nc,) 2 (2gJg)
• [(2~mkT/h2)~Vn] exp (--I/~T). The parameter B is the same as given by the right hand side of Eq. (1), and Eq. (13) reduces to Eq. (1) for K = 0, that is, negligible ionization in the gaseous phase. The parameter K relates the competition between thermionie emission and collection of electrons from thermal ionization of the gas by the electrostatic capacitance of the solid particles in the nature of a floating probe. ~ Equation (13), in general, gives a as a multivalued function for given B and K. However, the only values of a which are physically significant are those giving positive (or zero) values of n~ and hi, or a's are restricted to those giving n,=
(np41r~akT/e2)[B - (m/m~)I/2a exp ( - - a ) ~> 0 Eexp a-- ( m / m , ) 1/2 e x p ( - - a ) J
(14) and ( n p 4 ~ a k T / e ~ ) [ B -- ~ exp ~3 n~ ---- [ e x - - ~ - - ~ S e ~ - p - ~ - - ~ - ) ] > 0. (15)
Thus for given B and K, a is unique. Another asymptotic condition for ~ is that
(9)
sinh [~ + (1/4) In (mJm)3 > 0.
(10)
Therefore, the maximum negative charge that can be collected (besides the limits for electric breakdown s) by a solid particle is
(m~ being the mass of an ion); a < 0 for negatively charged solid particles. For small values of a, Eq. (10) reduces to that given by Rosen 3 JV~ = 2aZn~(2rrkT/m~)~12(1 -- a).
Eqs. (9) and (10) apply to all values of a. Substitution of these relations into Eq. (5) gives
(11)
> - - i In ( m J m ) ,
(16)
(17)
a condition limited by the rates of collision even
701
I N T E R A C T I O N OF S O L I D P A R T I C L E S W I T H I O N I Z E D GAS
B
/ J
f
f
~
~
AI20 3
)Cu [
-2
-I
0
I
2
{2
FIG. 1. Equilibrium of ionization of a gas (argon)-solid suspension. Circles show asymptotic states of experiments with various solids; dashed lines for each value of K gives the limit of m/m,~Ofor any gas. in the absence of thermionie emission. The relation between ~, B, and K for argon is shown in Fig. 1, which gives the trend for all gases. In this case, the value of rn~ for argon and m give :> --2.8 as the limit a for electron collection (the lowest is ~ > --0.94 for hydrogen atoms). Fig. 1 shows that for K = 0 the solid particles can only become positively charged, as dealt with earlier, 1 and this case gives the maximum value of a possible for given B. At higher values of K, depending on its relation to B, the solid particles can become positively charged or negatively charged (electrons are then effectively collected by solid particles). I t was seen that solid particles tended to become negatively charged with combination of low ionization potential of the gas and high thermionic potential of the solid. The circles in Fig. 1 are approximate asymptotic states of the experiments given below. The dashed lines for each value of K in Fig. 1 give the limit for any gas which gives heavy ions (m/m~~ 0). I t was seen that in the range of a near and above 0, the value of m/m, did not affect the relation between a, B, and K. Experimental Study The simplest model for ionization and recombination processes is an inert gas. However, measurable extent of equilibrium thermal ionization cannot be maintained in an inert gas at a temperature level of 3000~ and moderate pressures of tens of mm tIg. Therefore, our
experimental study was made with an arc flame of argon undergoing nonequilibrium recombination with or without addition of various solid particles. This was also a realistic model for recombination in the jet of a rocket after rapid expansion through a nozzle. Experiments were carried out with a subsonic arc-heated jet of argon (99.996% pure) with total temperatures ranging from 1000 ~ to 3000~ in a plenum chamber into which the arc-heated let and solid particles were delivered. The experimental system is shown in Fig. 2. When solid particles were not introduced, the conveyance gas (also argon) stream was maintained so that a total argon flow rate of 25.6 g/min was maintained in all tests. The power input to the arc ranged from 0.5 to 5.0 kw, 15 to 24 V at 30 to 210 amp. With the 88 sharp-pointed tungsten cathode, no erosion of the tip was noticeable over the test range. Feed rates of solid particles ranging from 0.08 to 4.5 g/min were metered using an S. S. White dental unit. Particle sizes were approximately 10 u for copper and alumina and 2 ~ for magnesia. A subsonic jet was produced by blowing down from the plenum chamber through a }-in.-diameter orifice into a vacuum duct (3-in. diameter, 12-in. long Vicor glass) at 40 to 90 mm Hg, connected to a vacuum tank and pump system. Measurements of charge density were made in terms of the saturation current to a rugged (to withstand the blast of solid particles and their coating action) double probe with water-cooled
702
ELECTRICAL PROPERTIES O F FLAMES
--~" III ~I++
III
I
I
TO 67 I/2 CU.FT. VACUUM
RESERVOIR
VlCOR GLASS [ l TEST SECTION " ~
/'
/PROBE
C.AM+
STILLING
I
L. .!
PLASMA
%
I
FIF. 2, S c h e m a t i c d i a g r a m of a p p a r a t u s .
copper electrodes of a__in, diam with 3 mm gap (potential difference was around 3 V). Measured current ranges from 0.001 to 1.0 ma were obtained with a Keithley electrometer. The probe faces were installed parallel to the direction of the jet to minimize coating by the solid material. The probe traverse in position was converted to the time of progression of the jet by measurement of the jet velocity (by a total head probe) and gas temperature (by a thermocouple probe). These probes (Fig. 3) were traversed along the axis of the jet. The temperature of the solid particles was measured with a pyrometer. Due to the necessary ruggedness of the probes,
only one of the probes (electric, pitot, and thermoeouple) can be accommodated during each run. Frequent cleaning of the experimental system was made necessary by the effective coating of the plasma sprayed solids, s Evaluation of D a t a Typical experimental results are shown in Figs. 4 and 5, with probe current vs time t (probe position in inches from the orifice of the jet is included in Fig. 4). Along this time scale, recombination took place in the ionized gas with or without addition of solid particles.
INTERACTIONOF SOLIDPARTICLESWITHIONIZEDGAS
TH E RMOCOU PLE
703
-~~ PITOTTUBE
PROB E
/ 0 - RING
GROOVES
\
SAUEREISEN
PORCELAIN
N ~ ~
Fro. 3. Probe construction. For the simple situation of an ionized gas without particles the recombination rate constant kr is defined according to 9 dnJdt
= - - krnen+ = - - krne 2.
(18)
The effect of ambipolar diffusivity is negligible for pressures above 10 mm Hg in the present investigation. 9 Integrating Eq. (18) gives kr =
(nJ -1-
ned-1)/(t-
to),
(19)
where subscript 0 denotes the initial time taken in the experiment. In terms of the probe current i which is proportional to n~ for the curves without solid particles such as in Figs. 4 and 5, taking ne ~ - nz and expressing d i / d t = - - a2i:,
(20)
where Ap is the area of the probe face and ~ is the average thermal velocity of the ions. Since ne ~ n~ between the probes, we have a2 ' ~ 4 k r / e A p y z
(23)
for ~, = ( S k T / T r m ~ ) 1/2, we get (for the experiments without solid particles) recombination coefficients as given in Table I. The data in Table I of kr for given P and ne compares favorably with data assembled by Loeb 9 and Bates. n When applied to the cases with solid particles (Cu, A1203, MgO), we postulate the variation of probe current i with time t in the form of a polynomial: di/dt = ao-
ali-
a2i:.
(24)
(21)
The physical meaning of this approximation is that:
which gives kr for a known relation between i and ne. With the approximation according to Talbot, ~o i,--~ A ~ n , e O , / 4 , (22)
1. a0 corresponds to the generation of current or charge carriers in the medium between the electrodes. This can arise due to thermionic emission from the solid particles,
we get a2 = (i- 1 -
i o - 1 ) / ( t - to),
704
ELECTRICAL
PROPERTIES
.OE
OF FLAMES
.0:2
~
.01
:---- "~ - W / O Alumina U .00~
d
.00
,002
k
0
LO Time (millisec)
Probe Position (inches f r o m orifice
~ol
.0ol ,.o,~o[, 0
,
I
45
4o
I
Time (milliseconds)
,
Fro. 5. Effect of alumina particles on the recombination of argon.
3
2
FIG. 4. Effect of copper particles on the recombination of argon. ionization of the vapor of the solid phase, or impurities on the solid particles. 2. al corresponds to a recombination with the solid particles by three-body collisions, i is first order here since the high electrical conductivity of a solid at high temperatures permits deionization through alternate collisions of the ions and electrons with the solids. 3. as has a similar meaning as before. It may include recombination of the ionized vapor of the solid phase and three-body recombination with the atoms or molecules of the solid phase when the concentration of the atoms or molecules of the solid phase is taken to be constant.
3.0
2.0
The above is necessarily a simplification of the real events. However, it serves to generalize the fact that copper particles increase in the over-all rate of recombination (Cases I and I I I ) , while AlcOa and MgO decrease the over-all rate of recombination (Cases IV, V, VI, and VII). The results of these computations are given in Table II. It was noted that for the curves with copper particles (Fig. 4), the increase of the recombination rate may be attributed to the vapor phase of the copper and the solid surfaces. For MgO and Al2Oa, kr decreases from the no-particle case by approximately an order of magnitude. This may be attributed to the scattering of the ions by positively charged solid particles. The coeiiicient a~ for MgO has a small negative value. Corresponding to al, we may
TABLE I Recombination of argon without solid particles Case
I
Ttot~l, ~ Ta, ~ P, mm Yig ~ho, g/rain Power input, kw ng/cm 3
n,0/cm3 v0, m/sec a2 k~, cmS/sec
2000 800 45 25.6 2.25 6.0 X 1017 3.0 X 10l~ 312 34.0* 1.4 X 10-~
* F o r all a2: i in m a ; t in reset.
III 3000 1300 60 25.6 4 4.9 X 1017 4.3 X 109 368 117 7.3 X 10-~
IV
V
2400 900 45 25.6 2.95 5.3 X 1017 5.4 X l0 s 330 370 2.3 X 10-6
1100 600 48 25.6 1 8.0 X 1017 3.2 X 109 250 3300 2.1 X 10-a
VI 2700 1200 93 33.1 3.4 7.5 X 1017 1.3 X 101Q 356 292 1.8 X 10-6
VII 2800 1200 130 33.1 3.7 1.05 • 10TM 2.5 X 109 360 850 5.3 X 10-6
705
INTERACTION OF SOLID PARTICLES WITH IONIZED GAS
TABLE II Recombination of argon with injection of various solid materials Case
III
I
Solid Size, tL dip, gm/min n.o ao al a2
Initial particle temperature, ~ Estimated: k~, cm3/sec % evaporated kl, 1/sec
IV
V
VI
VII
A1203 10 2 1.6 X 109 O. 0054 1.24 99
AI~O3 10 2 3.3 X 101~ O. 0027 0.67 160
MgO 2 0.08 1.3 X 101~ O. 0033
MgO 2 0.08 1.6 X 109 O. 0012
1000
1500
1500
1.3 X 10 -7 0.03
1.5 • 10-~ 0.03
1.7 • 10~ 0.86
1.3 X 10~ 0.65
Copper 10 4.52 5.6 X 101~ --0.48* --11.1" 25*
Copper 10 4.52 6.5 X 10g
1350
1500
1200
7.6 X 10-7 0.2
2.6 X 10-e 0.2
6.2 X 10-7 3.0 X 10-6 0.01 0.01 2.5 X 10-3 0.88 • 10-~ 1.5 )< 10s 2.4 • 103 0.47 0.76
416
n~/cm 3 4,ra2n~, m2/m3
4.4
29
* For all a0, a~, a:: i in ma, t in msec. denote the surface recombination coefficient as
kl
al X 10-3 - sec -1 47raZnp
(25)
for a total particle surface area 47ra2np (in me). Discussion
It was seen that for Z = O, ne - nz, ne >~ 0, Eq. (12) when substituted into Eq. (4) gives
(m/mz)l/2nz, and f ~
nz/n = (gz/g) exp E-- (I -- d?)/kT-],
(26)
the equation for surface ionization of an ideal metal given by Langmuir and Kingdon12 as a reduced form of Eq. (13). The same condition, when applied to Eq. (8), gives
nz/n = 2 (gJg ) ( 2=~k T/h~ ) ~' ( 2n, ) -'~ •
exp [ -
(I -- ~ --
89
(27)
showing that oxides, for instance, are more effective in producing surface ionization than metals. From the data given in Table II, estimated limiting values (based on the initial condition of the jet) of a, B, and K for various experiments are shown in Fig. 1. Cases I and I I I (copper) were computed from the ionization potential of their vapor, which is present in substantial
amounts (this changes the negative limit of in Fig. 1 to --2.9, but the modification of curves in Fig. 1 at the range of a of our interest is small). The copper particles, with a high thermionic potential of the solid (~b ---- 4.38 eV) and low ionization potential of their vapor (I = 7.68 eV), tends to become negatively charged or uncharged, thus enhancing recombination of argon ions (I -- 15.756 eV) at its surface. The oxides, due to negligible evaporation, become positively charged (r = 3.19 eV, r ---- 3.77 eV), and thus scatter the ions of argon and reduce its recombination rate. The increased rate at later times (Fig. 5) was due to cooling of solid particles. Therefore, if the solid particles were initially uncharged as in the above experiments (charging due to wall impact in the feeder is negligible), metals would be more effective in collecting free electrons. The really effective way of removing free electrons is by introducing significantly charged solid particles. 1 Conclusions
The nature of the basic interactions between an ionized gas and its entrained solid particles is seen clearly through the simplified model in the present study. Extension of the basic formulation to the case of a combustion product is a matter of further detail. When applied to the combustion product of a
706
ELECTRICAL PROPERTIES OF FLAMES
rocket motor, the problem of radio wave attenuation can be alleviated by keeping the electron concentration in the jet at a permissible magnitude through (i) proper selection of fuel components, such that the solid particles in the exhaust will be negatively charged; (it) addition of properly selected uncharged solid particles to the exhaust, such that electrons are efficiently collected; and (iii) addition of positively charged solid particles produced by intense corona charging. When applied to the case of a magnetohydrodynamic generator or accelerator, high electron concentration in the gas is desirable. The contribution of intentionally or unintentionally added solid particles in the ionized gas can be determined according to the above considerations. It is expected that ashes from combustion of a hydrocarbon fuel would increase the conductivity of the fluid medium, while metallic particles from erosion of a wall, if not oxidized, could decrease the conductivity of the fluid medium. ACKNOWLEDGEMENT
This work was sponsored by Project SQUID which is supported by the Office of Naval Research, Department of the Navy, under contract NONR 1858 (25) NR-098-038.
REFERENCES
1. See, S. L.: J. Appl. Phys. 34, 1689 (1963). 2. See, S. L. AND DIMICK, R. C.: "Experimental Study of Thermal Electrification of a Gas-Solid System," Multi-Phase Flow Symposium, Am. See. Mech. Engr., 1963. 3. Ros~N, G.: Phys. Fluids 5, 737 (1962). 4. ERLICH, G.: 1961 Trans. of 8th Vac. Symposium and 2nd International Congress, p. 126, Pergamon, 1962. 5. COSINE,J. D.: Gaseous Conductors, pp. 109-119, 173, Dover, 1958. 6. Tier HAAR, D. : Statistical Mechanics, p. 245, Reinhart, 1956. 7. BAROER, R. L.: Ionization and Deionization Processes in Low-Density Plasma Flows, p. 12, NASA TN ])-740, 1961. 8. G~ISAFF~bS. J. ANDSPrrziG, W. A. : Preliminary Investigation of Particle-Substrate Bonding of Plasma-Sprayed Materials, NASA TN D-1705, 1963. 9. LOEB, L. B.: Basis Processes of Gaseous Electronics, pp. 421, 479, 560, Ulfiv. of Calif. Press, 1955. 10. TALEOT, L.: Phys. Fluids 3, 289 (1960). 11. BATES, D. R.: Atomic and Molecular Processes, p. 267, Academic Press, 1962. 12. REIMANN, A. L.: Thermionic Emission, p. 298, Wiley, 1934.
COMMENTS Dr. S. C. Kurzius (AeroChem Research Laboralories, Inc.): A lack of consistency in the rate of recombination reported for argon plasma without solid t)articles, as shown, for example, by the data of Figs. 4 and 5 and Table I, is most evident. Is it not possible that the experimental set-up was subject to difficulties caused by contaminants, and that these difficulties are also reflected in the recombination results obtained with solids? Equations (9) and (10) imply that the current to a charged particle varies exponcntiaUy with the charge and, hence, the voltage of the particle. Experimental work with electrostatic probes demonstrate, however, that an exponential law is followed only in the region of the plasma potential. Prof. S. L. See: l)crivations of Eqs. (9) and (10) were presented in detail in a recent article f'DIMICK, R. C. XND See, S. L.: Phys. Fluids 7, 1638 (1964)]. The answer to the question on recombination rate is that the cases "without particles" do not reproduce easily from one case to the other, due to different contamination on the system after each "with-particle" measurement was made. Consistent comparison of "without-particle" run and "withparticle" run can only be made after each particular
"with-particle" run. This is because there is no real uncontaminated run, even with a new nozzle. However, the recombination rates from "withoutparticle" runs are, in general, consistent with temperatm'e.
Dr. G. N. Spokes (Stanford Research Institute): We have been doing some experiments on electronemission properties of alumina (unpublished). We find that the usually available high-purity alumina (Linde Corporation) contains several hundred parts per million of alkali-metal impurity. Is it possible that the author's alumina was similarly contaminated? If so, this could explain the change in apparent rate of electron loss. Ar2+ would, for example, disappear much faster than Na + or K +, due to the high recombination coefficient of the diatomic ion. ]n order to test the electron emission or absorption properties of alumina, a much purer grade of material would have to be used. Prof. S. L. See: We used alumina and magnesia of the Baker's reagent quality (Allied Chemical).
INTERACTION OF SOLID PARTICLES WITH IONIZED GAS These are known to contain up to 0.5% sodium and 0.005 % potassium. Although our paper included only results where the recombination rate was reduced by alumina and magnesia, recent experiments [DIMICK,R. C.: An Experimental Study of the Effects of Solid and Liquid Contaminants on the Deionization of a Gas, Ph.D. thesis, University of Illinois, October 19641 showed also cases where electrons were collected by the particles. The pres-
~07
ence of impurities is expected; the effects of the presence of particles, however, are consistent with particle temperature. We believe that, due to lower ionization potential of Na and 1K, depending on the temperature, their presence could enhance collection of electrons. This effect is substantiated in the case of cesium in the experiment of Balwanz (this Symposium p. 685). We agree t h a t spectrographic measurements of ion species will be worthwhile.