The Reaction of Hydrogen Chloride with Oxygen in an Electrodeless Radiofrequency Discharge Daniel 1. Flamm,*l Edwin R. Gilliland,2 and Raymond F. Baddour Massachusetts Institute of Technology, Cambridge, X a s s .
An investigation of the reaction between HCI and
0 2 in a 6-MHz radiofrequency discharge is reported, Eight different reactor geometries and a wide range of pressure ( 1 1-1 60 Torr), power (10-700 W), and flow rates (50-400 cm3(STP)/min) were used. Both quartz tube reactors with external sleeve electrodes and parallel electrode “pillbox” reactors were run in order to obtain a more nearly homogeneous plasma. The present results are compared with earlier investigations of the same chemical system made a t 2 0 and 2 4 5 0 MHz. The effect of driving frequency, pressure and modulation of the applied RF voltage on conversion are discussed. Theories in which E / p and electron energy are the proper variables for reaction are considered. It is suggested that conversions at high discharge powers are limited by thermal equilibrium. At low power, the reaction is rate-limited b y the supply of active species.
Electrically iiitensive chemical processes can offer a direct, and economic route for the product,ion of certain valuable chemicals and materials. Electrical discharges, a member of this group, have been used to manufacture nitric oxide (Mellor, 1940), acetylene, (Gladish, 1962), and ozone (A.C.S., 1959) and for the treatment of surfaces (Wechsburg and Weber, 1959). Discharges may be broadly divided into “hot” discharges or arcs and “cold” or glow discharges. d r c s are characterized by a free electron temperature relatively close to that of the discharge gas; the gas temperature typically may be several thousand degrees Kelvin to ten thousand degrees or more. Cold discharges are characterized by electron temperatures far above that of the discharge gas. Here the electron teniperature may be tens of thousands of degrees while the host gas is only a few hundred degrees. A good deal of success in predicting chemical synthesis in arcs has been attained by considering the body of the arc to be essentially in equilibrium (local thermodynamic equilibrium) and considering the transport of energy and chemical kinetics during the quench of high temperature species (Bronfin, 1969; Timmins and Xmmann, 1967). However, a like physical and chemical understanding of the reacting glow discharge has yet to be found. The classifications of arc and glow were originally operational in nature. There are other classes of discharges such as corona, spark, ozonizer, silent electric, and barrier which are not always grouped into one of the above two categories. These categories again are operational and, depending on the exact conditions under which these discharges are run, they may be placed in the spectrum running from “cold” discharge to arcs. Often the term glolv discharge is taken to further signify a state in which current flows continuously through the discharges with the steady emission of light. The work in this paper deals wit,h radiofrequency glow discharges of this type. Address all correspondence to this author at, the Department of Chemical Engineering, Texas A&3I University, College Station, Texas 77840.
* Deceased.
276
Ind. Eng. Chem. Fundam., Vol. 12, No. 3, 1973
The glow discharge has received much attention by chemish as a means to synthesize exotic chemicals and active species (Kana’an and Margrave, 1964; IIcTaggart,, 1967). It has been established that yields in excess of the chemical equilibrium constant can be obtaiiied (Blaustein and F u , 1969; ;Ilal’tsev, et al., 1959). Relatively little is known about the influence of basic discharge parameters on such chemistry. Some recent’ experimental studies, (Bell, 1967; Cooper, 1966; Cooper, et al., 1968) Fvere addressed to the relation between discharge processes and chemistry, using the oxidation of hydrogen chloride as a prototype reaction (eq 1). This reaction is thermodynamically favorable. However, without a 4HC1
+ 02 = 2C12 + 2HgO (AG2gg = -18.160 kcal/mole)
(1)
catalyst, this reaction does not proceed, even a t high temperature (Lewis, 1906). Cooper studied the reaction using a cylindrical quartz reactor in a tapered waveguide a t 2450 MHz, Bell used a similar reactor with 120-HZ modulation (two-tone) imposed on a 20-11Hz carrier. Both found that a t const,ant pressure their conversions exhibited maxima as a function of power (see Figure 6). They concluded that reaction of HC1 was inibiated by the dissociative attachment of electrons to hydrogen chloride e
+ €IC1 = H + C1-
(2)
The hydrogen atoms so formed were to react directly with oxygen to form species which, through a series of additional steps, produce chlorine and water. The rate of dissociative attachment is a function of average electron energy (Christophorou and Stockdale, 1968) arid gas temperature (Janev, 1967). For a gas near room temperature, the rate of eq 2 goes through a maximum a t a n electron energy of 0.82 eV (Christophorou and Stockdale, 1968). Bell and Cooper coricluded that elwtroii energy in the discharge is a fuiiction of EoT/pTo,where Eo i j the amplitude of the electric field, p is the pressure, T is the temperature, and To 15 a reference temperature. Consequently, the rate of eq 2 would pass through a maximuiii as EoT/pTo varied.
Bell proposed that overall conversion is rate-limited by the initiating step, eq 2 . Thus, conversion would display a maximum as EoT/pTo varied. Cooper found that his experimental conversions were more or less independent of flow rate. Instead of a rate-limited model, he suggested that eq 2 would govern a steady state between creation and destruction processes which would depend only on Eo/p (the factor T/To was dropped) and not on flow rate a t high power. At low power, the supply of species was to be limiting. Neither investigator measured the parameters necessary to determine field strength or voltage across the plasma gas but rather made certain assumptions in order to estimate these variables. I n the present work, the effects of frequency and modulation were analyzed, and the values of plasma current and voltage were measured for a number of different reactor geometries and sizes.
are taken to be independent of e , eq 6 has the steady periodic solution
where
is that mean energy attained in a dc electric field of magnitude equal to the peak ac value and f$ =
E 'v € 0
The primary parameters governing the behavior of a n operating discharge under different circumstances have been treated by Brown (1956), Francis (1960a), and Margenau (1947). The latter has shown that for a class of conditions where attachment and recombination control the electron density in an isothermal discharge between parallel plates, the electronic energy distribution is a unique function of the similarity variables
where p' is the reduced pressure p T o / T ,d is the distance between plates, w is the frequency of the applied field, and J is the electronic current density. I n an operating discharge, only three of these similarity variables can be independent. Later, Rose and Brown (1955) showed that for a diffusion-controlled discharge in hydrogen J / p f 2rather than J / p ' is the proper variable. Thus, even under the idealized conditions treated above, theory does not indicate that the electron energy depends on E/p' alone as assumed in earlier studies of the HC1-02 reaction. Frequency and the current-like parameter (J/p' or J / p f 2 )also affect electronic energy. The explicit effect of frequency upon average electron energy was first investigated by Townsend (1932). The change in the mean energy of an electron, e , may be equated to the difference between the energy gained from the field, EO sin ut, in moving a distance dz and the energy lost by collisions with the gas molecules =
e(Eosin wt)dz
- KPB
where p is the electronic mobility. Substitution of ( 5 ) into (4) gives
The collision frequency P is proportional to p' and p to l / p ' . Under some conditions, v , K, and p also depend on e and the current density in a discharge. However, if these parameters
>>
l), 6 ap-
sin2 w t
(10)
KV
2w
with a small ripple of magnitude K P / 2 W . When K , V , and p are taken as functions of e , the solution ( 7 ) no longer is exact. However, a t low frequency, when K V / 2w is large compared to unity, the terms on the right-hand side of (6) must balance each other for a periodic solution. Then the approximation (10) applies, providing that eo is taken to be a function of E ; that is
This may be solved explicitly for E . At high frequency, when K P / 2 W P and w >> K P , the voltage needed for a given power is high and the mean electron energy remains constant in time. The electrons oscillate out of phase with the field and undergo practically no collisions with the gas during a period 2 ~ / w .At a lower frequency we may have w < P but still w >> K P so that electrons undergo frequent collisions and move nearly in phase with the field; but the energy loss rate hu is still sufficiently low compared to the field frequency so that the energy does not relax (eq 11). Cooper's experiments a t 2450 N H z were conducted in this regime. Table I compares values of the parameters K Y / W and u / w a t low current density for 2450, 20, and 6 MHz, It is evident that in the present work a t 6 1 I H z and that of Bell (20 N H z ) the electron energy should oscillate 100%. Ind. Eng. Chem. Fundam., Vol. 12,
No. 3, 1973
277
;-L-; I
D
tD /CX+i IEACTOB CI c3
3
1(.
L
30
7.0
50
9.0
D WALC 1.2 .I3 0.9 . I O
25% OF MORE LONG
I
I
W L L THICK
PI
1.66
3.83
D. 3.3
PZ
090
4.10
3.5
,165
.z
P3
1.96
7.0
.33
.2
PM
1.66
1.0
,165
2
H
REACTOR
D
aoo 3.83
TOP S I D E ,165 2
REACTOR C X
(ALL DIMENSIONS I N CW)
(ALL IDNI M CE MN S I C dI
CYLINDRICAL REACTORS
PILLBOX REACTORS
Figure 1 . Discharge reactors
Table
I.
KV/W
Emeleus and Lunt (1936) formulated an expression for the rate of chemical reaction in a cold cathode glow discharge. The rate of a specific chemical reaction process is given by
a n d V / W at Different Frequencies in Pure HCb
Frequency,
MHz
h e n r collisions/cm3-see
VfW
KYfW
57 1.9 x 20 16 5 5 x 2450 0.13 4.5 x a E / p ‘ is 10 V/cm-Torr and p ’ is 10 Torr. These based on data from Healey and Reed (1941). 6
(17)
108 102 100 values are
where S is the rate coefficient of any specified electron-reactant collision and ne and n, are the respective concentrations of electrons and reactants. S is given by
If the stationary concentration of excited collision products is negligible compared with that of gas molecules in the ground state, electronic energy is determined by collision or reaction of electrons with the latter. Small concentrations of excited species will occur in the limit of small discharge currents. Thus, for sufficiently low current, Y ( E ) , K ( E ) , and p ( ~ )will not depend on the current-like variable of eq 3. If, furthermore, K V / 2 W is small enough for the temporal variation of electronic energy to be negligible, eq 11 becomes
where & ( e ) is the reaction cross section for the electrons of energy e, f is the energy distribution function, and K is a numerical factor, in the low current limit under conditions when both the mean electron energy i and f(e) are functions of &/p’ alone. Under other conditions S will depend additionally upon current and gas temperature.
-
when the dependence of l/p‘ and Y p’ let p(e) =
p,
Y,
and
P(e)/p’;
Y
on E is retained. Since p
Y(€)
=
;(E)$
-
(15)
so that
and then the energy E will indeed be a function of Eo/p’ alone. Lunt and Meek (1936a,b) as well as others (Corrigan and von Engel, 1958) have shown that in this special case of limiting current the fractional power input into each sort of excitation process in a discharge is also a function of Eo/p’ alone. 278
Ind. Eng. Chem. Fundam., Vol. 12, No.
3, 1973
Apparatus and Procedure
The range of parameters in the present investigation was selected to overlap as well as to greatly extend the range of the earlier work. Eight different reactor geometries and a wide range of pressures (11-160 Torr), power (10-700 W), and flow rates (50-400 em3 (STP)/min) were used. I n addition to quartz tube reactors with external sleeve electrodes such as used in earlier work (without any electrodes in the work of Cooper), parallel electrode “pillbox” reactors were used in order to obtain a more nearly homogeneous plasma. The reactors used are shown in Figure 1. I n the series P I , P2 and P3 the aspect ratio D / H was varied. PA1 was physically the same cell as P I , but the electrode diameter De and consequent discharge cross section was cut to one-third of the reactor diameter to determine what effects this would have on conversion. Tracer experiments with NO2 and a calculation of the Peclet number (about 2.5 for HC1 in P1 a t room temperature) indicated that mixing in the pillbox reactors
CWIAL
e
Coli
REP RENEE VAC.
b. Electronic Scheme
a, Gas Feed
TO UVAM cP
SHUT-OFF
STOPCOCK
ME& !! WNOMETEV
EXCHAHCER REACTOR COOLING
IN
bTopcOcK 1 & E TO PRESSURE
ROlAMElER
CONTROLLER SAMPLE
TRAP
PUMP VAC.
W
c. Sample Collection Figure
W
M
P
d, Calorimeter 2. Experimental apparatus
would be good, even in the absence of the thermal and electrical forces present in a n active discharge. Reactor CX was used to determine the composition of products formed from the central plasma of a cylindrical reactor. The experimental apparatus is shown in Figure 2. Standard purity commercial compressed tank gas flowed through individual rotameters a t a pressure of 6 psig. These gases were mixed and then throttled to the reactor operating pressure. Pressure was measured simultaneously with a bourdon-type gauge aiid a mercury manometer. Gas feed entered the quartz reactor which, in turn, was eiiclosed in a flow calorimeter. The calorimeter cooled the reactor and also gave a measurement of power. Silicone oil was used as the coolaiit. Effluent gases from the reactor were frozen in a liquid nitrogen-cooled trap and the condensate was analyzed by iodide titration of the chlorine and subsequent neutralization of HCl. Low voltage power from a 6-NHz oscillator &-as coupled through a coaxial line into a high Q, high impedance helical resonator (Westman, 1956). Because of this high Q, the resonator can develop very high voltages with negligible internal power loss. Thus, the net power fed through the cable, as monitored by a directional wattmeter, was taken as the power input to the discharge. This was confirmed by independent measurements with the flow calorimeter. The peak-to-peak voltage applied t o the “hot” reactor electrode was monitored on both a capacitive divider-VTVlI combination and a vacuum diode circuit. An RF thermocouple ammeter indicated R l I S current through the discharge a i d shunt capacitances, while peak current was simultaneously read as the voltage drop across a 50-ohm coaxial resistor in the ground lead. The voltage waveform was monitored with a small pickup capacitor connected to an oscilloscope. The temperature a t various stations in the reactors was investigated with a quartz-sheathed thermocouple.
i, cw RP
Figure 3. Discharge circuit model. The impedance z and voltage source V represent the RF generator
Computation of Plasma Current and Voltage. Under t h e present conditions (Ejp’ between 0.05 and 500 V/Torr-em) Y >> W . Actual values of Y can be estimated from the drift velocity using the formula (Francis, 1960b)
and tabulated data of b’d for the gases in question (EIealey aiid Reed, 1941). The upper limit for the electron deiisitj iii a “cold” plasma is about 10l2.When the calculated Y and present discharge parameters are inserted into the formulas of Everhart and Brown (1949), it 1.5 fourid that the imaginary part of the plasma conductivity n-ill be negligible for ne to and beyond this limit. I n order to determine the actual voltage across the plasma gas from total voltage and current measurements, the d13charge was modeled by the circuit 111 Figure 3. c s h representi the combined shunt capacitance of the lead5 aiid electrodes around the plasma, C, is the capacitance betneen the electrodes aiid discharge gas, and R, 16 the plasma impedaiice I\hich, as shown abo\ e, should be entirely resi5tir e. C q h was measured in the absence of a dlschaige; R, arid C, were then Ind. Eng. Chem. Fundam., Vol. 12. No. 3, 1973
279
60
.
-
t
II
A
22
: %I 44 0
-1
e
g50-
0
t
-
100 Iao
50 I00 20 0 40 0 100
44
160 160
-
400
8
-
z
0
t
z40-
K
w >
z
-*
0
~-.2"2.6L.:.--2''Ln
&,
-_,_
v30-
c
--0-
z
- - -@-c-
&.........., o t -
- m-la
w
V
a
l a .
-
,-.e0
e
0-
0
'b
e .
f 20-
-
c
9
OO
I 100
I
I
100
200
I 300
I
I
I
200
300
400
I
POWER ( W A T T S )
Figure 5. The effects of pressure and flow on conversion vs. power in PM. The points are for PM at: 0,50 cm3 (STP)/min, 11 Torr; 0, 100 cm3 (STP)/min, 1 1 Torr; A, 100 cm3 (STP)/ min, 22 Torr. The lines present P1 data from Figure 4 for -, 50 cm3 (STP)/min, 11 Torr; comparison: (100 cm3 (STP)/min, 1 1 Torr; 100 cm3 (STP)/ min, 100 Torr
----
. . . . . . . . . . .,
-,
calculated from the combined total voltage, power, and current data. Results
Voltages across the plasma gas remained fairly constant, insensitive to power and flow for a fixed pressure in each of the reactors used. The thermocouple temperatures in the discharges ranged from 400 to more than 1300°C. Under all conditions they increased rapidly with pressure a t constant power and with power at constant pressure. This is taken to indicate a similar trend in the gas temperature. Thus, the average value of Eo/p' should likewise increase with power because of its linear variation with temperature. 280
Ind. Eng. Chem. Fundam., Vol. 12, No. 3, 1973
I
I
I
400
500
600
-
I n the pillbox reactors, conversion generally increased to a n asymptotic value as power was raised (see Figure 4). Such an asymptotic conversion in the face of increasing E/p' indicates that E/p' does not control conversion. Furthermore, in no case here is the maximum, which was taken by previous investigators to characterize control by E/p' through the dissociative attachment process, observed. Figure 5 compares conversion in PM with that of PI. PM was not run at very high pressures or powers because the electrode spot appeared to become excessively hot (as evidenced by intense boiling of the silicone coolant). Figures 6, 7, and 8 show that conversion maxima were reproduced in the present work, but only in certain of the cylindrical reactors and, in all b u t reactor C3, only at 11 Torr. It is remarkable that conversions in CM were unlike those in C1 inasmuch as the reactors differed only in the size of exit arms downstream and out of the discharge zone. Reactor CX was dimensionally similar to C1 and C l I , but different in that gas entered and left in cross flow perpendicular to the axial direction of the discharge; its conversion curves bori a resemblance to those in the pillbox reactors rather than those of the other cylindrical reactors. Under most conditions the discharge was composed of two regions, a bright central core and a n outside sheath. Constriction of the central core increased with pressure at constant power but decreased with power a t constant pressure. A t high power the plasma core occupied most of the crosssectional area near the electrode surface of each reactor. The capacitance between the electrodes and plasma, as calculated from the model of Figure 3, was plotted against power. It increased with power to an asymptotic value that in each case gave good agreement with the geometrical capacitance calculated for the full electrode areas. Discussion
Figure 6 compares the present data for 12-mm reactors a t 11 Torr with those of Bell and Cooper under similar condi-
‘i
0 BMHZ C W 0 PO MHZ MOD. 0 2 0 M H Z MOD.
b-
6 2450 M H Z CW
A A
2 4 5 0 M H Z Cw 2450 MHZ C w 0 SMHZCW 0 BMHZ CW
I
I
100
ZOO
I NO
I
400
POWER (WATTS)
F IOOCC-STP/MIN F 100 CC-STWMIN F = 7 0 CC-STPMIN
= F = 390CC-STP/MIN F = 780CC-STP/MIN
BELL
BELL COOPER COOPER COOPER 6MM ARMS BMMARMS
F = 23OCC-STP/MIN
F F
= IOOCC-STP/MIN = 5OCC-STP/MIN I
I
500
600
I
700
CONVERSION I N I P M M TUBEAT I I TORR AND VARIOUS CONDITIONS ( COOPER POINTS AT IO TORR 1
Figure 6. Conversion in 12-mm tubes at 1 1 Torr and various conditions (Cooper points are a t 10 Torr). The line joins points for reactor CM. Bell’s data with the notation “MOD“ are for a modulated power source (see text)
1
‘“t Figure 7. Conversion vs. power for cylindrical reactors at 1 1 Torr. The flow rate is 100 cm3 (STP)/min
tioris. I11 spite of differences in flow rate, applied frequency, and the presence or absence of 120 Hz modulation, most of these conversion data agree; data points for the tubular reactor with small arms, CAI, are the exception. This agreement would not be expected if E/p’ controlled conversion in the discharge. -It all three frequencies ( u / v j 2 > wa, the change in sin w,t will be negligible over a period of the RF carrier, 2r/w. The average value of k for a period of the radiofrequency signal when 7
5t 5
7
-I-2 r / w
(28)
is very nearly 2n/w
kRF,av
282
=
k(e0
sin2 ut sin2 Wa7)dt
Ind. Eng. Chem. Fundam., Vol. 12, No. 3, 1973
F
over , ~ a~ period of sin
(29)
gives
Now for a particular value of T, the interior integral is identical in form with kaV(eo) in eq 24. Thus, the maximum value of kaudio,av must be less than the maximum of kav(e) in eq 24 since, in the presence of modulation, the interior integral can remain at any particular value (such as its maximum value) only a fraction of each period 2r/wa. For a given field distribution, power is proportional to the square of the average field power = CE2
(31)
where C is a constant of proportionality. For a radiofrequency field
E
=
Eo sin wt
the average power over a period is
CEO2 sin2 w t dt
=
CEO2 2 ~
(32)
while for a modulated signal
E
EO sin2 ut sin2 w,t]dt
R
(30)
zR/Ws
k s u d i o , av
~
(26)
where w is the frequency of the RF carrier and wa is the audio modulation frequency. A t low frequency ( K Y / W >> l ) , the average rate for this waveform may be written as
1
and the average of kaudio,sv
=
Eo sin wt sin w,t
(33)
the average power (Gray, 1954) will be
S,
2ir,/wa
power =
2 2T
Eo2sin2 w t sin2 wat dt
CEO’
= __
4
(34)
This indicates that a t constant power, the peak value of Eo/p’ in the presence of two-tone modulation should be .\/z times the peak obtained in the absence of modulation. The waveform must rise to a higher peak value with modulation in order to compensate for the longer time i t spends a t low values. Consequently, if k(e[Eo/p’,t])is a sensitive function
of Eo/p’, the mean value of k will generally change due to modulation. The above analyses can also be applied to the more general assumption that conversion exhibits a marked maximum as a function of electron energy. Conversion(€) is substituted for k ( t ) and the conclusions follow as before. Experimental data in Figure 6 show that the application of audio modulation in fact has no discernible effect on conversion. The data shown with modulation are due to Bell whose power source always was modulated 1 0 0 ~ oby a 120Hz two-tone note. Similar values were reproduced in the present investigation An electrical explanation of conversion also cannot account for the observed differences between C1 and C1I. The physical and electrical characteristics of CM were in every way identical with reactor C1; only the connecting arms outside of the discharge zone were different (12 mm for C1 and 6 mm in the case of CM). T h e results from the pillbox reactors can be taken in a similar vein. The data from reactor P1 in Figure 4 are typical. Conversion generally increased to an asymptotic value as power was raised, while E/p’ continuously increased with power. In no case was a maximum, which was supposed to characterize control by E/p’ through the dissociative attachment process, observed. Thermal Control. A number of observations strongly suggest that at high power conversion is regulated by temperature. These are (1) comparison of the conversion curves for reactors C1 and C3, ( 2 ) the fact that modulated voltage waveforms produced the same conversions as CW voltage waveforms a t constant power input, and ( 3 ) data consistent with the hypothesis that the observed product mix is described by a quench of molecular species that terminates in a state close to high-temperature thermal equilibrium. At low discharge powers or high flow rates the supply of active species should be limiting; this accounts for the observed rise in conversion with increasing power and decreasing flow rates near the origin of Figures 4-8. The conversion curves for C3 are similar in form to those of C1, but appear to be displaced toward low powers (see Figures 7 and 8). Now the temperature-power characteristic of C3 also must have been shifted toward low powers because of its greater power density a t each power level. This is supported by the experimental observation that in this reactor alone, the walls inside the electrode region glowed white at high power levels. It may be added that the electrical characteristics of C3 were nearly identical with those of C1 and CM. Cooper showed that if one of the reactants were put through the discharge arid the second added downstream, a reaction would still take place. Consequently, the observed yields may reflect the details of downstream quench as well as the compositions of gases emerging from the region of active discharge. The data taken in the pillbox reactors indicate that a t each pressure (for the high-poiver asymptotic regime), the final product composition is insensitive to power and flow rate. This could occur either because the gas emerging from the discharge has a nearly constant composition or because the state to which the products quench (at given pressure and geometry) is insensitive to power and the initial temperature of species leaving the discharge core. We favor the latter evplanation because: (1) the data for reactor PIlI agree with those for reactor P1 in spite of differences both in discharge core size and power density; ( 2 ) the
conversions for the Cl-CM electrode geometry are sensitive to reactor shape outside of the region of active discharge; and (3) Cooper (1966) found that conversion was altered by a nitrogen quench and was a function of its location downstream of the active discharge region. Other information suggests that the product composition may be determined b y thermodynamic equilibrium. It is possible that a t low flow rates and high powers the molecular species remain close to the thermodynamic equilibrium for eq 1 as they leave the discharge, move downstream, and finally quench. More precisely, as t’he gas flows downstream the active species supplied b y the discharge could act as a catalyst to carry the thermodynamically favorable reaction I, while the active species themselves need not be in equilibrium. The data from experiments using nonstoichiometric HCl0 2 mixtures in P I are consistent with the above proposition. The partial pressure products for these mixtures in the high power asymptotic conversion regime gave fair agreement with those values obtained using stoichiometric mixtures a t similar levels of power pressure (Flamm, 1969). Bell reported similar data that appeared to follow the law of mass action. Data on the reverse reaction
2C12
+ 2H20
=
4HC1
+
0 2
(35)
appearing in Bell’s work provide additional evidence. A t sufficiently high pressure and low flows the forward and reverse reaction approached a common limit. Bell observed that for alterations in pressure this limit changed in a direction again consistent with the law of mass action. He also associated a simultaneous rise in temperature with the observed decrease in conversion a t const’aiit’povier. However, Bell suggested a multivariate equilibrium as the proper explanation for this behavior (see beloit-). Cooper’s data for a nitrogen quench introduced downstream of the discharge region also are consistent with this view. Conversion a t 20 Torr and 200 W decreased from 50% with no quench to 44Yo as the nitrogen quench was brought closer to the active discharge region. The decline in conversion in going from reactor C1 to CAI can also be explained with this picture: when gases flow into the narrow exit arm on C I I the quench will be augmented by more diffusive flux of active species to the walls. This may complete bhe quench a t a higher temperature which, under the equilibrium hypothesis, mould exhibit lower conversions. I n the present pillbox reactors an increase in power or pressure always produced a coincident increase in temperature. Here again it is plausible bhat the faster collisional relaxation of active species with greater pressures gives rise to a more rapid quench that outweighs competing fact’ors. Then, any relaxation of product distribution from conditiolis existing in the active discharge region should terminate a t a temperature that increases with pressure-because both temperature and quench rate simultaneously increase with pressure. I n general then, discharge temperature is not expected to equal the equilibrium temperatures calculated from conrersion data. At low power, when conversion is limited by the number of active species present, the yields will correspond to an equilibrium temperature higher than that in the discharge. .It high powers, on the other hand, the continuing react,ion during quench of the esit gases will give a product mix corresponding t o temperatures below those in the discharge. L-nfortunately, the present data do not permit the indicated comparison between actual yields and equilibria a t the Ind. Eng. Chem. Fundom., Vol. 12, No. 3, 1973
283
loo0
c
I
I
I.
7
\
I
I
100
I
/
00’
0
I
I
I
300
200
I
400
I
POWER, CWATTS)
Figure 9. Comparison of measured temperatures (a, 0, I:, I) with equilibrium temperatures calculated from composition ( 0 , m) in reactor P l . Circles are a t 1 1 Torr, squares a t 22 Torr. 0,a are for probe location A just outside of the discharge region. a, 11 were taken a t location B in the downstream arm
temperatures in and downstream of the discharge. An energy balance shows that most of t’he input’ power is lost from the discharge as nonequilibrium radiation and this radiat’ion impinges on the temperature probe. If the radiation were isotropic, the difference betn-een the gas and thermocouple temperatures should be on the order of several hundred degrees. Equilibrium temperatures calculated from t’he asymptotic yields do lie within this band near the measured temperatures. Typical values of these temperatures for P1 are compared in Figure 9. The radiation appears to be produced by vibrational relasation of excited HCI. Dell (1967) presented evidence that t’his was the case while Firidlay and Polanyi (1964) have found that more than 10% of the heat of reaction of hydrogen atoms with chlorine niag go direct,ly iiito vibration. This reaction is fast and is probably important in the present system. Calculations indicate st’imulated emission is a primary mechanism for vibrational relaxation. The Einstein coefficients for spontaneous emission, A , and stimulated emission, B , are (Benedict, et al., 1957; Bourgin, 1926) -101 N
40 5ec-I; Bo]N 7 X loz6Hz-cm”erg-sec
(36)
for the first lines of the P or R branches in pure HCl. As an estimate, the line width will be taken to be 0.25 em-’ atm-I (Benedict, et al., 1957) and the entire discharge energy assumed to be emitted in this line. Assuming isotropic radiation and 200 W a t 10 Torr in P I , the energy density thus calculated is pv N
1 . 5 x lo-” ergIHz-cm3
(37)
and then Bp, 1 :1 . O
x
104 sec-l
(38)
This compares ivit,h a collisional relaxation rate of 1.5 X l o 4 284
Ind. Eng. Chem. Fundam., Vol. 12, No. 3, 1973
to 0.033 X lo4 see-I at 10 Torr and lOOOOK (Bowman and Seery, 1969; Breshears and Bird, 1969). The increase of temperature with pressure then must in part be due to increasing collisional deactivation of the vibrationally excited HCI. The occurrence of maxima in C1, CM, and C3 still remains to be explained. Pressure gradients and compressibility effects were negligible. Since the forms of the curves were different in the electrically similar reactors C l l , C1, and CX, reactor geometry may effect a more rapid increase of temperature with power in the electrode regions of the cylindrical reactors than in the pillbox and cross-flow reactor cores. Multivariate Equilibrium. Potapov (1966) suggested that the products of reaction in a discharge may sometimes be described by a multivariate “equilibrium constant” determined from a set of partition functions in which each degree of freedom is characterized by a distinct temperature. I n one of the earlier investigations (Bell, 1967) i t was theorized that conversions were generally in excess of thermodynamic equilibrium. Cnder certain conditions the yield approached a steady-state value which, as mentioned above, appeared to obey the law of mass action. It was thought that a multivariate equilibrium, with high temperature in internal degrees of freedom due to the energetic free electrons, might provide a proper explanation for this behavior. However, it appears that for the present reaction an internal temperature above that of the gas would actually produce a lower conversion. For a uniform internal temperature T i n t and gas translational temperature T,,Potapov’s theory gives
where pi are the partial pressures, v i the stoichiometric coefficients, and zZ(Tint)are the partition functions for internal degrees of freedom. When Tint equals T,, eq 39 reduces to the usual equilibrium expression. For the present reaction Yt
=
-4 - 1
z
+2 +2
=
-1
(40)
so that there is a power dependence on T , from the last two factors in eq 39. Since the true thermodynamic equilibrium constant decreases faster than the - 10th power of temperature (Dow, 1960) an increase in Tlnt must product a decrease in the right-hand side of eq 39. Mechanism. L-nder t h e present discharge conditions, free charge is destroyed principally by the volume recombination of positive and negative ions rather than by other competing processes such as diffusion, recombination of electrons with positive ions, or radiative processes (Flamm, 1969). Electrons are formed by ionization due to fast electrons; dissociative recombination of negative ions with atoms appears to be a much slower process with present estimates of species concentrations. The newly formed electrons are rapidly converted into negative ions by the dissociative attachment reaction discussed by Bell and Cooper
e
+ HC1 = H + C1-
(41)
These ions may be clustered and react with HCI to form HCl2- (Dickson, et al., 1967) before their usual fate, recombination. It appears unlikely that hydrogen atoms from a discharge in pure HCI would react with O2 added downstream via the reaction
H+0
2
+ 11 = HO? + 11
(42)
Table II. Comparative Rates of Eq 24 M = Hz) and Eq 25. 500’K
2 3 X lo-” 5 5X
liH+CI2 (cm4/molecule*sec) kH+O,+M (cm3jmolecule-sec)
T, T,
(for
= electron temperature,
Tint
TO 1 1 OO’K
ud
1 5 X 10-l0 11 X
kH+02+\r as given by Thrush (1965);it has an efficiency relative to H Pof 0.36 for 11 = 0 2 and 7.0 for lI = HQO.Rates for eq 26 are calculated from k ~ 1 + ~(Trotman-Dickenson % and X l n e , 1967), ~ C . + E C I / ~ H + C I ? (Davidson and ilrmstrong, 1968), and equilibrium data from Dow (1960).
VD 2%
= HC1
+ C1
electronic energy, J peak electronic energy epEo*,K Y , J electronic mobility, m2/V-sec = fraction of energy lost per electron-molecule collision = collision frequency for electrons, sec-] = stoichiometric coefficient for the ith species = electromagnetic energy density, ergs/Hz-cm3 = radian frequency of the applied field, see-1 = radian frequency of audio modulation, see-’
EO
I.1
vi
Pu W
(43)
is much faster under the present range of conditions (see Table 11).Thus, hydrogen atoms would consume the product faster than the supposed reactant so that negligible chlorine would form. The slower reaction
H
+ HC1
=
H2
+ C1
(44)
will also lead to the formation of‘ chlorine atoms. These atoms may then react directly with oxygen. Conclusions
A n analysis of voltage, pressure, current, and temperature data does not confirm the conclusion of previous investigators that Ejp’ controls the reaction; the present results suggest that conversions a t high discharge powers are controlled by thermal equilibrium. At lower power, the reaction is ratelimited by the supply of active species. Nomenclature
A
B d
D D,
J li li
t
first Einstein coefficient, sec-’ second Einstein coefficient, Hz-cm*,’erg-see = widt’hof discharge gap, m = diameter of pillbox reactor, em = Diameter of pillbox reactor electrode, cm = electronic charge, C = peak electric field, T’I m = electronic energy distribution function = Free energy of reaction. kcallmole = Planck’s constant, erg-see = overall height of pillbox reactor, em = current density, h i m 2 = Boltzmana constant, erg,j°K = rate constant, cm6,/molecule2-sec, cm3, moleculesec = average rate constant without modulation = average rate constant with audio modulation = average rate constant’ during a period of the RF carrier = electronic mass, kg = molecular mass of the i t h species, g = number density of electrons, emp3 = number density of reactant molecules, = pressure, Torr = partial pressure of the i t h species, dynes/cniZ = reference pressure, Torr = pT01T , the reduced pressure, Torr = input power to electrons, \T,:cn13 = reaction cross section, m2 = rate coefficient for electron-reactant collisions, cm3/molecule-sec = time, sec =
=
K
= = =
E
Y
H + Clz
OK
translational gas temperature, OK temperature for internal degrees of freedom, O reference temperature, OK drift velocity for electrons] m/sec peak voltage, V internal partition function for the i t h species
GREEKLETTERS
K
proposed by Cooper, et al., (1968) since
= = = = = =
Wa
Literature Cited
American Cheniical Society, Adaan. Chcm. Ser. No. 21, 286 (1959). Bell, A. T., Sc.D. Thesis, Xassachusetts Institute of Technology, Cambridge, Mass., 1967. Benedict, J. G., Herman, R.,Moore, G. E., J . Chem. Phys. 26, 1671 (1957). Blaustein, B. D., FLI,Y. C., Advan. Chenz. Ser. No. 80, 269 (1969). Bourgin, D. G., Phys. R C V29, . 794 (1926). Bowman, C. T., Seery, D. J., J . Chem. Phys. 50, 904 (1969). Breshears, W. D., Bird, P. F., J . Chem. Phys. 50, 333 (1969). Bronfin, B. R., Adcan. Chem. Ser. No. 80, 423 (1969). Brown, S. C., “Handbuch der Physik,” 5’01. 2Zj pp 531-576, Springer-Verlag, Berlin, 1956. Christophorou, L. G., Stockdale, J. A . D., J . Chem. Phys., 48, 1956 (1968). Cooper, W. IT., Sc.D. Thesis, Massachusetts Injtitute of Technology, Cambridge, ?\[ass., 1966. Cooper, W. IT., Mckley, H. S., Baddour, R. F., IND.ESG. CHEX, FUSDAU.7 , 400 (1968). Corrigan, S. J. B., von Engel, A,, Proc. Phys. Soc. London 72, 786 (1958). Davidson, 1%.S., Armstrong, D. A,, J . Chem. Phys. 48, 1235 (1968). Dickson, H. W.,Christophorou, L. G., Compton, R. ?J., Oak Ridge Xational Lab. Report ORSL-TlI-1724 (1967). Dow Chemical Co., “Janaf Thermochemical Tables,” llidland, Mich., 1960. Emeleus, K. G., Lunt, R. IT,,Trans. Faradau Soc. 32, 1504 (1936). Everhart, K. G., Brown, S.C., Phys. Rer. 7 6 , 839 (1949). Findlay, F. D., Polanyi, J. C., Can. J . Chem. 42, 2176 (1964j. sachiisetts Institute of TechFlanini, D. L., Sc.D. nology, Cambridge, Francis, G., “Ionization Phenomenon in Gases,!’ p 59, Academic Press, Sew- York, K.Y., 1960s. Francis, G., “Ionization Phenomenon in Gases,” pp 8.7-89 ;Icadeniic Press, Xew York, S . Y., 1960b. Gladish, T. S.,Hgdrocarban Process. Petrol. Rejincr 41, (6), 1.59 11962).
Gray, T. S.,“Applied Electronics,” p 703, l I I T Press, Cambridge, lIaas., 1954. Harries,’W.L., von Engel, A, Proc. Roy. Soc., Ser. -4 222, 490 (1954).
Healey, 11. H., Reed, J. W.,“The Behavior of S l o Electrons ~ in Gases,” Amalgamated Wireless Ltd., Sydney, 1941. Janev, 11. K., “Dissociative dttachrnent of Electrons to 02 Molecules and Temperatiire Dependence of the Cross-Section,“ Proceedings of the 8th International Conference 01 Ionized Gases, p 21, \.ienna, 1967. Kana’an, A . P.,lIargrave, J. L., “Advanres i n Inorganic Chemistry,” T’ol. 6, p 143, Academic Press, Yew I-ork, S . Y.!1964. Lewis, G. S . ,J . A n i e r . Chem. Soc. 28, 1380 (1906). Lunt, 11. W.,IIeek, C. h.,PTOC.Bo!/. Soc., Sw. A . 156, :194 (1936a). Lunt, 11. W., lleek, C. A,, Proc. Roy. SOC.,Scr. A 157, 146 (1936b). Mal’tsev, A. S . ,Eremin, E. N.,Vorob’eva, I. S . ,Russ. J . Phys. Chem. 33,79 (1959). llargenau, H., I’hys. Reo!.73, 326 (1947). Ind. Eng, Chem. Fundom., Vol. 12, No. 3, 1973
285
McTaggart, F. K., “Plasma Chemistry in Electrical Discharges,” Elsevier Publishing Co., Amsterdam, 1967. Mellor, J. W., “Alellor’s Comprehensive Treatise on Inorganic and Theoretical Chemistry,” Vol. 8, p 367, Longmans, Green & Co., London, 1940. Potapov, A. V., High Temperature,4,48,(1966). Rose, D. J., Brown, S. C., Phys. Rev. 98, 310 (1955). Thrush, B. A,, Progr. React. Kinet. 3, 1 (1965). Timmins, R. S., Ammann, P. R., “The Application of Plasmas to Chemical Processing,” Chapter 7, p 99, R. F. Baddour and R. S. Timmins Ed., AIIT Press, Cambridge, Mass., 1967. Townsend, J. S., Phil. Mag. 13,745 (1932).
Trotmsn-Dickenson, A. F., Milne, G. S., “Tables of Bimolecular Gas Reactions,” U. S. Printing Office, Washington, D. C., 1967.
Wechsberg, H. E., Webber, J. E., Mod. Plast. 36, 101 (1959). Westman, H. P., Ed., “Reference Data for Radio Engineers,” 4th ed, pp 600-603, IT&T, New York, N. Y., 1956. RECEIVED for review March 29, 1972 ACCEPTEDApril 12, 1973 This work was supported by a grant from the National Science Foundation.
Comments on Transition from Laminar to Turbulent Flow H. Dennis Spriggs @’est Virginia College of Graduate Studies, Institute, W . Va. 26112
Observations have been made concerning various aspects of transition to turbulence in single-phase and two-phase flow. For single-phase flow, a simple model i s proposed which allows calculation of the friction factor in the transition regime. This result is, in turn, used to interpret the point of transition. For two-phase flow, Hanks’ stability criterion i s used in an attempt to predict transition. It i s shown that this criterion fails and that stabilizing forces are operative which postpone transition in such systems.
I t is a well established fact that transition from laminar to turbulent flow is not a n abrupt phenomenon. Rather, as flow rates are increased, the fluid passes from a stable, rectilinear, or laminar state through various intermediate regimes and finally into a turbulent state (Seneca1 and Rothfus, 1953). True laminar flow exists for Reynolds numbers up to about 1000 (for circular pipes). -1bove 1000 a stable or laminar sinuous motion begins which grows in amplitude as flow rates are increased to a Reynolds number of about 2000. I n the range extending approximately from 2000 to 3000 transition between the various laminar states and various turbulent 5tates occurs. The transition regime is characterized by a n intermittent series of laminar and turbulent patches whose appearance marks the point of departure from the usual laminar flow relationships. Turbulent flow relationships are not valid until the end of the transition regime and even then these relationships vary v ith increasing flow indicating a change in the nature of the turbulent flow. For purposes of simplification i t is often convenient to characterize this complex progression of flow regimes as being merely from laminar to transition to turbulent, ignoring the more subtle changes in the flow. Whereas methods exist for deriving relationships such as those for friction factors for both laminar and turbulent flow, the transition regime has proven to be more elusive. Friction Factor in Transition Regime
-1quantity called the intermittency factor defined as the fraction of time the flow is turbulent is one convenient char286 Ind.
Eng. Chem. Fundam., Vol.
12, NO. 3, 1973
acterization of the transition regime. It has been found that a probability plot of the intermittency factor vs. Reynolds number yields a straight line; Le., there is a normal distribution (Spriggs, 1968; Stellmach 1967). Construction of a simple model of transition is possible by visualizing this regime as being just a combination of laminar flow and turbulent flow. The intermittency factor is used as a weighting factor. For example, the friction factor for transition would be (for circular pipes)
s = (lin,> - ( l - - Y ) + ( s ) Y where y is the intermittency factor. To test this model, it would be desirable to have friction factor and intermittency factor data from the same system, say for flow in circular pipes. Rotta has measured the intermittency factor for flow in pipes using a hot wire anemometer (Rotta, 1956; Schlichting, 1968). He found that this quantity is dependent upon both the radial and axial positions in the pipe as well as the Reynolds number
r X
Y = Y
(5’0,
For example, see the data in Table I. These observations suggest two problems regarding the direct application of intermittency factor data to eq 1.
