literature Cited
Amer, H. H., Paxton, R. R., van Winkle, M., Znd. Eng. Chem. Data Ser. 3, 224 (1956). Baitinper., W. F.. - Schlever. P. von R.. Murtv. T. S. S. R.. Robinson,-L., Tetrahbdron 26, 1635 (1964).’ Ballard, L. H., van Winkle, M., Ind. Eng. Chem. 44,208 (1952). Barker, J. A., J.Chem. Phys. 20, 1526 (1952). Bellamy, L. J., Hallam, H. E., Williams, R. L., Trans. Faraday SOC.54, 1120 (1958). Bittrich, H. J., Fleischer, W., J.Prakt. Chem. 4, 151 (1963). Black. C.. Derr. E. L.. Pauadououlos. M. N.. 2nd. Enp. Chem. 55. No: 8, 40, NO. 9, 38’(1963). Brandmuller, J., Seevogel, K., Spectrochim. Acta 20, 453 (1964). Burke, D. E., Williams, G. C., Plank, C. A., J . Chem. Eng. Data 9, 212 (1964). Cole, A. R. H., Little, L. H., Michell, A. J., Spectrochim. Acta 21, 1169 (1965). Copp, J. L., Everett, D. H., Discussions Faraday Sac. 15, 174 (1953). 56, 13 (1960). Copp, J. L., Findlay, T. J. V., Trans. Faraday SOC. Finch, J. N., Lippincott, E. R., J . Phys. Chem. 61,894 (1957). Findlay, T. J. V., Kidman, A. D., Australian J . Chem. 18, 521 (1965). Flory, P. J., J . Chem. Phys. 10, 51 (1942). Gordy, W., J.Chem. Phys. 9,215 (1941). Gramstad, T., Acta Chim. Scand. 16, 807 (1962). Hildebrand, J. H., Scott, R. L., “Regular Solutions,” PrenticeHall, Englewood Cliffs, N. J., 1962. Hill, W. D., van Winkle, M., 2nd. Eng. Chem. 44, 205 (1952). Hipkin, H., Myers, H. S., Ind. Eng. Chem. 46,2524 (1954). Horsley, L. H., Advan. Chem. Ser., No. 6, 35 (1952, 1962). Krueger, P. J., Mettee, H. D., Can. J. Chem. 42, 288 (1964). Liddel, U., Becker, E. D., J.Chem. Phys. 25,173 (1956). Malesinski, W.,“Azeotropy and Other Theoretical Problems of Vapor-Liquid Equilibrium,” Interscience, New York, 1965. Mitra, S. S., J.Chem. Phys. 36, 3286 (1962). , I
~
-
Nagata, I., J . Chem. Eng. Data 7, 367 (1962). Nakanishi, K., Chem. Eng. ( J a p a n ) 10,1122 (1965). Nakanishi, K., Nakasato, K., Toba, R., Shirai, H., J . Chem. Eng. Data 12, 440 (1967a). Nakanishi, K., Shirai, H., Ichinose, S., Kyoto University, unuublished results. 1967b. Nakanishi, K., Sh&ai, H., Minamiyama, T., J . Chem. Eng. Data 12, 591 (1967r). Nakak h i , K., Shirai, H., Nakasato, K., J . Chem. Eng. Data 13, 181S (1968). Padg itt, F. L., Amis, E. S., Hughes, D. W., J. A m . Chem. Sac. 64, 122 . - 3 l (1942). Pierotti. G. J.. Deal. C. H., Derr, E. L., Ind. Enp. Chem. 51, 95 (1959). Pimentel, G. C., McClellan, A. L., “The Hydrogen Bond,” W. H. Freeman, San Francisco, Calif., 1960. Prigogine, I., Defay, R., “Chemical Thermodynamics,” Longmans Green, London, 1954. Privott, W. J., Paul, D. R., Jolls, K. R., Schoenborn, E. M., J.Chem. Eng. Data 11, 331 (1966). Redlich, O., Derr, E. L., Pierotti, G. J., J. A m . Chem. SOC. 81, 2283 (1959). Rius, A.; Otero, J. L., MaCarron,A., Chem. Eng. Sci. 10,105 (1959). Searles, S., Tamres, M., J.Am..Chem. SOC.73, 3704 (1951). Shirai, H., Nakanishi, K., Kagaku Kogaku ( J a p a n ) 29,180 (1965). Sweeny, R. F., Rose, A,, A . I . Ch. E. J.9, 390 (1963). Ungnade, H. E., Roberts, E. M., Kissinger, L. W.,J.Phys. Chem. 68.3225 (1964). Weimer, R’. F., ‘Prausnitz, J. M., Hydrocarbon Processing 44, 237 (1965). Wilson, G. M., Deal, C. H., IND.ENC.CHEM.FUNDAMENTALS 1, 20 (1962). Yoshimoto, T., Nippon Kagaku Zasshi 82,530 (1961). \ - . -
- I .
I
RECEIVED for review September 5, 1967 ACCEPTED February 19, 1968
REACTOR DESIGN AND CONTINUOUS SAMPLING CRITERIA FOR AN ULTRASONIC REACTION SCOTT FOGLER
Department of Chemical and Metallurgical Engineering, University of Michigan, Ann Arbor, Mich.
Ultrasonically induced cavitation can bring about increased rates in liquid-phase chemical reactions. If the variation in chemical yield is to remain at a minimum in an ultrasonic reaction, certain limits of the acoustic pressure must not be exceeded. If these limits are exceeded in some instances, the acoustic pressure will drop below the cavitation threshold and the reaction will cease. Design criteria for a continuous stirred tank reactor and batch reactor, along with the maximum sample size, are developed which meet the prescribed restrictions.
NE
of the usual techniques for obtaining rate data from a
0 chemical reaction is by sampling the reaction vessel con-
tents a t various time intervals after the reactants are mixed. By plotting the proper function of concentration against time, one can then determine the various reaction rate parameters for simple reactions. I n liquid-phase reactions where no ultrasonics are applied to the reacting species, the amount of sample withdrawn a t any time interval will not affect the remainder of the chemical reaction. However, when a n ultrasonic wave is applied to a chemical reaction or extraction, the amount of liquid sampled for concentration determination can have a
dramatic effect on the rate of a chemical reaction. This paper gives an approximate set of conditions under which continuous sampling of an ultrasonic reaction is permissible. These results are extended to continuous ultrasonic processing in the design consideration of a continuous stirred tank reactor
(CSTR) . Various investigators (Chen and Kalback, 1967; Ostroski and Stambaugh, 1950; Weissler et al., 1950) have applied ultrasonics to liquid-phase chemical reactions and withdrawn samples for titration continuously throughout the course of the reaction. Further search of recent literature on ultrasonic VOL. 7
NO. 3
AUGUST
1968
387
chemical reactions reveals that a number of other investigations show plots of concentration us. time. These latter authors appear to have sampled continuously, but they d o not state specifically if this was the case or whether each point represents an entire run. Unless certain criteria are met, the results obtained from a continuous sampling technique can lead to erroneous conclusions. Theory
Ultrasonic reaction systems will vary in vessel design and in type of ultrasonic generator used to apply the waves. I n general, most reaction vessels are vertical cylinders, and plane waves are radiated axially to the gas-liquid interface from a source a t the bottom of the vessel. T o keep the following method as applicable as possible to various generators and systems used in sonochemical research, we specify the electrical impedance circuitry or transducer areas to be such that the reference amplitude of the acoustic pressure, Po,is constant at the solid-liquid surface. The height of the reacting liquid above the transducer greatly affects the increased reaction rates brought about by the presence of the ultrasonic wave (Aerstin et aZ., 1967). Aerstin measured the yield of the carbon tetrachloride-water reaction as a function of the liquid height above the transducer surface. Upon decreasing the height, he found the yield first increased then alternately increased and decreased. The distance between the points of maximum yields was equal to one half the wavelength of the ultrasonic wave in the liquid. The distance between the minimum yields (which were essentially zero) was also equal to one half the wavelength. The mathematical analysis showed that the acoustic pressure varied in the same manner as the yield. The term “chemical yield” as used in this paper is defined as exactly that given by Aerstin and most other workers in sonochemistry-that is, milliequivalents of product per unit volume of solution. This variance of acoustic pressure with distance of the gas-liquid interface above the radiating surface, in turn, affects the cavitation intensity. Within a certain frequency range, the high temperatures and pressures developed in an ultrasonic cavitating liquid result in the observed accelerated reaction rates (Griffing and Sette, 1955; Jarmen, 1959; Park and Taylor, 1956; Sirotyuk, 1963). A thorough discussion and review of cavitation phenomenon and its effects are given by Flynn (1964). As the acoustic pressure increases, the cavitation intensity increases, provided that the Rayleigh or bubble collapse time is less than one half the period of ultrasonic oscillation. Variations in the acoustic pressure can produce variations in the chemical yield. Equally important is the fact that if the acoustic pressure is decreased to the, point where it drops below the cavitation threshold, cavitation ceases altogether and the chemical yield produced by ultrasonics is zero. The acoustic pressure as a function of liquid height for negligible attenuation (Aerstin et al., 1967) is
1
plpo = [(I
- a)’(1 - Cos 2kL)2 f (1 4-a2
+
+
(1 a)%Sin2 2kL]1/2 2a Cos 2kL)
(11 For perfect reflection a t the solid-liquid boundary, a = 1, the variation of acoustic pressure with liquid height is
Vb = rR2AL
The fractional volume of sample drawn, X,from the reaction volume is related to the decrease in height above the vessel, AL,by the expression (4) One now asks: For a set decrease in the acoustic pressure ratio, E, which will not affect the cavitation intensity significantly, what is the fraction of liquid we may sample? The change in height corresponding to a change in acoustic pressure is (5)
where S is the average rate of change of P/Po with L between L and ( L - AL). Combining Equations 4 and 5, the allowable fraction sampled before a set drop in acoustic pressure is e x c e e d e d - e g , 100 E %-is given by
x
388
l&EC FUNDAMENTALS
= e/SL
(6)
The amount of sample one may withdraw depends upon the wavelength and the distance between the gas-liquid interface and the transducer surface. Since S is a function of AL and X,Equation 6 must be solved by an iterative technique on the digital computer. Convergence was usually achieved within 10 iterations. Equation 4 was also evaluated by a second method which consisted of differencing Equation 1 and solving for L . This technique did not yield an explicit solution for X and was used primarily to verify the more conveniently expressed closed form solutions given by Equations 7 and 13. For a = 1:
where @$
=
i-
X N
Equation 7 predicts that the greatest permissible amount of sampling is possible when the height of the interface approaches a n antiresonant (nodal) condition. This is of little practical importance, since the acoustic pressure a t these points is approximately zero. I n other words, Equation 7 does not take into account the fact that the acoustic pressure may become very small and fall below the cavitation threshold even though the prescribed pressure variation, e, is not exceeded. This situation can be corrected by imposing the following limitations. Let p be the acoustic pressure ratio below which it is impractical to operate. If (P/Po)is initially below p before the sample is drawn, the reaction will not be carried out. Therefore, a t these points, X i s set a t zero and LR2 at m
.
If then
(9)
The other restriction concerns the possibility that during sampling the acoustic pressure ratio falls below p even though e is not exceeded. This restriction is readily incorporated into the computer program by the following logic statement:
If The total volume of the sample drawn during the experimental run, V s , from a vertical cylindrical reaction vessel containing a liquid of volume Vis
(3)
then
Thus Equations 9 and 10, together with Equation 7 , give the allowable portion to be sampled without exceeding a preassigned variance in the acoustic pressure, E, and also without having this ratio fall below some set value, /*, below which cavitation will not ensue. Sampling Criteria
Figure 1 shows a plot of the allowable fraction sampled as a function of the ratio L/X for e = 1, a = 1, and p = 0.01. The value of the solid-liquid reflection coefficient, a , is dictated by
the particular liquid and vibrating surface used in the system. For the ideal case, a = 1, there are certain heights of the interface above the transducer a t which no liquid can be sampled without affecting the cavitation intensity. These heights can be grouped into two sets: those which produce a resonant 1)/ 41 A, and those which propressure condition, L = [(2n duce a nodal condition, L = n / 2 X. As the height of the liquid approaches a resonant condition, the variation of (P/P,) with L becomes large. As a result, the set limit of the acoustic pressure ratio, 6 , is easily exceeded with a small change
+
r-1.00 0=1.00 /&
=o.oI
Figure 1. Fraction sampled as a function of ratio of liquid height to wavelength for perfect reflection for an acoustic pressure limit of 1.0 and cavitation threshold limit of 0.01
0.3
-
A
0,o
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.0
2.0
L/X
"O
Figure 2. Fraction sampled vs. L/X for various acoustic pressure limits with perfect reflection a t boundary
VOL. 7
NO. 3
AUGUST 1 9 6 8
389
mately linear portions of this plot where L / h is slightly greater than 0.51, 1.01, 1.51, and 2.01. In Figure 1 p was set a t 0.01, while in the remaining figures it was set a t 0.1, to show briefly the effect of p upon X without producing a n additional series of figures for various 1.1’s. Over-all the allowable fraction sampled in the region of the nodal condition decreases with increasing ,u. The allowable fraction sampled, as a function of the ratio L/X for set acoustic pressure decreases of 10, 50, 100, and 150%, is given in Figure 2. As can be seen, the
in liquid level. Hence, only a small fraction of liquid may be sampled. As the height approaches a nodal condition, L = n / 2 A , the acoustic pressure falls below the cavitation threshold, and thus the system will not be operated in this region--e.g., 0.49 < L / h < 0.51. Even though the rate of change of (P/P,) with L is smallest a t the node, very little liquid can be sampled in this region, since liquid withdrawal will cause (P/P,)to fall below p. This consideration is represented by the approxiI O
I
I
i
i
i
1
i
-
i
0.0
a = 1.0
p’o. I 0,O
I. a = 0 . 4 2. ( 1 . 0 . 6 8 = 0.8 4, o l z 1 . 0
3. 0.7
0.8
Figure 3. Fraction sampled vs. L/X for an acoustic pressure limit of 1 .O for various reflection coefficients
x
0,s
0.4
0.3
0.2
01
0.0
0.1
0.2
0.3
0.4
0.5
0.6
07
0.8
0.9
1.0
0.9
1.0
L/X 1.0 .)
I
I
1
,
4
1
0.1
0.2
0.3
0.4
0.5
0.6
1
0.9
0.8
0.7
0.6
Figure 4. Fraction sampled vs. ratio of liquid level height to wavelength for various limits of acoustic pressure for a reflection coefficient of
0.4
)f, 0.5
0.4
0.3
0.2
,0.1
0.0 0.0
L/X
390
I&EC FUNDAMENTALS
0.7
0.8
greater the allowed acoustic pressure variation, E , the greater may be the fraction of liquid sampled. When the wavelength is large compared to the depth of liquid, a large portion may with L is small in be sampled, since the rate of change of (P/P,) this region. O n the other hand, for short wavelengths which correspond to high frequencies, only a small fraction of the reaction volume may be sampled. Figure 3 shows the allowed fraction sampled, X,as a function of L/X for various values of the solid-liquid reflection coefficient,
a. Sharp peaks occur near the resonant condition of the wave for small values of the reflection coefficient. These smaller values of a produce a smaller variation of acoustic pressure with liquid level height a t the antinode, and thus permit a greater degree of sampling. The opposite is true for small values of a as the liquid level approaches a node-that is, the rate of change of (P/P,)with L a t L/X = n / 2 becomes greater for small values of a, thus permitting less sampling than with larger values of the reflection coefficient.
Ioo.r I
eo.
no.
-
ro.
-
eo.
-
LR~
0.1 p.0.
-
so.
-
40.
-
v,.
Figure 5. Modified batch reactor volume at various L / X values necessary to permit total sample volume of 1 cc. without exceeding an e of 0.2 for perfect reflection at boundary
J
I/ !I I,
0.4
0.2
0.6
0.8
!II ,
I
I
0.0
It
a- I .
1.2
1.0
1.4
1.6
1.8
2.0
L/k
1.0 1.0 )I. 0.1 U'0.8
V'.
Figure 6. Modified batch reactor volume at various L / X values necessary to permit a sample volume of 1 cc. without exceeding an acoustic pressure ratio limit of 1 .O for a reflection coefficient of 0.8
0 0
01
02
03
84
0.6
0 5
L/
0.7
08
09
IC
x VOL. 7
NO. 3
AUGUST 1968
391
I n Figure 4, X is given as a function of L/X for set acoustic pressure decreases of 20, 50, 100, and 150% for a reflection coefficient of 0.4 and a value of p of 0.1. I t can be seen in Figure 4, as well as in Figure 3, that the maximum allowable fraction sampled a t a resonant condition shifts to the right of 1)/4, for small values of the reflecthe antinode, L/X = (272 tion coefficient. These shifts correspond to an increase of the same size with an increase of liquid level height directly above the antinode and are to be expected. The smaller the values
of CY for constant e or the larger e for a constant but small a, the further will be this shift. The liquid levels which are initially directly above a pressure antinode will approach the antinode when the first portions of the total sample volume, V,, are withdrawn. For CY = 1, the level cannot drop below the antinode during sampling; for CY < 1, it may drop below this point. For small values of the reflection coefficient a t this point, the variation of (P/P), with L is even smaller than a t the level prior to sampling. This permits a greater amount of
+
15.
I
-
I
' C
v,=
I
I
I
I
I
1.0 I,O
p' 0.1 a = 0.6
-
10.
I
L R ~
-
Figure 7.
Modified batch reactor volume vs.
L / X necessary to permit a sample volume of 1
-
0.0
cc. without exceeding an acoustic pressure ratio limit of 1 .O for a reflection coefficient of 0.6
0.2
0.1
0.5
0.4
0.5
0.6
0.7
0.8
0,s
I
I
I
I
1.0
L/ X SO.
I
I
I
1
2 5.
v,.
1.0
p 9 0.1 a = 0.4 20.
1. e = 0.2 2. e * 0.5 3. C 1.0 4. € 8 1.5
-
15.
Figure 8. Modified batch reactor volume vs. L/X necessary to permit a sample volume of 1
L R ~
cc. for various acoustic pressure limits for a reflection coefficient of 0.4
IO.
5.
0.0
0.1
0.2
0.3
0.4
0.5
L/X
392
l&EC FUNDAMENTALS
0.8
0.7
0.8
0.9
1.0
I
e=
0.5
a = 1.0 VS' I O t L = 0.1 X = 3.0
I.
0.
3.
2.
5.
4.
6.
L Figure 9. Ratio of batch reactor radius to liquid height in reactor as a function of I necessary to permit 1 cc. of sampling for an ultrasonic wave length of 3 cm., an acoustic pressure limit of 0.5, and a reflection coefficient of 1.0
e?
46.
so.
-
25.
-
35,
L R ~
20.
=
1 I
1.0
a
0.8
p=
$3.1
Ve:
1.0
I
1
I I
0.0
0.1
02
0.3
0.4
0 5
0.6
07
OB
os
1.0
i/x Figure 10. Modified CSTR reactor volume vs. L / A for a fluctuation in the flow rate above the steady state which will not exceed an acoustic pressure limit of 0.2 for a reflection coefficient of 0.8 VUL.
/
NU. 3
AUGUST
1968
393
100.
SO..
c 1
0.2
= I,O
u.o.1 Is= 1.0
80.
70.
SO.
SO.
L R~ 40,
30.
20.
IO.
0.
0.0
0.:
0.4
0.8
0.8
1.0
1.2
1.4
1.6
1.8
2.0
L/X
Figure 1 1. Modified CSTR reactor volume vs. ratio of height to wavelength for fluctuations in flow rate above or below steady state which do not exceed acoustic pressure limit of 1.O for perfect reflection at boundary
7.
6.
LR2
5,
4.
3,
2
I,
0.
00
0.1
0.2
0.3
0.4
05
0.8
0.7
0.8
0,s
I O
L/X
Figure 12. Modified CSTR reactor volume vs. I / X for fluctuations in flow rate above or below steady state which do not exceed acoustic pressure limit of 1 .O for a reflection coefficient of 0.4
394
I&EC FUNDAMENTALS
sampling and produces the shift of the maximum sample size (peaks) observed in Figures 3 and 4. Reactor Design
The next problem is that of reaction design considerations which will permit negligible variations in the reaction product. When there is a certain minimum sample size, V,, which one must draw to determine the concentration with any reasonable accuracy, one may ask how the vessel should be designed so that the cavitation intensity is insignificantly affected by the change in liquid height.
V, = xR2AL =
x R2€ --
S
As the resonant condition of the wave is approached, 2kL = (2n l)x, the radius of the vessel must become large for large values of a. Figure 5 shows a plot of the product of the height of liquid in the vessel and the square of the vessel radius, LR2, as a function of the liquid height ratio, L/h for E = 0.5, a = 1, and p = 0.1. This figure is based on 10 equal samplings of 0.1 ml. each for a total sample volume, V,, of 1 cc. The quantity LR2 is also termed the modified reactor volume, as it is the actual reactor volume divided by T . If the liquid level is close to a resonant condition, the reactor volume must be large for either sampling or reactor volume fluctuations to be permitted. The further removed from a resonant condition, the smaller will be the required ratio of radius to liquid level. The dashed lines surrounding L/X = n/2 represent the region in which (P/P,)< p and the reactor operation is impractical. Figures 6 and 7 show the reactor design curves for values of a = 0.8 and 0.6, respectively. The valleys at L = [ ( 2 n 1)/4] X result from the smaller variance of (P/P,)with L a t the antinode for small values of a. Figure 8 relates the variation of LR2 with L/X for various values of the allowed variation in acoustic pressure, e, when a is set a t 0.4, p a t 0.1, and V, a t 1.0. T o illustrate the use of these figures, the following numerical example, in which the reaction medium has acoustic properties similar to water, is considered. For a frequency of 56 kc. and a liquid height of 3.5 cm., L/X is 1.31. From Figure 5, one finds that a t this value of L/X the value of LR2 is 99 cc. From this the radius is calculated to be 5.3 cm. I n other words, for these values of L and h , the diameter of the reactor must be a t least three times the liquid height for a volume fluctuation or sampling of 1 cc. to be permitted. For a wavelength of 3 cm., the ratio of radius to liquid depth is given as a function of L in Figure 9. The results obtained for batch reactor design can be extended to continuous processing. One such application would be a series of CSTR's sonically irradiated from beneath. This extension can be accomplished by replacing the volume sampled, V,, by the volume fluctuation in the tank, V,, These fluctuations would result from variations in the flow rates. By determining the deviation from the steady-state flow rates, f ( t ) , in a given period of time, T , one could obtain the maximum volume fluctuation, V,, from the following expression :
By appropriate use of Equation 13, along with Figures 5 through 9, one could determine the necessary reactor design for either a batch reactor or a CSTR with negative volume is, fluctuations occurring only below the fluctuations-that steady-state value. Figure 10 gives LR2 for a positive fluctuation in flow with parameter values of a = 0.8, e = 1.0, and p = 0.1. By superimposing the values of LR2 for a positive fluctuation-i.e., deviations only above the steady s t a t e - o n those for a negative fluctuation and then taking the greater of the two values a t every point, L/X, one obtains the plot shown in Figure 11. This figure, along with Figure 12, gives the necessary reactor dimensions in which either a positive or negative volume fluctuation of 1 cc. may exist without exceeding the set limits of the acoustic pressure variation. The parameter values in Figure 11 are a = 1.0 and e = 0.2; in Figure 12, a = 0.4 and E = 1.0. If one is operating a system where the electrical impedance characteristics are not constant, transducer loading will occur. I n this case Po must be appropriately modified before using the figures presented, Over-all, the criterion for continuous sampling and batch or continuous stirred tank reactor design is roughly the requirement that
+
+
R
>>
I1 L
Summary
The increased liquid-phase reaction rates brought about by ultrasonic waves result from cavitation. If the product variation is to remain a minimum, the cavitation intensity must remain constant. The amount of sample that may be drawn from a vessel in which an ultrasonic chemical reaction or extraction is taking place without significantly changing the cavitation intensity depends upon the wavelength and the height of the liquid above the transducer surface. If a certain minimum sample size is to be drawn in a batch reactor, or a known fluctuation in the CSTR volume exists, the design of the reaction vessel must be such that the radius of the reaction vessel is much larger than the depth of the liquid in the vessel. The magnitude of the quotient of reactor radius to liquid depth depends upon the wavelength and the particular liquid height above the transducer surface.
Acknowledgment
These results are one part of the work being supported by
NSF Grant No. GK-815.
Nomenclature
f ( t ) = difference between inlet and outlet volumetric flow rates in a continuous stirred tank reactor (CSTR), cc./sec. i = integer, 0, 1, 2 . . . k = wave number, cm.-l L = height or level of gas-liquid interface above transducer, also identically the liquid depth in the reactor, cm. LR2 = modified reactor volume, V / x , cc. AL = decreases in liquid height due to sampling, cm. n = integer, 0, 1, 2 . , . iV = number of points used in determining average value of S, O(50). P = acoustic pressure a t integral half wavelengths in reaction vessel, atm. Po = reference acoustic pressure a t transducer surface, atm. R = radius of reaction vessel, cm. VOL. 7
NO. 3
A U G U S T 19.58
395
s
=
t
=
Y
=
v = v, = v, = x =
average rate of change of ratio P/Po with L, between L and ( L - AL), cm.-’ time, sec. volume of liquid in reaction vessel, cc. volume fluctuation in CSTR, cc. total volume of sample, cc. fraction of liquid sampled PlPO
GR.EEK SYMBOLS reflection coefficient a t liquid-solid surface
a
=
E
= wavelength, cm. = set allowable change in acoustic pressure ratio
x
7r
ai 7 /.l
3.1416 variable defined by Equation 8 period of time over which fluctuation in flow rates produce maximum variation in reactor volume, sec. = acoustic pressure ratio below which acoustic pressure is below cavitation threshold and reaction operation impractical
= = =
SUBSCRIPTS 1 = point a t which sampling begins 2 = calculated point a t which sampling terminates = point a t which P/Po = p p Literature Cited
Aerstin, F. G., Timmerhaus, K. D., Fogler, H. S., A.Z.Ch.E. J. 13, 453 (1967). Chen, J., Kalback, W., IND.ENG.CHEM.FUNDAMENTALS 6, 175 (1 967 ). Flynn, H. G., “Physical Acoustics,” W. Mason, Ed., pp. 58-168, Academic Press, New York, 1964. Griffing, V., Sette, D., J . Chem. Phys. 23,503 (1955). Jarmen, P., Proc. Phys. SOC. 73, 628 (1959). Ostroski, A . S., Stambaugh, R. B., J . Appl. Phys. 21, 478 (1950). Park, A . V. M., Taylor, D., J . Am. Chem. SOC.4, 1442 (1956). Sirotyuk, M. G., Soviet Phys. Acoustics 8, 201 (1963). Weissler, A,, Cooper, H. W., Snyder, S., J . Am. Chem. SOG.72, 1769 (1950). RECEIVED for review June 27, 1967 ACCEPTED May 8, 1968
ACTION OF ULTRASOUND ON AQUEOUS SOLUTIONS OF METHYL IODIDE T E D M. TUSZYNSKI
AND W I L L I A M
F. G R A Y D O N
Department of Chemical Engineeriq and Applied Chemistry, University of Toronto, Toronto 5, Ontario, Canada
The effect of ultrasound on aqueous solutions of methyl iodide has been investigated at a frequency of 820 kilohertz and a transducer acoustic output o f 3.0 watts per sq. cm. Quantitative chromatographic analysis using a hydrogen flame ionization detector revealed the following products: iodine, hydrogen iodide, methanol, hydrogen peroxide, methane, ethane, ethylene, propane, propylene with traces of acetylene, and methylene iodide. The sonochemical decomposition was zero order with an average rate constant mole per (liter) (sec.) at 18’ C. The results are discussed on the basis of cavitation of 3.20 X phenomena, and a free radical mechanism i s proposed.
ultrasonic waves bring about a wide variety of changes Currell et al., 1963; Lliboutry, 1944; Lur’e et al., 1962, 1963; Prakash et al., 1964a; Prakash and Prakash, 1960; Prudhomme and Grabar, 1949; Weissler, 1958, 1960; Weissler et al., 1950). Current theories as to the mechanism by which these changes are brought about involve the phenomenon of cavitation: the formation of cavities in the liquid and their subsequent collapse resulting in a local release of a large amount of energy. Seeking further insight into the nature of ultrasonic reactions, the authors investigated the effects of ultrasonic energy on aqueous solutions of methyl iodide. Methyl iodide was chosen because it was a simple molecule and one readily decomposed HAT
Tin liquids is well known (Anbar and Pecht, 1964;
Experimental Details
Equipment. T h e source of ultrasound employed was a Macrosonics Corp. Multisons generator with a modified output stage as shown by Tuszynski (1966). T h e generator had a continuously variable power output of 0 to 500 watts with a frequency band width of 5 kilohertz to 2 megahertz. 396
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FUNDAMENTALS
The transducer elements were Clevite Corp. 2400-PZT-4, lead titanate-lead zirconate disks with a thickness-mode resonant frequency of approximately 820 kHz. The glass reactor shown in Figure 1 with a silicone rubber sampling plug, thermocouple well, and blown-out extra-thin bottom was used for all runs. The reactor was 8.5 inches long with 1.125-inch i.d. and an approximate total volume of 130 ml. A Varian-Aerograph Model 600 D Hy-Fi hydrogen flame ionization detector with Matheson dry nitrogen as carrier gas was used for analysis. Reagents. Fisher Scientific, 99.8% pure C H d with a boiling point of 42.4’ C. was used. Compressed gases, used for column calibration, were a t least C.P. grade 99.0% pure from the Matheson Co. All others were standard reagents commercially available from Fisher Scientific and the British Drug House. Procedure. T h e glass reactor was clamped over the transducer (Figure 1) in a position giving maximum fountain height inside the reactor. T h e assembly was then immersed in a cooling water bath (10’ to 14’ C . ) . I n a typical run, 65 ml. of aqueous methyl iodide solution were subjected to ultrasonic
