PULSATION AND VIBRATION 4. For practical application, it must be possible to produce or distribute the required sonic energy in all parts of the bed, which may be large. This specification, combined with the well-known rapid absorption of sonic energy in porous materials, would suggest multiple small sources, rather than a single large source.
a
+
Of the various known methods of producing sonic energy, only three seem a t all likely to be practical, namely: sirens, whistles, and vibrating diaphragms. Both sirens and whistles can be designed to produce high pressure sonic energy at low frequency, but they suffer from the serious disadvantage of requiring very large flow rates of gas. I n many cases, this would make these devices impractical for promoting fluidization without special arrangements to separate sound-producing gas from the fluidization gas while simultaneously transmitting vibrations to the boiling bed. This complication becomes particularly serious if multiple sound-producing units are to be used in large beds. Furthermore, high power sirens and whistles are so bulky that their use would be difficult. Vibrating diaphragm units seem much more likely to be successful for this application. Those presently on the market in the form of loud-speakers are unsuitable because of low power rating and difficulty of isolating from reaction conditions. However, the principles of design of vibrating diaphragm devices are sufficiently well understood that special units can be built, perhaps embodying as power sources high power, low frequency vibrators of the types used for vibrating bins and conveying dry powders; such vibrators are made both for air actuation and for electrical powering. Such units could be designed with their actuating elements enclosed between double vibrating diaphragms, thereby exposing only the diaphragms, cables, and pressure-balancing line to the materials in the bed. It seems reasonable to believe that such units could even be made to withstand moderate temperatures.
Conclusions This work shows results to be expected in the application of sonic energy t o the promotion of fluidization. The mechanism by which sonic energy unlocks the particles and enables them to be fluidized vi11 be an interesting field for further research. Sonic energy will cause nonfluent materials of small particle size to flow sufficiently well that good fluidization is possible without channeling and stagnation. With materials which are normally fluent, the effect, if any, on fluidization is too small to be observed visually, or found with the capacitometer. The sound pressure used must be above some minimum value peculiar to the material but certainly sufficient to secure approximately 110 decibels after absorption in beds about 1 foot deep. The sound frequency in the range from 40 to a t least 400 cycles per second is not important as long as the sound pressure is adequate. Through resonance with the natural periods of the apparatus, the use of a particular frequency will permit higher sound pressure to be secured from a given sound energy source. Vibration of the column is also effective in promoting the flow of nonfluent materials of small particle size, but its effectiveness may be of limited range because of the poor mechanical coupling between walls and particles, and the consequent vibration damping in the intermediate layers of material. If the vibration can be transferred t o the fluid, it becomes sonic energy.
literature Cited (1) Lamb, H., “Dynamical Theory of Sound,” 1st ed., Article 360a, Arnold Publishers, London, 1910.
(2) Morse, R. D., and Ballou, C . O., Chem. Eng. Progr., 47, 199-204
(1951).
(3) Morse, R.D., and Von Wettberg, E. F., Jr., U. S. Patent 2,667,706 (Feb. 2, 1954). RECEIVED for review December 20, 1954.
ACCEPTED March 19, 1955.
Effect of Vibration on Natural Convective Heat Transfer ROBERT LEMLICH Deparfmenf o f Chemical Engineering, Universify o f Cincinnafi, Cincinnafi 2 I , O h i o
In order to study the effects of vibration on heat transfer, an experimental investigation was carried out involving natural convection from electrically heated wires of three different diameters subjected. to transverse vibration in air. Marked improvement in the coefficient of heat transfer was obtained b y using vibration in the range of 39 to 122 cycles per second, even to the extent of quadrupling the film coefficient. An increase in coefficient was observed for an increase in amplitude or an increase in frequency. No effect was observed for a change in the direction of vibration. In an effort to account for this latter observation, the concept of a stretched film surrounding the entire path of vibration was proposed. In addition, a pair of dimensionless correlations based on a vibrational Reynolds number were presented for vibration in air or other diatomic gases. An approximate extension to other fluids was also proposed.
0
F THE many variables that affect the rate of heat transfer, the effects associated with vibration are among the least known. Patents on the subject ( 1 , 12, 14-16, 18) offer little quantitative data. However, the meager information that is available indicates that considerable improvement in the rate of heat transfer is possible u-here vibration is employed. West and Taylor ( 1 7 ) obtained improvements to 70y0in heat transfer coefficient by applying 100 pulses per minute t o water in a June 1955
double pipe exchanger. Martinelli and Boelter (10, 1 1 ) reported increases in coefficient to fivefold by vibrating a 0.75-inch cylinder in natural convection under water. However, Boelter ( 8 ) indicated that results obtained from a later check on some of the experimental data by Mason (IS)did not, agree with the original. Accordingly, the present study is an investigation of the effect of vibration on heat transfer in a simple experimental system in
INDUSTRIAL AND ENGINEERING CHEMISTRY
1175
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT which all the variables may be independently measured and their effects incorporated in an over-all dimensionless correlation. Tabulation of data and results together with a more extended discussion of this investigation is available in the dissertation (7).
Experimental The system selected was that of natural convection from a horizontal, electrically heated Nichrome wire, undergoing transverse vibration in room air. As shown in Figure 1, the wire was stretched between a pair of bridges 36.3 inches apart and allowed to vibrate. Vibration was induced by connecting the armature of an electric interrupter-type buzzer t o the wire a t a point about 9 inches t o the left pf the right hand bridge. By temporarily allowing the center of the wire to vibrate a t right angles to a uniform magnetic field, picking up the induced electromotive force, amplifying it, and projecting it on an oscilloscope screen, the vibrational wave form was shown t o be essentially sinusoidal. POTENTIOMETER-
n
the thermocouple to the surface in question is small. For the present work this fact was further checked by temporarily replacing the Nichrome wire with a length of electrically heated hypodermic tubing through which an electrically insulated thermocouple was threaded and centered longitudinally. A split junction thermocouple of the type described above was then wrapped around the outside of the tube and also centered longitudinally. For various levels of heat flux, whether the tube was vibrated or not, the temperature indicated by the outer thermocouple was lower than that of the inner by 2 to 3y0 of At, the difference between surface temperature and ambient temperature. This corresponds to a difference of only 2 to 3% in the heat transfer coefficient, h. Thus the error is not only small but roughly constant, so that i t tends to cancel in the final correlations. The vibration itself generated no appreciable heat as shown by the absence of any measurable At when current to the vibrating wire or tube was shut off.
Results
AM METE R
h
The effects on h of 5 major variables were investigated in a total of 100 runs carried out with vibration. These variables included wire diameter, D,in three different sizes, namely 0.0253, 0.0396, and 0.0810 inch; At ranging from 7" t o 365' F.; amplitude of vibration a t the center of the wire, H (defined as the distance between extreme positions of the center line over the course of of one cycle) ranging from 0.055 to 0.231 inch; frequency, F, ranging from 39 to 122 cycles per second; and direction of vibration, that is, whether the vibration was horizontal or vertical. In addition, 37 control runs were conducted without vibration. These latter agreed with McAdams (9) generalized correlation for horizontal cylinders with an average deviation of about 2 ~ 6 % for the points themselves and about 3% for the trend. The value8 of h which were determined under vibration are for the central portion of the wire where the thermocouple is located and not for the ?ire as a whole, since the amplitude of vibratory displacement necessarily varies along the length of the wire. However, because the central portion of the vibrating wire represents the top of a sine wave and as such is quite straight (flat) even a t the crest of a vibration, these values of h which are calculated and later correlated are essentially for vibrating horizontal cylinders. Despite the fact that vibration increases h and so cools the middle portion of the wire more than the ends, calculation based on the low temperature coefficient of electrical resistance for Nichrome showed that no appreciable error was introduced by using the average heat dissipation for the entire wire in computing h. Similarly, numerical analysis, reinforced by auxiliary evidence of a direct experimental nature, indicated the heat conducted along the wire was negligible. I n addition, unsteady-state calculation, as well as considefations based on heatup time, showed the rapid 60 cycles per second alternations in current induced no appreciable alternation in wire temperature. Finally, calculation for the smooth, shiny, Nichrome surface yielded only a negligible rate of heat transfer by radiation, the effect of which was reduced even further by cancellation in the ratio of coefficients appearing in the final correlations. Thus, no spurious heat effects interfered with the study. Effects of Vibrational Variables. The effects of amplitude and frequency are illustrated in Figures 2 and 3 for the 0.0396-inchdiameter wire. Holding other variables constant, h increases with both amplitude and frequency of vibration. This is in accord with the film concept and follows from the increased magnitude and frequency of the disturbance a t the film, which in turn decreases its thickness. Furthermore, the effect of frequency on h is greater a t a larger amplitude of vibration than a t a smaller amplitude. This also follows, since increasing the number of times per second that a large disturbance occurs
I U IISV. AC
Figure 1.
'
Schematic diagram
The amplitude of vibration, which was controlled by varying the dry cell voltage to the buzzer or by changing the linkage between armature and wire, was measured with a calibrated low power microscope, the precision of which was =!=0.0003 inch. The frequency of vibration, which was varied by altering the tension on the wire, was determined with a stroboscopic light calibrated to an accuracy of =k1%. The 60-cycle electrical power input to the wire (and hence the rate of heat dissipation) was measured with a voltmeter and ammeter; their accuracies were &2%. Temperature Measurement. The temperature a t the middle of the Nichrome wire was measured by a calibrated 0.005-inchdiameter Chromel-Alumel thermocouple connected to a potentiometer with an accuracy of & l o F. The cold junction was at room te,mperature so that the temperature difference between wire surface and room air could be measured directly. Attempts a t welding a hot junction to the Nichrome wire failed under sustained vibration. Other techniques such as the use of a plated junction or the setting of the thermocouple wires in a groove would also have proved unsatisfactory since they would have resulted in a local resistance irregularity and, therefore, a local temperature irregularity a t the very point where the temperature was being sensed. Accordingly, each wire a t the hot end of the thermocouple was wrapped around the main wire so as to give a split hot junction but with a separation of less than 0.3 inch. The technique of utilizing the electrical resistance of the main wire as a measure of the temperature (requiring a wire composition with a high temperature coefficient of electrical resistance rather than Nichrome) would also have proved unsatisfactory. The frequent changes in wire tension required for changing the frequency would have repeatedly altered the resistance of the wire, necessitating continual recalibration. Previous investigators in natural convection (6, 6 ) found that the error incurred in measuring surface temperature by securing
1176
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. 6
--
PULSATION A N D VIBRATION for vertical vibration would be less than that for horizontal vibration. Now, no difference could be discerned between the effects of horizontal and vertical vibration. Therefore, it is unlikely that the wire could have carried its film back and forth in the manner indicated in Figure 4,A, but apparently stretched it, as indicated in Figure 4,B. 2. The shape within the stretched film (shown shaded) would Drobablv have much the same rate of naturaf conveciive heat transfer in a horizontal position as in a vertical position. While the author knows of no data for such a configuration, correlations ( 4 ) are available for plane surfaces (Figure 4,D) in air a t moderate conditions of temperature and ressure which indicate that for fixed dimensions a n f a t , the total natural convective heat loss from both surfaces of a vertical plate is only 4% higher than that from both surfaces of a horizontal plate. 3. A simple experiment was conducted wherein a lighted cigarette was held under one of the wires in horizontal vibration. The smoke appeared to curl up and around the vibrating path, as illustrated in Figure 4,E. This would seem to indicate the existence of a stretched film.
40
3
20
t;;
rK W
L
-
I
-zw
Oiometr 0.0396 inch
2
::
Frequency 90 vibmtions/ ucand
-
Y W LL
2
I 6
810
I I1IIll
I
20 40 60 80 100 TEMPERATURE MFFERWGE At IN OF.
Figure 2.
eo0
I I,
I
400
Effect of amplitude
results in a greater over-all disturbance a t the film than would result from correspondingly increasing the frequency of a small disturbance. These figures also show that a given increase in amplitude or frequency produces a smaller increase in h a t higher values of At tJhan a t lower values of At. I n other words, the effect of amplitude and frequency diminishes as At increases. This can be explained in terms of the increased disturbance a t the film due to natural convection currents produced by a high At. Under these coiiditions the additional disturbance caused by an increase in amplitude or frequency represents a smaller proportion of the total disturbance than it does for the situation with a low At wild feebler natural convection currents. I n the extreme a iwgative slope appears a t high amplitude in Figure 2. Since the data were gathered for an over-all correlation, little a,ttempt was made a t deliberately keeping the parameter of amplitude or frequency constant from run to run. The scatter in Figures 2 and 3 is thus largely due to lack of complete constancy of parameters from one run to the next, rather than to experimental error. The direction of vibration has no effect within the limits of experimental error. This can best be seen from Fiaures 5 and 6. where the solid points represent vertical vibration and I I I I 6 30 *I-Y. the hollow points represent horizontal a20 vibration. No differencein trend between the t n o types of points can be discerned.
These arguments, of course, do not represent rigorous proof of this stretched film concept. However, they do constitute evidence in its favor.
Correlation Attempts were made to correlate the data by utilizing appropriate modifications of a relationship proposed by Martinelli and Boelter for their work, but without success. Other attempts, which included endeavoring t o account for h in terms of a known natural convective effect added to known forced convective effect, also failed. Generalized Correlation. The only method of attack which did prove successful was that of correlating dimensionless groups. By dimensional analysis these groups are Nusselt number, Nu; Grashof number, Gr; Prandtl number, Pr; vibrational Reynolds number, Re, H I D , and @At where 0. is the thermal coefficient of volumetric expansion. The Reynolds number is defined in terms of the average velocity 0 = 2HF by the expression
Re
Dtip
= -
(1)
c1
where p is density and p is dynamic viscosity. A somewhatj similar term was utilized by Martinelli and Boelter.
Y
I I l l
I
I
1
I
I 1 1 1 1
I
-
I
1
-
-
I
A
Physical Picture With regard to a physical picture, the experimental data seem to indicate, at least as an approximation, that within the limits of the present range oE variables the vibrating wire does not carry 8 4 the film back and forth with it, as represented in Figure 4 4 , but rather that the B E LL film surrounds the entire vibrating path, I I 1 w 2 8 2 4 as represented in Figure 4,B. The evidence to support this contention is threefold. 1. If the wire did carry its film back and forth, there would be something of a vector summation of velocities a t right angles between the horizontally moving wire and the rising convection current, as shown in Figure 4, C. This vector sum would never be less than the vertical current itself, and except for the two instants a t either crest of the cycle, would always be greater. On the other hand, the vector summation for a vertically moving wire would result in a net addition half the time and in a canceling subtraction during the other half. Thus the average effective velocity over a cycle
t i -
lune 1955
I
-
Diameter 0.0396 inch
I 1 1 1 1 6
I
I
I
I I l l l l
810 20 40 6 0 80 100 TEMPERATURE DIFFERENCE AT IN O F .
Figure 3.
I 200
I
I 400
I 600
Effect of frequency
Combining the groups with considerations based on the data itself h F-l='p (2) where h' is the heat transfer coefficient for the same diameter wire without vibration but a t the same At as with vibration;
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
1177
.
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
-
t
8. STRETCHED F I L M
-
E. SMOKE PATTERN
A. MOVING FILM C. INSTANTANEOUS VECTOR SUMMATION
Figure 4.
Film considerations
that is, a t the same Gr X Pr, since the effect of small changes in room temperature on the properties of air is slight. Pr for air is virtually constant, and the inclusion of H I D was unnecessary. All fluid properties are evaluated a t the arithmetic mean film temperature. Figure 5 shows a plot of Equation 2, the generalized correlation for air. It should also be applicable to other diatomic gases as well, since they all have virtually the same Pr. The quantity h/h' - 1 is the fractional increase in coefficient resulting from vibration, and is given directly. This improvement reached over 3009.'0, which corresponds to a quadrupling of the coefficient. Another advantage to having the correlation in terms of the ratio of coefficients in that any errors in their determination tend to cancel each other. I n addition, due to the generality inherent in the expression h/h' - 1 which involves only the improvement in coefficient rather than the coefficient itself, the form of the correlation may also be applicable, at least in a general way, to bodies of noncylindrical shape. The average deviation for the correlation is about &13%, where % refers to percentage improvement in coefficient. For a given h' the average error in h itself is about &8%. For improvements in coefficient of over loyo,which covers most of the experimental range, the curve is closely approximated by
h
0.75
+ 0.0031
the Reynolds number and the generalized correlations. Since the room temperature varied only very moderately, an increase in At corresponded to an increase in average film temperature. This in turn decreased density and increased viscosity, so that for a fixed amplitude and frequency the Reynolds number decreased. Now, as is evident from the logarithmic nature of the correlations, a t high Reynolds numbers (corresponding to high parametric values in Figure 2 ) even a small decrease in Re or Re, induces a considerable decrease in h. Thus for the highest amplitude in Figure 2 the increase in At actually reduced h despite the increase in Gr. Extension to Other Fluids. I n an effort to extend the correlation to include other fluids, the data of Martinelli and Boelter on water were employed. Pr was taken into account by multiplying the abscissa of Figure 5 by the quantity 0.80/PrO.'6. For air and other diatomic gases, this reduces to unity (8)leaving the correlation unchanged.
I 4-
-
(pAt)0.33 (Gr)o.41
Re2.05
The quantity h' may be estimated from the McAdams correlation for stationary horizontal cylinders ( 9 ) for which Bosworth ( 3 ) has fitted an equation. An alternative correlation based on the stretched film concept is also possible by making use of D H , the longer linear dimension within this film, rather than the shorter dimension, D. A modified Reynolds number may then be defined for the stretched film by
I
I
I I I I l l
WIRE SYMBOL DIAMETER 0.0253 INCH 0 0.0'253 0 0.0396 0 0.0396 A 0.0810 A 0.0810
I
I
1 1 1 1 -
-
VIBRATION DIRECTION VERTICAL HORIZONTAL VERTICAL HORIZONTAL VERTICAL HORIZONTAL
0.8
+
A plot of h/h' - 1against Re, is shown in Figure 6. The resulting correlation is simpler than that of Figure 5 , but the scatter is greater. By fitting a straight line to the results, this alternate correlation may be expressed by
--1
h'
=
0.00265 Ree2.'3
(5)
Attempts t o utilize some other characteristic stretched film dimension in the Reynolds number, such as the hydraulic radius, correlated no better. Nevertheless, the greater simplicity and partial success of the alternate correlation represent further support in favor of the stretched film concept. Referring back to the earlier discussion of Figure 2, the negative slope in this plot now may be readily explained in terms of 1173
Figure
5. Correlation for vibration in air
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 41, No. 6
PULSATION A N D VIBRATION 6
WIRE SYMBOL DIAMETER
VIBRATION DIRECTION
0.0253INCH VERTICAL OM53 HORIZONTAL 0.0396 VERTICAL 0.0396 0.0810
0.0810
/*
"J-
1
-
I
I
I
I
I I I l l
I
I
I
-
I l l
-
4 -
1
DATA OF PRESENT AUTHOR
7
o DATA OF MARTINELLI AND BOELTER
&
7
0
2 -
HORIZONTAL VERTICAL HORIZONTAL
0.6 0.4 I -
0.8
L-
-I
:I 0.2I
PRESENT AUTHOR
-
I
0.2
-
=I==
0.06 0.04 0.1
0.08
0.04
0.02
:f 1 . 0
I.
I 2
I
I 4
I
i
I 1 1 1 1
6
810
I
I
20
I 40
I l l 60 80
Res Figure
6. Correlation for vibration in air based o n
Figure 7.
stretched film concept Figure 7 shows the final plot for both the water data of Martinelli and Boelter and the air data of the present investigator. The general trend of the two sets of results are in agreement with each other. A curve based on the combined results and a curve based on those of the present author alone are shown. The latter curve is basically the same as that of Figure 5 , but includes the Pr modification. With regard to these two curves shown in Figure 7 , if a single correlation is to be selected for all fluids, both liquid and gaseous, the curve based on the author's data alone is believed to be the more reliable. This contention is supported by the greater scatter among the plotted results based on the work of Martinelli and Boelter, and the previously mentioned doubt cast on their validity. Therefore, modifying Equation 3 to include the effect of Pr and combining with Bosworth's equation yields the following for improvements in excess of IO'%:
~
[0.63
+ 0.35(Gr X P r ) o . 1 7 ] 2(6)
Thus the solid curve of Figure 7 , or alternately Equation 6 makes possible an estimation of the effect of vibration on natural convective heat transfer in other fluids as well as in diatomic gases. Summary of Conclusions 1. Vibration can materially increase the coefficient of heat transfer, a quadrupling of the coefficient having been obtained. 2 . Holding other variables constant in turn, the heat transfer coefficient increased with both amplitude and frequency. The direction of vibration was without significant effect. 3 . The film about each wire was apparently stretched to cover the entire path of vibration rather than carried back and forth by the wire. 4. The effect of the vibrational variables may be correlated
lune 1955
Comparison with d a t a of Martinelli a n d Boelter
in terms of a vibrational Reynolds number defined as twice the product of amplitude] frequency, linear dimension] and density, divided by viscosity. 5 . The improvement in heat transfer coefficient for the central portions of the vibrating wires which are essentially horizontal vibrating cylinders in air is dimensionlessly correlated by Figure 5 . For improvements in excess of loyo,this correlation is fitted by Equation 3. As an alternative, a simpler but less precise dimensionless correlation based on the stretched film concept is presented by Figure 6 or Equation 5 . 6. For an approximate extension to other fluids (as well as for diatotnic gases such as air) a modified dimensionless correlation is presented in Figure 7 . For improvements in heat transfer coefficient greater than lo%, this modified correlation is fitted by Equation 6. Acknowledgment
The author is indebted to William Licht for reviewing the manuscript and for his helpful encouragement. I n addition, the author wishes to thank Erica M. Houser for assisting with some of the tedious calculations and Roger Keith for preparing the figures. The experimental work was performed by the author a t the Polytechnic Institute of Brooklyn. Nomenclature
D F Gr h h'
H
Nu Pr Re Re,
diameter, f t . or inch frequency of vibration, sec.-1 = Grashof number, dimensionless = coefficient of heat transfer, B.t.u./hr. ft., F. = coefficient of heat transfer for same diameter a t same Pr X Gr as occurs without vibration = amplitude of vibration, it. or inch = Nusselt number, dimensionless = Prandtl number, dimensionless = vibrational Reynolds number, dimensionless = vibrational Reynolds number for stretched film, dimensionless = =
INDUSTRIAL AND ENGINEERING CHEMISTRY
O
1179
ENGINEERING, DESIGN, A N D PROCESS DEVELOPMENT At
V p p p (p
=
temperature difference,
O
F.
= av. velocity over one cycle, ft./sec.
thermal coefficient of volumetric expansion, dynamic viscosity, lb./ft. sec. = density, lb./cu. f t . = function = =
O
F.-1
Literature Cited (1) Andreas, A., Ger. Patent 717,766 (Feb. 5, 1942). (2) Boelter, L. &I. K., personal communication, 1953. (3) Bosworth, R. C. L., “Heat Transfer Phenomena,” p. 101, Wiley, New York, 1952. (4) Ibid., p. 104. (5) Colburn, A. P., and Hougen, 0. A,, IXD. ENG.CHEM.,22, 522 (1930). (6) Fa;ber,‘E. A., and Scorah, R. L., Trans. Am. SOC.Mech. Engrs., 70, 369 (1948). (7) Lemlich, R., dissertation for Ph.D., University of Cincinnati, June 1954.
ULTRASONIC CHEMICAL EFFECTS VIRGINIA GRlFFlNG The Cafholic Universify o f America, Washington, D. C .
U
LTRASONIC chemical effects have been studied to determine why any chemical reactions occur when a system is irradiated with a high intensity ultrasonic beam rather than to concentrate on which reactions go and by what chemical kinetics. The experimental fact exists t h a t no observable chemical reactions take place unless there is a permanent gas dissolved in the solution and the sound intensity is sufficiently high to make the liquid cavitate. Thus it is assumed that a gas dissolved in the solution will form minute bubbles in the sound field. The liquid serves as an efficient transducer which carries the energy of the-high intensity sound wave from the source to the interfaces between the small bubbles and the liquid. I n the adiabatic compression of a sound wave, the production of a high temperature is dependent on the existence of a large difference between the adiabatic and isothermal compressibility. As the sound wave of 5 to 10 watts per sq. cm. travels through the liquid, the temperature difference due to the adiabatic compression is of the order of a few degrees centigrade while a t these intensities a sniall bubble of gas may be compressed to half its volume, producing a temperature variation of several hundred degrees. A temperature gradient in the gas bubble is then set up, which produces periodic temperature variation in the liquid adjoining the gas bubble. If one assumes the model there are two possibilities for explaining the chemical reactions to be effected. The chemical reactions could be gas phase thermal reactions taking place in the gas bubble or the chemical reactions might take place a t the liquidgas interface, but still be due to the high gas temperature in the bubbles. These same thermal processes are responsible for the loss of acoustic energy. According to this idea, two thermal properties of the gas content of the bubble are important. First, y will determine the temperature reached in the compressed bubble. As the y of the gas approaches one the temperature inside the bubble becomes much lower. This explains why vapors such as ether inhibit these
1180
(8) Mcddams, W. H., “Heat Transmimion,” 2nd ed., p. 242. McGraw-Hill, Kew York, 1942. (9) Ibid., p. 243. (10) Martinelli, R. C., M.S.thesis in mechanical engineering, University of California, 1938. (11) Slartinelli, R. C., and Boelter, L. M. K., PTOC. 6th I n h . Congr. A p p l . Mech., 578 (1938). (12) Maschinenfabrik Oerliken, Brit. Patent 532,144 (Jan, 17, 1941). (13) Mason, W. E., personal communication, 1954. (14) Ormell, E. A. I., Ger. Patent 736,883 (May 20, 1943). (15) Robinson, R. S., U. S. Patent 2,514,797(July 11, 1950). (16) Schrey, A., French Patent 806,030 (Dec. 5, 1936). (17) West, F. B., and Taylor, A. T., Chem.. Eng. Progr., 48,39 (1952). (18) Worn, G. A , , and Rubin, F. L., U. S. Patent 2,664,274(December 29, 1953). RECEIVED for review December 20, 1954. ACCBPTEDApril 1 1 , 1955. From a dissertation presented b y R. Lemlioh, in partial fulfillment of the requirements for the doctor of philosophy degree at the University of Cincinnati, June 1954.
reactions even if the solution is saturated with air. Thus one would expect the rate of a chemical reaction to increase as the y of the dissolved gas increases whether the reaction occurs in the gas bubbles or in the liquid phase. Secondly, the thermal conductivity of the gas will determine how long the high temperature is maintained inside the bubble. If the reaction takes place inside the bubble the gas with the lower thermal conductivity will give a higher chemical yield than one with high conductivity. On the other hand, for any thermal reaction in the liquid phase, the thermal conductivity of the gas should have the opposite effect. A series of experiments was conducted to answer these questions. The chemical effects directly produced by ultrasonics are thermal gas phase reactions; they take place inside the gas bubbles. In water solutions, the reaction is the production of radicals by the thermal decomposition of water-probably OH radicals .4 similar reaction has not been obtained when water is not present even though a wide variety of organic substances has been tried. If another reactive gas or vapor is present in the bubble, the OH radical attacks the vapor forming other products within the bubble-e.g., carbon tetrachloride. These products then diffuse in the solution; various secondary reactions between these products and the species dissolved in the solution have been observed. Another secondary effect of the chemical reactions is luminescence ( 1 ) ; the intensity of luminescence shows the same general behavior as the chemical yields. The degradation of polymers, although due to cavitation, is not due to “hot spots” developed in and around the gas bubbles It is postulated that polymer degradation is caused by the same type of force that is so effective in mechanical dispersion and scrubbing action a t a low frequency of the order of 20 kc. Although the experiments have conclusively proved that the chemical reactions take place in the gas phase, it is impossible to rule out completely that the mechanism may be gaseous discharge inside the bubble rather than temperature Presentlv the data are being re-examined and new euperiments undertaken to settle this question.
literature Cited (1) Griffing, V., and Sette, D., J . Chem. P h y s . , 23, 503 (1955).
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