ENGINEERING, DESIGN, AND EQUIPMENT (9) Ibid., 22, 436-7 (1954).
(IO) Jost, W., “Diffusion in Liquids, Solids, Gases,” Academic Press, New York, 1952. (11) Keyes, F. G., and Burks, H. G., J . Am. Chem. SOC., 49, 1403 (1927). (12) Michels, A.,and Gibson, R. O., Proc. Roy. SOC.(London),A134, 288 (1931). (13) WIichels, A., and Michels, C., Ibid., A153, 201 (1935). (14) Michels, A , , Michels, C., and Wouters, H., Ibid., A153, 214 (1935). (15) Pollard, W.G., and Present, R. D., Phys. Rev., 73,762 (1948). (16) Robb, W.L.,and Drickamer, H. G., J. Chem. Phys., 19, 1504 (1951).
(17) Smith, L.B.,Beattie, J. A., and Kay, W. C., J . Am. Chem. SOC., 59, 1587 (1937). (18) Timmerhaus, K. D., and Drickamer, H. G., J. Chem. Phys., 19,1242(1951). (19) Ibid.,20,981 (1952). (20) Winn, E.B.,Phys. Rev., 80, 1024 (1950). (21) Winter, E.R. S., Trans. Faraday Soc., 47, 342 (1951). RECEIVED for review May 21, 1954. ACCEPTEDJune 20, 1955. Division of Industrial and Engineering Chemistry, 125th Meeting, ACS, Kansas City, Ma., March 27, 1954.
l o w Frequency Bubble Formation at Horizontal Circular Orifices ROBERT J. BENZlNGl
AND
JOHN E. MYERS
School of Chemical and Metallurgical Engineering, Purdue University, W. Iafayetfe, Ind.
G
AS bubble formation a t horizontal submerged orifices is characterized by two different mechanisms which are related to the frequency of formation. At low frequencies, generally below 100 bubbles per minute, the frequency of bubble formation is almost directly proportional to the rate of flow of gas to the orifice while the bubble size is almost constant. This is referred to as the region of static bubble formation. At higher rates, generally above 500 bubbles per minute, the volume of the individual bubbles formed increases with increasing rate of flow of the gas supplied to the orifice while the frequency of formation remains almost constant. This is known as the dynamic region. The work described in this paper is limited to studies made in the static region. While the bubble is growing but still attached to the orifice, the adhesive force due to surface tension is
ad
COS
e
(1)
where d is the orifice diameter, u is the liquid-vapor surface tension, and 8 is the contact angle between liquid, solid, and vapor. For all the systems used, the liquid wetted the orifice readily so that the contact angle was assumed to be zero and cos 8, therefore, equal to unity. The buoyant force may be written as V(P1
-
P,)9
(2)
where V is the bubble volume, p1 is the liquid density, p g is the gas density, and g the acceleration due to gravity. At instant of rupture these forces may be considered equal:
V
(PI
-
p,)g
=
(3)
If the volume of the bubble is considered to be equal to the volume of a sphere of diameter, D, and p g is small compared with p l . then n- 0
3
--g-
pig =
nd u
(4)
a constant for any particular gas-liquid system a t a fixed temperature. For air bubbles formed in water a t 20” C. V/d = 0.231 sq. cm., ideally. However, Datta, Napier, and Newitt ( 1 ) report results for this system ranging between 0.17 and 0.44. In the same paper a comparison is made of the results of Maier (6),Owen (Y), and Swinden (8). Considerable variation is also evident in their work which gave values of V/d extending from 0.04 to 1.0. Eversole, Wagner, and Stackhouse (3) measured bubble volumes a t rates of formation between 40 and 90 bubbles per second. Under these conditions the mechanism of static bubble formation was apparently not applicable. This is indicated by their results which gave values of V/d between 0.114 and 0.628 sq. cm. Guyer and Peterhans ( 4 ) investigated the effects of fluid properties on bubble size using 20 liquids. Most of their data are taken a t a frequency of one bubble per second. For the airwat,er system values ranged from V/d = 0.136 sq. cm. a t an orifice diameter of 0.264 cm. to V/d = 0.227 a t an orifice diameter of 0.0045 cm. The over-all trend in their data indicates that V/d increases with decreasing orifice diameter. However, for orifice diameters between 0.1 and 0.014 cm. the values of V/d decrease from 0.180 t o 0.168sq. cm. for no apparent reason. Recent work by van Krevelen and Hoftijzer ( 5 ) measuring bubbles formed from capillaries a t rates less than one bubble per second check the theoretical results much better. Twentytwo runs with air and water gave values of B/d between 0.207 and 0.270 and an average value of 0.246 sq. cm. Davidson ( d ) , who reports data over a wide frequency range, is one of the few investigators who has studied the effect of orifice geometry in bubble size. His results indicate a relationship between the size of bubble formed and the upstream volume of the gas chamber leading to the orifice. Experimental equipment and technique are outlined
This equation may be rearranged and expressed in terms of dimensionless groups
The experimental equipment is shown schematically in Figure
A number of observers have studied gas bubble formation a t circular orifices. -4convenient method of comparing their results is to express them in terms of the ratio of the bubble volume, V , to the orifice diameter, d . This ratio V/d (Equation 3 ) is
The backflow check is used to prevent the liquid in the humidifier from flowing back to the surge tank. The general control valve, 4, gives an approximate setting while the fine control valve, 5, gives close adjustments and uniform flow control. The length of pipe between control valve, 5, and the orifice chamber is approximately 3 feet: f/8-inch galvanized pipe is used throughout the system. The liquid bath consists of a large glass container.
1. The gas enters the surge tank a t approximately atmospheric pressure after being reduced from pressures ranging between 35 and 1500 pounds per square inch. It then flows to the humidifier - - 1.82 (1)1’3 (5) where it is saturated with the liquid being used in the system. d Sd2 P1
1
Preaent address, Wright-Patterson Air Force Base, Dayton, Ohio.
October 1955
INDUSTRIAL AND ENGINEERING CHEMISTRY
2081
ENGINEERING, DESIGN, AND EQUIPMENT
Table 1. Orifice Number
C
Cm. 0.201 0.243 0.293 0.326 0.361 0.400 0.438 0.477
Cm. 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.87
0
Cm. 3.81 3.81 3.81 3.81 3.81 3.81 3.81 3.81
1
Cm. 1.27 1.27 1.27 1.27 1.27 1,27 1.27 1.27
4
t
Cm. 2.54 2.54 2.64 2.54 2.54 2.54 2.54 2.54
h IO
The collecting system, consisting of a funnel and inverted buret is simple but adequate. All orifices are of brass stock and have dimensions indicated in Figure 2 (Table I). The orifices are cleaned thoroughly before each run to ensure complete wetting. Most of the runs were made with air and liquid systems of water, water-ethanol, sugar-water, Drene-water, ethylene glycol, and Wesson Oil, all a t room temperature. Carbon dioxide and hydrogen were also used in some runs with water. Each run for a given orifice and fluid system consisted of 3 to 6 shorter runs of 50 bubbles each. The cumulative bubble volumes were determined from buret readings and the average value taken. The results are given in Table 11.
Figure 1. 1 2 3 4 5
= Backnow check = Humidifier = General control valve = Fine control valve
Average Bubble Volumes and Diameters Assuming Perfect Spheres 2
V, cu. om. D , cin.
0.0420 0.431
0.0650 0,472
V , CU. om.
D, om.
0.0340 0.402
0.0520 0.463
Water-Hydrogen, 84' F. 0.0720 0.0830 0.0980 0.516 0.541 0.572
0.1160 0.605
0.1310 0.630
0.1400 0.644
V , cu. om.
D , om.
0.0210 0.342
0.0270 0.372
95% Ethanol-Air, 87' F. 0,0380 0.0440 0.0495 0.417 0.438 0.455
0.0520 0.463
0.0580 0.480
0.0600 0.486
V, cu. cm.
0.0280 0.377
0.0432 0.435
7.5% Ethanol-Air, 89' F. 0.0580 0.0680 0.0820 0.480 0.506 0.539
0.0900 0.556
0.1040 0.683
0.1150 0.603
V,
em.
0.0240 0.358
0,0355 0.408
15% Ethanol-Air, 91° F. 0,0480 0.058.5 0.0880 0.451 0.481 0.506
0.0800 0.535
0,0880 0.552
0.1003 0.576
V, cu. om. D , om.
0.0230 0.353
0,0333 0.3990
Ethylene Glycol-Air, 84O F. 0.0410 0.0483 0.0563 0.475 0,428 0.452
0.0660 0.501
0,0740 0.521
0.0827 0.540
V, CU. om.
0.0320 0.394
0.0480 0.451
25% Sugar-Air, 89" F. 0.0740 0.0870 0.0628 0.493 0.521 0.550
0.1020 0.580
0,1080 0.591
0.1240
0.0920 0.560
0.1050 0.585
0.1180 0.608
0.0920 0.560
0.1023 0.580
0.0620 0.491
0.0740 0.521
D , cm.
6
7
8
0.1107 0.595
0.1203 0.612
0.1360 0.638
D, om.
V, cu. om.
0.0360 0.410
0.0460 0.444
45% Sugar-Air, 89O F. 0.0600 0.0670 0.0796 0.486 0.504 0.533
V, cu. om.
D,om.
0.0362 0.410
0.0425 0.433
0.1% Drene-Air 8 6 O F. 0.0627 0.0618 0.0710 0.490 0.514 0.467
0.0356 0.547
D,om.
V, ou. om.
0.0200 0.337
0.0243 0.359
1.0% Drene-Air, 86' F. 0.0520 0.0340 0.0460 0.463 0.402 0.444
0.0590 0.483
V, cu. om. D , om.
0.0260 0.368
0.0297 0.384
Wesson Oil-Air, 84' F. 0.0363 0.0400 0.0470 0.411 0.424 0.448
0.0550 0.472
2088
CY
=
1.73
This equation indicates the extremely slight effect of viscosity on bubble diameter so this term was dropped from a second dimensional analysis which resulted in
1
D , om.
b = -0.24
(7)
Bubble
CU.
6 = Gas thermometer = Orifice = Buret = Funnel = Liquid bath and tank
7 8 9 10
Rewriting the equation without the use of the dimensionless groups on the right hand side
(60 bubbles/min.) Orifice K'umber 3 4 5 M'ater-Air, 84' F. 0.0703 0,0880 0,0980 0.512 0.539 0.572
D, cm.
--
The values of the constants as determined from the experimental data by the method of least mean squares were a = 0.25
Relationship between the bubble diameter, D, and the properties of the system was investigated using dimensional analysis. The independent variables chosen were the diameter of the orifice, d, liquid density p ~ surface , tension, u, liquid viscosity, p , and the acceleration due to gravity, g. The following equation may be obtained using any consistent set of units:
fE3
Diagram of apparatus
= Surge tank
Dimensional analysis i s used to correlate results
Table II.
1
Principal Orifice Dimensions
d
0.619
The constants were determined from the best fitting straight line plotted through the data as shown in Figure 3. All the points shown on this figure were determined a t a frequency of 60 bubbles per minute using long-necked orifices. The standard deviation of the percentage error in fitting the straight line to the data is 4.0%. The results obtained with the airwater system are shown in Table 111, expressed in terms of the ratio of the bubble volume, V , to the orifice diameter, d. This measured ratio increases from 0.209 to 0.285 with increasing orifice diameter, 0.201 and 0.477 cm. These results tend to confirm the approximate applicability of the equations derived assuming static bubble formation. The effect of bubble formation is shown in Figure 4 where bubble volume is plotted as a function of frequency (bubbles per minute) for various systems. In all cases there is a tendency for the bubble volume to increase with frequency. The kinetic energy effect due to the higher velocity of the gas flowing into the bubble a t higher flow rates tends to dislodge it a t smaller bubble volumes. However, this apparently is more than compensated for by the greater amount of gas flowing into the bubble during the breakoff period.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 41, No. 10
ENGINEERING, DESIGN, AND EQUIPMENT
0 14
1
i
0
L
0.13
0.12
0.1I
t
I Figure
2.
0.10
Water
Q.OE -
Typical orifice
0.00
The effect of the properties of the gas on bubble size is indicat d in Figure 5. Although there is considerable difference in the properties of air and hydrogen the resulting bubble volumes are almost identical. Data were also taken using carbon dioxide bubbles in water but the effect of dissolved carbon dioxide made it difficult to determine the surface tension of the water so that the data were of little value for this comparison. Data were taken on the formation of air bubbles in Drenewater solutions of 0.1 and 1.0 wt. % concentrations. The results are shown in Figure 6 compared with data taken for airm-ater on the same orifice. The static surface tension, measured on a D u Noiiy tensiometer, of the 0.1% solution was 30.6 dynes per cm. and for the LOTosolution was 26.0 dynes per cm. While
0.12
0.2
-
0.4
Water Air Water Hydrogen W a t e r - C a r b o n Dioxide 95 Wt. % Ethanol- Air I5 Wt. Ye Ethanol Air 7.5 Wt. 'L Ethanol - A i r
-
0.8
0
E i h y l e n e Glycol - A i r
c+ p A
2 5 Wt. % S u g a r - A i r 45 W t . % Sugar - A i r 1.0 W t . % D r e n e - A i r Wesson O i l - A i r
v
Figure
October 1955
Q6
3.
Correlation of data
-
- Air
i
25 W t . % Sugar - Air
d'
Wesson Oil -Air
7
-
0.07 0
25
50
75
100
125
BUBBLES PER MINUTE
Figure 4.
Effect
of
frequency on bubble volume
these two values vary by only a small amount, the effect of the two different concentrations on bubble size are quite different. The more concentrated solution contained sufficient surface active agent so that the measured surface tension was probably very nearly the same as the dynamic surface tension. This is indicated by the fact that bubble frequency had almost the same effect on the bubble volume in 1% Drene solution as it did on bubbles in pure water. Further confirmation of this was obtained when the data for the 1% solution were plotted in terms of the dimensionless groups as shown in Figure 3. Using the measured static surface tension as part of the group (u/gd2pL)1 these data have been brought together in a single correlation 1.0 1.6 with the data for all the pure substances and nonsurface active mixtures. The 0.1% Drene solution showed a marked increase in bubble volume a t high A frequencies indicating the lesser extent of 4 surface orientation occurring during the L rapid formation of new surface. However, X at low frequencies the bubble volume of the 0.1 wt. yosolution approached that of the 1.0 wt. yo solution indicating that,
INDUSTRIAL AND ENGINEERING CHEMISTRY
2089
,
ENGINEERING, DESIGN, AND EQUIPMENT
I
rn
I
O'I3
-
0.12 0
V
u,
0.11
W
B
3 J
9
0.10
J W
0
1 2 m m
Figure 5.
0.5
Effect of gaseous density on bubble volume
Water - A i r
I
0
Figure 0.10
0.09 -?
0
0.08
- 0 0 Wt. % Orene
x
0.1 W t . % D r e n e
o
Wt.% Drene
A
- 1.0
W
3
0.07
> W
-I
0.06
2
m. Orifice 5
0.05
System
0.0e 2
THROAT
0,
Orifice 7
0.09
0.3 a4 ORIFICE DIAMETER (CM.)
0.2
7.
3
LENGTH
4
5
(CM.)
Bubble volume versus throat
length
The properties of the gas and the viscosity of the liquid have no effect on bubble size. Frequency of formation has a moderate effect with higher frequencies giving larger bubbles. This may account for some of the discrepancies in the previous literature that have been observed even a t low frequencies. The effect of surface a,ctive agents could be predicted if the concentration of the agent were large enough to give rapid orientation. For low concentrations longer orientation times are required with the result that the dynamic surface tension of the system cannot be determined except at low frequencies where it approaches the static surface tension. The effect of orifice length is negligible except where the throat of the orifice is somewhat shorter than the orifice diameter. There is a slight effect of orifice diameter on bubble size with larger diameter orifices giving higher values of the ratio V / d than smaller diameter orifices. This effect is probably related to the effect of frequency on bubble formation in that the larger orifices permit a greater flow of gas into the bubble during the breakoff period. Acknowledgment
0.04 0
25
50
75
100
125
BUBBLES PER MINUTE
Figure
6. Effect of frequency on volume using surface active agent
when more orientation time was available for the dilute solution, its bubble surface exhibited a dynamic surface tension approaching its static surface tension. The final variable studied was orifice geometry. Bubble size is obviously a function of orifice diameter as shown in Equation 5. Not shown in this equation is the effect of orifice throat length (dimension 1 in Figure 2). An orifice 0.438 cm. in diameter with a throat length of 4.6 cm. was run a t the rate of 60 air bubbles per minute in water. The throat length was then decreased by drilling it out between successive runs and the results obtained are shown in Figure 7 . The effect was negligible until t.he throat length was approximately 0.33 cm. a t which point the bubble volume decreased sharply. All data other than that shown in Figure 7 were taken on orifices with a throat length of 1.27 cm. Conclusions
The data for low frequency bubble formation may be satisfactorily correlated in terms of bubble diameter, orifice diameter, and the physical properties of the liquid as shown in Equation 8.
The authors gratefully acknowledge the assistance of Ronald P. Lance in the preparation of this paper. Nomenclature
D = diameter of bubble, cm. d = diameter of orifice, cm. g = accelerator due to gravity, 980 cm./(sec.)z V = volume of bubble, cu. cm. u = surface tension of liquid, dynes/cm. p o = gasdensity p~ = liquid density gm./cu.cm. A, = liquid viscosity gm./(cm.) (sec.) e = contact angle a t liquid-gas-solid interface literature cited
(1) Datta, R. L., Napier, D. H., and Newitt, D. M., Trans. Inst. Chem. Engrs. (London), 28, 14-26 (1950). (2) Davidson, Leon, Ph.D. thesis, Columbia University, New York, 1951. ( 3 ) Eversole, W. G., Wagner, G. H., and Stackhouse, E., IND.ENG. CHEM.,33,1459-62 (1941). (4) Guyer, A,, and Peterhans, F., Helv. Chin%.Acta, 26, 1099-1107 (1943). (5) Krevelen, D. W. van, and Hoftijrer, P. J., Chem. Eng. P r o p . , 46,29 (1950). (6) Maier, C.G., U. S. Bur. Mines Bull. 260, 62-120 (1927). (7) Owen, J. S.,Engineering, 112,458 (1921). ( 8 ) Swinden, N., Proc. Chem. Eng. Group, 10, 116 (1928). RECEIVED for review August 7, 1953.
ACCEPTED May 5, 1955.
END OF ENGINEERING, DESIGN, AND EQUIPMENT SECTION
2090
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Vol. 47, No. 10
