November, 1941
INDUSTRIAL AND ENGINEERING CHEMISTRY
perature and rate. When a level (about two thirds gage) is obtained in the reboiler, full heat is applied to the reboiler, and bottoms product is slowly removed to keep the level constant. The rate of removal decreases as reflux increases. As soon as reflux is obtained at the condenser, the inner lagging heat is cut off and enough heat to keep the column adiabatic is applied through the outer windings. It has been found that a pressure of about l/a-inch gage in the reboiler is satisfactory when equilibrium has been reached.
Determination of Efficiency. Two distillations of mixtures of cyclohexane and toluene were run to determine the efficiency of the unit. The data obtained are given in Tables I and 11. During these runs the whole glass condenser and take-off assembly was heavily lagged. Reflux ratio was calculated from the inlet and outlet temperatures and volume of the condenser water. I n run 1 the rate of feed was 1090 cc. per hour, and its composition was 31 mole per cent methylcyclohexane. The overhead product had a composition of 91.9 mole per cent methylcyclohexane and the bottoms product, 14.7 mole per cent. The reflux ratio (total moles of vapor above feed point to total moles of overhead product) was 9.32to 1. I n run 2 a somewhat greater throughput of 1182 cc. per hour was obtained. The feed had a composition of 22.4
1459
mole per cent methylcyclohexane. The overhead and bottoms products had 91.5and 10.75 mole per cent methylcyclohexane, respectively. The reflux ratio was calculated to be 11.73 to 1. By applying McCabe and Thiele's graphical method (2) for calculating the number of theoretical plates in a column under continuous operation a t equilibrium, values of fifty-six and fifty-two plates were obtained in the two runs. These values include the fractionating capacity of the condenser and reboiler.
Typical Distillations. Table I11 gives the results of a few of the distillations that have been run in the unit. The data represent standard Engler distillations with the exception that thermocouple was substituted for the thermometer.
Acknowledgment The writers wish to acknowledge aid received from M. R. Fenske who provided the packing used in the column and the equilibrium curves required for calculating the results.
Literature Cited (1) Kirkpatrick, S. D., chem. & Met. Eng., 46, 400 (1939). (2) McCabe and Thiele, IND.ENQ.C H ~ M 17, . , 606 (1925).
Rapid Formation of Gas Bubbles in Liquids, Gas bubbles were formed in pure liguids and solutions by passing nitrogen gas through submerged orifices (radii of 0.0069 to 0.017 cm.) at rates of 0.125 to 0.7 cc. a second. Bubble size was determined from stroboscopic frequency measurements and rate of gas flow, and from micrometermeasurements of the photographic images. As the bubble frequency was relatively constant in all pure liquids, the bubble volume in pure liquids was found to depend principally on the rate of gas flow. GENERAL study of the production of small gas bubbles in liquids by a submerged orifice was carried out by Ralston and Maier (4) because of its importance in a mining process. Although more enlightening than subsequent studies, the methods used became inexact in the practical region of high rates of gas flow. Schnurmann (6) concluded, after an exhaustive qualitative study of many pure liquids and solutions, that the size of bubbles formed by passing a gas through a porous diaphragm into a liquid is dependent on the viscosity of the liquid in the case of pure liquids and solutions of nonelectrolytes. However, he concluded that this effect is altered in the case of solutions of electrolytes because of the electrostatic nature of the bubbles.
A
W. G. EVERSOLE, G. H. WAGNER, ANI) EUNICE STACKHOUSE The State University of Iowa, Iowa City, Iowa
Calling the sire of bubbles formed in water large and comparing other bubbles to them, Schnurmann used a category of large, medium, and small in classing bubble sizes. The results of the more quantitative investigation of Halberstadt and Prausnitz (%)indicate that the surface tension of the liquid is an important factor in determining bubble size. The object of this investigation was to make a more systematic study of the factors which influence bubble sire in the practical range of high rates of gas flow. In order to accomplish this, a single glass capillary was used in preference to a porous diaphragm, and the formation of different sized bubbles due to variations in pore size was thus eliminated. Nitrogen was used throughout as the gas phase, and all measurements were made with liquids in an open vessel at atmospheric pressure.
Apparatus Many glass capillaries were made by drawing out capillary tubing of 1-mm. boFe in the blast lamp and breakin it off at points at which the bore appeared suitable for use. %he tip of each was' then ground until the face was flat and perpendicular to the axis of the tube. The radius of the orifice at each capillary tip was measured with an ocular micrometer, and four capillaries approximately 1.1 cm. in len th were selected which were circular to *0.0002 cm. at the tip. %he polished tip was submerged t o a
the dimensions were determined from ocular micrometer measurements of the photographic
OF BUBBLES IN PURE LIQUIDS TABLEI. FORMATION
VfQ Cc./sec.
Y
No./eec.
P Cm. Xg
-
n-Butanol (T = 25; Y. 0.105 0.164 0.218 0.301 0.311 0.387 0.426 0.525
.Nitrobenzene 0.132 0.217 0.243 0.292 0.341 0.372 0.420 0.456
24.2; p = 0.8064; P h Pressure = 0.64) 0.71 0.07 0.87 0.06 1.02 0.05 1.29 0.05 1.39 0.05 1.63 0.04 1.77 0.04 2.15 0.04
54.0 47.7 42.2 48.4 51.2 45.8 51.2 51.6
Ethanol (T = 24.8; u 0.118 0.151 0.180 0.219 0.257 0.320 0.378 0.439 0.479
=
44.6 44.6 33.2 44.3 42.5 45.5 39.5 41.1 46.0
-
P,
Pz
Cm.Hg Cm.Hg = 0.24; Vapor
0.31 0.52 0.72 1.05 1.10 1.41 1.58 2.05
o,09 0.05 0.01 -0.05
-!:
-0.09 -0.18
21.9; p = 0.786; P h = 0.24; v. P. = 5.9) 0.65 0.76 0.88 0.98 1.12 1.32 1.58 1.83 1.95
(2‘ 24.6; u 43.3; p 1.08 46.1 1.25 51.7 1.35 38.7 1.55 40.3 1.69 39.2 1.79 46.6 1.97 43.6 2.19 43.3
n-Propanol (T = 25; u 50.0 0,099 48.4 0.149 35.3 0.177 44.7 0.230 44.7 0.313 48.8 0.324 46.2 0.418
Pu Cm.H g
I
-
-
0.07 0.06 0.04 0.05 0.04 0.04 0.04 0.04 0.04
0.35 0.46 0.57 0.72 0.86 1.13 1.39 1.64 1.83
1.1983; Ph = 0.36; 0.39 0.11 0.69 0.10 0.81 0.09 1.02 0.08 1.22 0.08 1.35 0.08 1.55 0.07 1.72 0.07
A::!-
0.03
-0.03 -o,02
1:::; -0.09 -0.19
v. P. N 0 )
Method I with Pure Liquids Measurements were made by method I, using glass capillaries with radii varying from 0.0069 to 0.017 em., in pure liquids and solutions. The results with an orifice radius of 0.0085 em. are shown in Table I for four pure liquids. P was read from the manometer when the gas was discharging a t a steady rate through the liquid. P,, was determined in the same way when the gas was being discharged at the same rate into air at atmospheric pressure. The rate of gas flow into air was measured by a carefully calibrated capillaryorifice flowmeter. Ph was calculated from the density of the liquid and the depth of immersion of the tip (4.1 em. in all cases). P , was estimated from the surface tension of the liquid and the time average of the radius of the bubble during its formation. Assuming a spherical surface, the excess pressure in the bubble resulting from surface tension is given a t any time by 2a/rt (1). If it is assumed that the volume of the
0.22 0.10 0.09 0.08 0.03 0.00
-.0.01 0.04
23.4; p = 0.8; P h = 0.24: V. P. = 2.01) 0.00 0.07 0.29 0.60 -0.04 0.06 0.45 0.71 0.05 0.57 0.00 0.86 -0.04 0.05 0.75 1.00 -0.22 0.04 1.11 1.17 -0.08 0.04 1.14 1.34 -0.21 0.04 1.55 1.62
depth of 4.1 cm. in the liquid. The rate of gas flow was regulated by means of a reducing valve, needle valve, and series of stopcocks. The pressure difference under which the gas was being discharged through the apparatus was measured t o 1 0 . 0 1 em. by an open mercury manometer (Figure 1). Two methods were used in this study. In method I the bubble volume was determined from stroboscopic frequency measurements of the bubble stream and the rate of gas flow. A 20-cc. buret, filled with the same liquid as that in which the bubbles were forming and inverted over the capillary orifice, was used to find the rate of gas flow; the time necessary to displace approximately 15 cc. of liquid from the buret was measured with a stop watch. The buret and stop watch could be read to 0.05 cc. and 0.1 second, respectively. An overflow on the liquid container maintained a constant head. This method cannot be used if the frequency is irregular or if there is too much bulk turbulence in the liquid. The gas volume was measured when saturated with the vapor of the liquid being used. It was corrected to “dry” volume by using the vapor pressures of the different liquids. This gives the rate of gas flow through the capillary and the volume of the .“dry” bubble a t atmospheric pressure. Actually the volume of the rising bubbles will increase slightly as the hydrostatic pressure decreases and the bubbles become saturated with vapor. In method 11, which is applicable to all conditions of flow, the
Pure ethanol
40.7% ethanol
FIGTJRF, 2. PHOTOGRAPHS ( X 2.3) OF BUBBLE STREAM WEBRE V, &% 0.22 Cc. PER SECOMD, AND T = 23.6’ C.
INDUSTRIAL AND ENGINEERING CHEMISTRY
November, 1941
Vi E 0.16 cc./aec. ( A )
0.35 ( B )
( x 2.3) FIQURE 3. PHOTOGRAPHS
0.47 (0) OF
= rb(Yt)'/a
30 dt = - dynes/sq. om. la
3u P u = -Tbx - 13.53 cm.Hg.
As revealed in Table I, the bubble frequency is surprisingly constant, rarely deviating by more than * 0 bubbles per second from a value of 45. Table I1 shows that the same frequency was found for all other tips used with one unexplained exception. This exceptionally high value probably resulted from some unusual condition a t the tip during this particular measurement. I n other measurements this tip gave approximately the same range of frequency as the others. TABLE11. EFFECTo CAPILLARY RADIUSON BUBBLEFREQUENCY IN n%RoPmoL (v*= 0.00639 c c . ) ra, Cm. 0.0069 0.0085 0.0122 0.0170
v,
0.85 ( E )
BUBBLES IN 70 PERCENTETHANOL AT VARIOUS RATESOF FLOW
bubble increases at a constant rate from a negligible value a t zero time to a value V! at time l / v ,
or
0.6 ( D )
1461
No./Seo. 42.6 40.0 57.0 42.9
Thus, in so far as the assumption of a constant bubble frequency is justified by the data, it may be concluded that the volume of dry gas in a bubble is directly proportional to the rate of gas flow, and is independent of the properties of the (pure) liquid and the size of the capillary a t which the bubbles are formed. A steady state of flow which was essential for stroboscopic study could be obtained only between the lowest and the
highest rates of flow shown for each liquid in Table I. The upper limit was probably reached as the result of excessive turbulence in the liquid. The lower limit will be discussed in connection with the pressure effects. The authors' extended efforts to devise a theory to account for a constant bubble frequency have been without success. The values of P, P,,Ph,and P, are included in Table I to indicate their relative magnitudes under the experimental conditions used and require little comment. P is the sum of all pressure effects associated with the process. The values of P,, depend on the viscosity and density of the gas and on the dimensions of the capillary and the rate of gas flow. Pu is relatively small but varies significantly with rate of flow. Ps,which includes all pressure effects not otherwise accounted for, is small but probably significant. Other pressure effects, which may reasonably be assumed and may largely compensate each other, can be mentioned. The rapidly varying volume of the bubble a t the tip requires the oscillation of the liquid in the immediate vicinity a t a frequency equal to that of bubble formation. The energy required to set up and maintain this liquid motion may be appreciable. On the other hand, a t the instant the neck of the bubble pinches off, the newly released bubble is left with a cone of gas pointing downward. This tail quickly snaps up even beyond the equilibrium point and sometimes sends a cone of liquid up through the bubble. It seems possible that the time required for this contraction may be related to the maximum bubble frequency. This sudden motion resulting from surface tension may well produce a reduced pressure a t the tip of the capillary and help to initiate the formation of the next bubble. It may also account for the negative values of P,. It is also possible that a part of the kinetic energy of the gas stream emerging into the expanding bubble may be converted into pressure energy which would help to inflate the bubble. At any rate, a considerably higher pressure difference is required to form the first bubble than to maintain a
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1462
namic surface tension of the solutions probably varies with the rate a t which the surface area of the bubble is changing may be a factor in this phenomenon.
TABLE111. FORMATION OF BUBBLES IN AQUEOUSSOLUTIONS OF ETHANOL ( T ~= 0.0085 Cm.)
9 Co./sec.
vi x
Y
No./sec.
20.2% Alcohol by 0.151 0.167 0.249 0.291 0.298 0.375 0.435 0.501
Wt. (T = 24.4; a
=
Pa Cm. H a
PZ C m . Ha
32.25; P = 0.966; Ph = 0.29; Vapor
Pressure = 4.41)
42.9 56.6 49.6 57.1 50.0 44.7 44.5 47.8
40.7% Alcohol 0.115 0.152 0.202 0.251 0.295 0.339
P Cm.Ha
103
cc.
(T = 24.4; u 55.5 81.0 84.6 89.6
89.6 92.5
-
70.070 Alcohol (T 24.4; u 0.117 40.1 0.171 91.0 0.19s 85.2 0.220 75.0 0,262 64.5 0.287 50.1 0.354 48.5 49.3 0.417 0.419 50.5
0.98
3.52 2.95 5.02 5.10 5.96
1.10 1.30 1.47 1.57 1.85 2.12 2.45
8.39
9.78 10.48
0.08 0.07 0.07 0.07 0.06 0.06
0.13 0.20 0.09 0.09 0.17 0.13 0.14
0.06
0.16
0.08
29.63; p = 0.930; Pfi = 0.28; V. P. = 5.36) 2.07 0.72 0.09 -0.01 1.88 0.84 0.09 -0.01 2.39 0.96 0.09 -0.08 2.80 1.14 0.08 -0.09 3.29 1.31 0.08 -0.08 3.66 1.52 0.08 -0.05 = 25.71; 2.92 1.88 2.32 2.93 4.06 5.73 7.30 8.46 8.30
II
= 0.863; Pfi = 0.26; V. P. = 6.17)
0.71 0.86
0.08 0.09
-0.01
0.08 0.07
0.03 -0.02 0.04 0.02 -0.06 0.05
0.06 0.06
1.91
0.05 0.05
1.80
0.00 -0.02
0.08
0.99 1.07 1.21 1.37 1.62
steady bubble stream a t the minimum rate. This effect largely determines the lower limit of V, a t which a steady stream of bubbles could be obtained in these experiments. If the gas from the high-pressure source was admitted to the apparatus a t a slow rate, the pressure would slowly build up to the point required to form the first bubble. The accumulated pressure then would form a stream of bubbles until the pressure dropped too low to maintain it. The result was an intermittent bubble stream. This effect could be overcome by reducing the volume of gas behind the capillary (or by increasing the length of the capillary) so that the flow of gas would not be sufficient to complete the formation of a second bubble before the effect of the first had disappeared. Under such conditions the bubble frequency a t low rates of flow would probably be almost proportional t o the rate of flow and the bubble volume approximately constant. With the apparatus used, it was found impossible to form a stream of bubbles in water which was suitable for stroboscopic observation. Therefore water was not used as a pure liquid in this work. It seems probable that a smooth bubble stream could be obtained in water by using a longer and perhaps smaller capillary.
Method I with Alcohol Solutions Table I11 shows that the frequency of bubble formation in solutions is, in general, higher and much less constant than in pure liquids. Also V! goes through a minimum with increased rate of flow. The minimum bubble volume was checked in the 70 per cent solution by the photographic method and was found to occur a t the same rate of flow. Ralston and Maier (4) also found similar minima when using pure water with various capillaries. In the alcohol solutions the bubbles are probably charged, as shown by McTaggart (S), which may have some effect on the size as suggested by Schnurmann (5). The pressure relations in the solutions are similar to those in pure liquids, as shown by the relatively small values of P,, the pressure difference not accounted for by the viscosity of the gas, the surface tension of the liquid, and the hydrostatic pressure a t the tip of the capillary. However, the values of E', fail to show the same regular decrease with increasing rate of flow as in the case of pure liquids. The fact that the dy-
Vol. 33, No. 11
Method I1 with Pure Liquids and Solutions Figure 2 shows a bubble stream in pure and in 40.7 per cent ethanol. The rate of flow is the same in both. The smaller bubble volume resulting from the higher bubble frequency in the solution is easily observed. Figure 3 shows the bubble stream in 70 per cent alcohol a t different rates of flow. A corresponds very nearly to the minimum bubble volume for this solution. The progressive increase in the size of the bubbles with increase in rate of flow is clearly shown. This results partly from the increase in rate of flow and partly from the decrease in frequency as shown in Table 111. C is a t about the upper limit for stroboscopic observation. D and E are considerably above this limit, but the photographs seem to show that the bubble volume is still increasing. The small bubbles are torn from the large primary bubbles by the violence of the motion in the liquid. The kinetic energy of the emerging gas stream is probably a factor. Also, the bubbles rise for some distance parallel to the capillary even a t the higher rates of flow.
Summary 1. When a smooth stream of gas bubbles is formed in a pure liquid, the bubble frequency is relatively independent of the rate of gas flow, the properties of the liquid, and the size of the capillary a t which the bubbles are formed. Under these conditions, therefore, the bubble volume is proportional to the rate of gas flow. 2. I n solutions of alcohol in water, the bubble frequency is higher than in pure liquids and varies much more with rate of gas flow. 3. The bubbles rising in a stream through a liquid are flattened more in liquids of low surface tension.
Nomenclature g
P
= =
Ph =
Pu
=
P7
=
P, = rb
=
rc
=
yt
=
acceleration of gravity, cm./sec./sec. pressure above atmospheric on nitrogen gas in apparatus, cm. Hg hydrostatic pressure at submerged tip, cm. Hg av. pressure resulting from surface forces during time of formation of bubble, em. Hg pressure difference required t o discharge gas from capillary into air at atm. pressure, cm. Hg P-(Ph PV Pu) = pressure difference not otherwise accounted for, em. Hg radius of bubble (assumedspherical), cm. radius of capillary orifice at ti of capillary, cm. radius of bubble being formelat capillary tip at time t,
+
+
cm.
time, sec. temperature, ' C. volume of bubble (saturated with vapor), cc. Vg = volume of bubble, corrected t o zero vapor content, cc. V, = rate of gas flow (saturated with vapor), cc./sec. V; = rate of gas flow through Capillary (zero vapor content), t
= T = Vb =
cc./sec.
frequency of bubbles, number/sec. = density of liquid, grams/cc. = surface tension of liquid, dynes/cm. =
a
Literature Cited (1) Adam, N. K., "Physics and Chemistry of Surfaces", 2nd ed., p. 8 , London, Oxford Unlv. Press, 1938. (2) Halberstadt, S., and Prausmtz, P. H., 2. u w e w . Chem., 43, 970 (1930). (3) McTaggart, H.
A.,Phil. Mug., 27, 297 (1914). (4) Ralston, 0. C., and Maier, C. G., U. S. Bur. Mines, Bull. 260 119271.
(5) Schnurmann, R., Z. physik. Cheh., A143,456 (1929).
