RISE OF AIR BUBBLES IN OILS
431
T H E RISE OF AIR BUBBLES I N LUBRICATING OILS J. V. ROBIYSOX' Department of Chemistry, Stanford r'nivei sill/, California Received J u l y 16,1346
It was the purpose of the experiments described in this report to expose thc mechanism by which additives in a lubricating oil stabilize the "emulsified" air incorporated into the oil ciruculated through a high-speed gear pump. By measuring the velocity of rise of air bubbles in a column of quiescent oil, with and without additives, the presence or absence of thick layers of liquid on the bubble surface and moving with the bubbles could be ascertained. The presence of such thick layers of liquid moving vith the bubbles in oils containing additives is demonstrated in the experiments described in this report, and their absence is demonstrated in an oil containing no additives. ST.\IBOLS
Stokes's law: V = 2ga2(di - dz);9q V = velocity of fall of spherical body in viscous medium (cm./sec.), g = acceleration of gravity = 980 dynes per gram, a = radius of spherical body (cm.), d, = density of spherical body (g./cc.), d2 = density of medium (g./cc.), q = absolute viscosity of the medium (poises), do = density of the oil (0.9 g./cc. a t 25"C.), d. = density of the air (0.00129 g./cc. at 25"C.), Q, = effective density of air bubble surrounded by a rigid shell of oil, r,, 0. = radius and diameter, respectively, of the air bubble, measured optically, r,, D: = radius and diameter, respectively, of the air bubble, calculated from Stokes's law from its observed velocity of rise, r,,, D, = radius and diameter, respectively, of the rigid shell of oil surrounding the air bubble, v, = volume of air bubble = 47rrj/3, vo = volume of the rigid oil shell around the air bubble,
+
,0
Y
= vo 00, = kinematic viscosity = q/d2 or ?/do.
of the liquid medium or oil (Stokes),
THEORY O F THE RISE OF AIR BUBBLES THROUGH OIL
Applying Stokes's law to the rise of air bubbles through oil, dl becomes d., dz becomes do, and a becomes ra). Within 0.1 per cent, (Q - Q) = -Q. This approximation permits the substitution of the kinematic viscosity, P, for 'Present address: The Mead Corporation, Chillicothe, Ohio
432
J.
V.
ROBINSOK
?/(dl - dz). With these substitutions, the equation may be solved for the square of the bubble diameter:
(DL)’ = 18vJ-/g
=
0.0183GvT’
In oils containing no additives, the velocity of rise of air bubbles was proportional to the square of the observed diameter, in accordance with Stokes’s law. In oils containing additives an abnormally slow rise was observed, which may be accounted for by assuming that the air bubble is accompanied by a shell of oil (or additive, or both), thus increasing the resistance to passage of the bubble with no compensating increase in the oil displacement. It is desired to calculate the apparent radius of this shell. The effective density of the bubble with its shell is d, = (v.4 v,&)/v,. Considering the bubble as truly spherical, v, = 4m:/3, v, = 4&,/3, and vo = 47r(r03, - ra)/3. Stokes’s law becomes
+
and
r, = 2g(d0 - 4 ) r : h V Substituting Y for ?/do, and the approximation (do - &) = do, then r, = Zgr1/9vV. However, 9vV/2g = (rL)2;whence r, = &‘(r:)2. That is, the radius of the rigid shell of oil carried along by the air bubble is equal to the ratio of the cube of the observed radius of the air bubble divided by the square of the apparent radius calculated from the observed velocity of rise substituted into Stokes’s law. Similarly, D, = Df/(D:)?. The ratio Di/(DL)zis the factor by which the observed diameter is multiplied t o obtain the outside diameter of the rigid shell of liquid carried by the air bubble. The proportion of this shell is thus indicated for any size of bubble. EXPERIMESTAL XETHOD
.
Into oil contained in a 100-ml. graduated cylinder immersed in a water thermostat, air bubbles were released from an extended syringe pipet. Through a window in the back of the thermostat, illumination was provided by a lamp. Through another in front, the rate of rise of the air bubbies was observed. The time was measured for the passage of a bubble between each pair of 10-ml. graduations (equal to 1.90 cm.), using two stopwatches to make the record continuous. The bubble diameter was measured by comparison of its image with a calibrated ocular micrometer set in a travelling telescope, at a magnification of about ten times. The telescope was used also t o measure the vertical distance between the graduations on the cylinder. In the case of large bubbles, the diameter could be measured only once or twice during the rise, and the measurement required rapid manipulation. With small bubbles there was ample time for the observation, and the diameter of the bubble was measured between each pair of graduations.
RISE OF AIR BUBBLES I N OILS
433
The temperature was read from a thermometer graduated in O.l"C., immersed in the oil. Owing to absorption of heat from the illuminating lamp, the temperature of the oil rose about 0.2"C. per hour during the observation. The bubbles were formed in a capillary tube, with a U-turn on the end, which was inserted to the bottom of the cylinder. Bubbles were released from the tip when the plunger of the connected syringe was gently pressed. The position of the jet with respect to the cylinder wall is critical. If it is too far from the cylinder wall, the bubbles cannot be seen clearly; if it is too close to the wall, the bubbles run into the wall, according to Bernoulli's theorem. There are many sources of possible error in the measurements. The bubble diameter was measured with a maximum error, for the smallest bubbles, approaching 5 per cent. The magnification of observed horizontal diameter by the curved wall of the cylinder Tyas neglected; it varied if the bubbles deviated from
FIG.1. The apparatus
the same vertical path in their upward journey. Owing t o velocity pressure, the bubbles are actually not quite spherical. L-nfortunately, these two errors are additive. The timing of the bubbles was accurate to better than 1 per cent. The greatest error is caused by the convection currents in the oil. Despite 9 in. of water between the oil column and the light source, appreciable radiation was absorbed, causing small density and viscosity gradients in the oil. The relative viscosities of the oils used in the calculations were carefully checked and found precise within 5 per cent. Because of these variations and the small magnitude of the effect being sought, a large number of data. were necessary for valid comparison. RESULTS .13D DXSCLXSXOL-
The rise of bubbles in four oils was observed. One was a lubricating oil containing no additives. Two others \\-ere the same oil t o which foam-inhibiting compounds were added. The fourth was an oil containing lubricating additives.
434
J. V. ROBINSOX
The results of the measurements are expressed by the ratio D:/(DL)z. This ratio of the square of the observed diameter to the calculated bubble diameter is also the ratio of the observed to the calculated velocity of bubble rise and in addition the ratio of the outside diameter of a shell of oil carried by the bubble to the diameter of the bubble itself. Provided the absolute values of all constants used are exact and the measurements accurate, this ratio must be unity unless there is some difference between the bubble in actuality and a smooth sphere rising through a Kewtonian liquid. The results are summarized in table 1, in which are sho\\n average values, the average deviation from the average, and the number of determinations averaged (in parentheses). In oil A, containing no additives, bubbles behaved as expected, the rate of rise being directly proportional to the observed diameter. The data were homogeneous. The difference between the ratio of the squared diameters and unity in the case of oil A is ascribed to the accumulated absolute errors in the TABLE 1 -1ueraged oalues of U:/(D:)z* Oil 4,containing no additives.. . . . . . . . . . . . . . . . . . . Oil A, containing O.Oi5 per rent glycerol and0.025 per cent Aerosol O T . . . . . . . . . . . . . . . . . . . . . . . . . o i l A, containing 0.1 per c r n t of Daw Corning Fluid I Type ZOO.. . . . . . . . . . . . . . . . . . . . . . . . . Oil B, containing lubricating additives.. . . . . . . . .. ,
0.879 -i: 0.033 (45)
2.05 -i: 0.23
(16)t
1.35 i= 0.15 1.02 -i: 0.07
(21) (17)
*Figures in the table are averaged values of D : / ( D A ) z , plus or minus the average deviation from average, giving the number of measurements averaged in parentheses. t The oil column was not thennostated when these data were obtained, but t h e oil temperature was measured.
constants used and in the measurements themselves. Such errors should appear approximately proportionately in the other values in table 1, so that the relative values are significant. A phenomenon not shown by the averaged data is that the velocity of the bubbles rising through oils containing additives, in particular oil B, became slower as the bubbles rose. This effect was completely absent in oil A, which contained no additives. Care was taken to avoid having the bubbles rise too close to the wall, which they would then tend to approach, causing a decreasing velocity similar to that, observed. It is considered likely that t,he adsorbed material on the bubble, and hence the diameter of the shell moving with the bubble, increases as the bubble travels. Data illustrating the phenomenon are shown in table 2. These are consistent with the direct observation that thc additive material in oil B is greatly concentrated in the liquid collected when the froth formed by air bubbles rising through a column of the oil is collected and segregated. To illustrate further the homogeneity of the measurements and the absence of a changing velocity with time of rise, data for oil h containing no additive are shown in table 3. From the data in tables 2 and 3, the method of calculation may be followed in detail.
435
.RISE OF AIR BUBBLES IK OILS
These phenomena are of great interest theoretically as regards the structure of liquids. The additives in the oils add a shell to the air bubbles which can have a TABLE 2 Rise of air bubbles lhrouyh oil B U T I 0 OF
SQUARED IIAYETEBS
~-
30 40 50 60 70 80
21.8 23.5 25.4 29.0 33.0 37.5
0 0872 0 OS08 0 0740 0 0655 0 0575 0 0506
20 t o 30 30 to 40 40 t o 50 50 t o 60 60 to i n 70 t o 80
25.8 27.8 31 .O 35.5 41.6 45.4
0.0736 0.0664 0.0614 0.0535 0.0456 0.0419
20 30 40 50 60
41.6 46.0 54.6 50.2
0 0413 0 0342 0 0321
to to to to 60 t o i0 t o
20 30 40 50
tri 30 t o 40 t o 50 t o 60 t o 70 i0 t o SO
t 0 30 t o 40 to 50 t o 60 t o id io to 80
50 67 75 89 112 121
20 t o 30 t o 40 t o 50 to 60 to 70 t o
i8.4 89.1 100.4 120.9 155.6 169.2
10 30 40 50 60
30 -10 50 60 70 80
x
___
-~
10-4
(DL)*
6 5
0 ~
'
~
1
0 031h 0 02h4 0 0252 0 0212 0 0170 0 015; O.OZ~? 0.0214 0,0189 0.0157 0.0122 0.0112
176 163 151 132 116 102
6 5 3 6
0.921 0,992 1.04 1.15 1.27 1.48
23.4 23.4 23.4 23.4 23.4 23.4
11.35 11.35 11.35 11.35 11.35 11.35
0.0806 0 0749 0.0672 0.0584 0.0498 0,045:
154 143 128 111 95.0 87.2
0.936 1.01 1.13 1.30 1.41 1.49
23.3 23.3 23 3 23.3 23.3 23.3
11.45 11.45 11.45 11.45 11.45 11.45
0.0502
86.9 72.0 67.5 53 5 48 3
1.04 1.25 1.23 1.56 1.73
23 23 23 23 23 23
0.1198 0.1160 0.1140
- -,.-
0
11 05 1 0 0925 0 0857 11 05 0 0795 11 05 11 05 1 0 0695 1 0 0610 11 05 11 05 1 0 053i
0 12i3 0 1253 0 1234 0 1216 0 1234
u .uim
8
1
__ "C
sa.
0 0950
9 9 9 9 9 9
O.Oi99 0,0779 0.0760 0 .OiW
23 i 23.7 23.7 23.7 23.7 23.7
O.Oi22 0.0722 0.0703 0.0685 0.0665
23.5 23.5 23.5 23.5 23.5 23.5
0. O B l i
~
~
~
'
11.17 11.17 11.17 11.17 11.1; 11 17 11.30 11.30 11.30 11.30 11.30 11.30
~
0.0155 O.03ii 0.0354 0 0280 0 0253
,
--
0342 0.0305 0.0270 0.0228 0.0183 0.0169 0.0263 0.0232 0.0205 0.01il 0.0133 0.0121
1
i ~
~
4
5
65 58.2 51.5 43.5 34.9 32.2 50.2 44.3 39.2 32.6 25.4 23.1
1
i
1.03 1.15 1.24 1.40 1.66 1.79 1.04 1.18 1.33 1.51
1.85 1.91
* Each group of data set off by spaces represents a single bubble, observed over different intervals. diameter half again as great as the air bubble itself. This must mean that a gel-like structure, possibly a plastic solid, extends from the air interface far into the oil. The great extent of this structure (great in terms of molecular size)
436
J. V . ROBIXSOK
may be due principally to the motion of the bubbles. Similar experiments on the adsorption of solutes in aqueous solutions show that the concentration adTABLE 3 Ilise of air bubbles throuqh oil A
1 CAUXILATEI DLAMEIER INTERVAL
(GBADUAIIONS)*
ilSCOSlTY (v)
TIME
~
VELOCITY
412S'C.
'
,
I ~
,
30 40 60 70 80
18.4 18.4 36.3 19.2 19.0
0.1032 0.1032 0.1046 0,0990 0.1000
0,1198 O.lli9
T. 24.1 24.1 24.1 24.1 24.1
50 t o 60
19.6
0.0969
0.1140
24.7
8.55
20 to 30 30 to 50 50 to 70 70 to 80
21.0 40.0 38.6 20.8
0.0905 0,0950 0.0986 0.0914
0.1140 0.1102
24.7 24.7 24.7 24.7
30 to 40 t o 50 to 60 to
30.2 30.5 30.4 31.8
0.0629 0.0623 0.0625 0.0597
to 30 to 40 t o 60 to 70 t o 80
37.8 37.7
0.0503 0.0504
40.6 41 .O
0.0468 0.0464
20 to 30 40 to 50 50 to 60 60 to 70 70 to 80
45.0 46.2 47.3 48.6 50.4
20 30 40 50 60 70
64.0 65.7 66.2 67.1 70.4 71.1
SCC.
20 to 30 to 40 to 60 to 70 to
20 30 50 60 70
40 50
60 70
to 30 to 40 to 50 to 60 to 70 to 80
SQUARED
8.87 0.1090 ' 8.87 i 0,1090 8.87 0.1104 ' 8.87 0.1046 0,1057 8.87
x lo-'
U T I 0 OF SQUARED IIAYETERS
(0,)1
(4)'
168 168 170 161 163
0.858 0.858 0.846 0.869 0.853
0.0986
151.8
0.856
8.55 8.55 8.55 8.55
0,0920 0.0966 0.1003 0.0930
141.8 149.0 154.5 143.2
0.917 0.872 0.792 0.850
24.7 24.7 24.7 24.7
8.55 8.55 8.55 8.55
0.0640 0.0634 0.0636 0.0608
98.6 97.6 98.0 93.6
0.844 0.853 0.850 0.889
9.95 9.95 9.95 9.95 9.95
0.0595 0.0596
91.6 91.9
0.871 0.869
0.0554 0.0549
85.5
0.893
0.0874
22.1 22.1 22.1 22.1 22.1
84.6
0.y02
0.0422 0.0411 0,0402 0.0390 0.0377
0.0760 0.0760 0.0760 0.0741 0.0722
24.1 24.1 24.1 24.1 24.1
8.8i 8.87 8.87 8.87 8.87
0,0480 0.0439 0.0425 0.0412 0.0398
69.4 67.5 65.5 63.5 61.4
0.833 0.855 0.882 0.866 0.852
0.0297 0.0289 0.0287 0.0283 0.0270 0.0267
0.0665 0.0646 0.0646 0.0626 0.0589
24.1 24 1 24.1 24.1 24.1 24.2
8.87 8.87 8.87 8.87 8.87 8.81
0.0314 0.0305 0.0303 0.0299 0.0285 0.0282
48.4 47.0 46.6 46.1 44.0 43.5
0.895 0.921 0.896 0.907 0.894 0.796
0.0912 0.0912 0.0912
0.0893
1
* Each group of data set ofl by spaces represents a single bubble, observed over different intervals. sorbed on the surface of moving bubbles may be from twice to many times the concentration adsorbed on a plane quiet surface at equilibrium (2,3).
RISE O F .4IR BUBBLES IX OILS
437
The wholly or partially immobilized liquid may contain chains of oriented molecules of additive extending outwards from a primary sorbed layer on the surface of the bubble, as suggested independently by McBain (2) and by Hardy (1) in 1927. This may well be supplemented by cybotactic arrangement of the hydrocarbon molecules in the same region, as McBain has also suggested. The practical significance of the observations is that the reluctance of finely “emulsified” air to separate in lubricating oils containing additives has been accounted for. CONCLUSIONS
In the oils containing additives, there is a thick shell of material surrounding moving air bubbles, which moves with the bubbles, impeding their passage through the oil. SUMMARY
The rates of rise of small air bubbles, up to 2 mm. in diameter, were measured at room temperature in an oil containing no additives, in the same oil containing foam inhibiton, and in an oil containing lubricating additives. The apparent diameter of the air bubbles was measured visually through an ocular micrometer on a travelling telescope. Additives in lubricating oils may impede the escape of small bubbles from the oil, by forming shells of liquid with a quasi-solid or gel structure around the bubbles. ’ The bubbles in the oil containing no additives obeyed Stokes’s law, the rate of rise being proportional to the square of the apparent diameter and inversely proportional to the viscosity of the oil. The bubbles in the oils containing additives rose more slowly than predicted by Stokes’s law from the apparent diameter, and the rate of rise decreased as the length of path the bubbles trahyelled increased. A method is derived for calculating the thickness of the liquid shell which would have to move with the bubbles in the doped oils to account for the abnormally slow velocity. The maximum thickness of this shell, calculated from the velocities observed, was equal to the bubble radius. The information contained in this paper was obtained in connection with an investigation sponsored and financed by the National Advisory Committee for Aeronautics and carried out under the supervision of Professor James W. McBain. REFERENCES (1) HARDY,W . B.: J. Gen. Physiol. 8, 641 (1927). (2) MCBAIN,J. W., AND DAYIES,GEORGE P.: J. Am. Chem. SOC. 49, 2230 (1926). (3) BICBAIN,J. W . , AND WOOD,L. A , : Proc. Roy. SOC. (London) A174, 286 (1940).
