Viscosity of Fire-Fighting Foam C. 5. GROVE, JR., GEORGE E. WISE, JR., WILLIAM C. MARSH1, AND JOSEPH B. GRAY Syracuse University, Syracuse, N. Y .
T h e effects of pressure, rate of shear, and ratio of air to water on the apparent viscosity of fire-fighting foam were studied in a flow-type viscometer to provide data which could be used for predicting pressure drops when foam is transported in pipes. It was found that the viscosity, calculated from a plot of friction factor versus Reynolds number, is nearly independent of the rate of flow- of foam for the conditions
studied. The viscosities of all foams of the same density are the same over a wide range of pressures and ratios of air to water. The viscosity of foam approaches that of water as the total pressure on the system is increased to 90 pounds per square inch gage. The data presented are useful for preliminary estimates of pressure drops, even though the effect of variations in pipe diameter on apparent viscosity is uncertain.
F
bore). Four pins 0.06-inch in diameter are placed a t each end of the rod to hold i t concentrically within the glass tube. The displacement of the rod by the fluid flowing past is determined by noting the location of the pins with respect to a scale adjacent to the glass tube. The spring is made of steel piano wire, which is copper plated to prevent corrosion.
IRE-fighting foams which are generated by mechanically mixing air, water, and a foaming agent are usually considered to be relatively resistant to flow. Measurements of the viscosity of various foams are reported b y Clark ( 3 , 4). However, there is some evidence that the resistance decreases appreciably as the rate of flow increases, Sibree ( 7 ) reports that the viscosity of foam decreases with an increase in velocity gradient. Blackman (3)showed that foams become fluid when passed through a hose or when a cylinder is rotated in a vessel containing foam. HOWever, very few data are available on the viscosity of fie-fighting foam. I n this investigation, the viscosity of foam was determined for foams of various proportions of air and water, and a t various total pressures and rates of shear. Other variables, which affect the viscosity, such as the type and concentration of foam agent, temperature, bubble size, age of foam, and dimensions of e q u i p ment for measuring viscosity, were not studied. The equipment constructed to study the effect of rate of flow and total pressure on foams for a wide range of proportions of air and liquid is described. The results obtained are presented as a correlation of viscosity and foam density.
CALIBRATION O F VISCOMETER
FOAM GENERATOR AND VISCOMETER
A flow sheet of the apparatus used to generate foam is shown in Figure 1. Air supplied a t 95 pounds per square inch is mixed with water containing the foam agent in a standard l/r-inch pipe tee. A gear pump is used to increase the foam solution pressure to the pressure of the air. Another gear pump is used to mix the air in the foam solution and increase the pressure on the foam, thus generated, to the desired value. A heater or cooler is provided to permit adjustment of the temperature of the foam or other fluids pumped through the foam viscometer.
v BOOSTER
COMPRESSED AIR
@
* T O FOAM VISCOMETER
G E A R PUMP FOAM AGENT WATER SOCU TlON
GEAR
PUMP
Figure 1.
DRAIN OR RETURN
Foam Generator
The a p aratus used to measure the resistance to flow of foam (viscosityyis shown in Figure 2. A brass rod 0.250 inch in diameter is suspended by a spring in a 30-inch length of 0,3750-inch inside diameter round tubing (Fischer and Porter Co. precision 1
Present address, The Nestle Co., Marysville, Ohio.
Figure 2. Foam Viscometer
Water and aqueous sugar solutions were used to calibrate the foam viscometer for viscosities ranging from 1 to 220 centipoises (0.000672 to 0.147 pound per foot per second). In these calibrating tests, the solution was pumped through the apparatus at velocities ranging from 1 to 19 feet per second in the annular space between the brass rod and glass tube wall. The results were plotted as a Fanning friction factor versus Reynolds number. This type of correlation has been used by Squires and Dockendorff (8) for Stormer viscometer studies. The friction factor was calculated using the Fanning equation :
where P = pressure drop, pounds per square foot L = pipe length, feet p = fluid density,.pounds per cubic foot f = Fanning friction factor, dimensionless V = fluid velocity, feet per second g = 32.2 feet per second* D = pipe diameter, feet
In applying this equation to the data obtained on the foam viscometer, the pressure drop was calculated by dividing the force extending the spring in pounds by the cross-section area of the brass rod (0.000341 square foot); the length of the brass rod (1.041 feet) was substituted for L; and the width of the annular opening (0.00521 foot) through which fluid flows, for D. The velocity was calculated from data taken on the weight of fluid collected in a measured interval of time. The force extending the spring was obtained from measurements of the position of the brass rod. This was calibrated in terms of pounds by hanging various weights on the spring, prior to assembling the viscometer, and noting the extension. The viscosities of the sugar solutions used were obtained from tables of viscosity as a function of density, temperature, and concentration of sugar (6). 1120
May 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
1121
&fear1 Corp., Roselle Park, N. J. This agent is hydrolyzed protein with iron salts added as a stabilizer. A concentration of 6% b y volume in water was used in all experiments. CALCULATION OF FOAM VISCOSITIES
The viscosity of foam was calculated using a modification of the method described by Alves (1). First, the friction factor, f, and the product, DVp, w e r e c a l c u l a t e d . Then the Reynolds number, DVp/p, corresponding to each f was read from Figure 3. These data are also presented in Table 11. The foam viscosity was calculated by plotting DVp against the DVp/p read from Figure 3. The slope of the line through the points in such a plot is the viscosity. In Figure 4 are shown the data plotted in this way with the
c
F i g u r e 3.
Calibration of Viscometer
The data obtained on the flow of water and various aqueous sugar solutions are presented in Table I. The values of the friction factor,f, and Reynolds number, DV,,/&, where El isviscosityin pounds per foot per second, are included in this table. I n Figure 3 the friction factor is plotted against the Reynolds number. It is seen that a smooth curve is obtained from Re = 10 to Re = 10,000 with no break between viscous and turbulent flow. This curve is similar to the one obtained by Squires and Dockendorff
FOAM VISCOSITY TESTS
a
*
Tests on the flow of foam through the viscometer were carried out in a manner similar to the tests on flow of water and sugar solutions. The force extending the spring and the mass flow rate were measured in t h e same way. T h e density was calculated from measurements of pressure in the viscometer and the weight of foam in a known volume collected a t room temperature and pressure. The velocity in the annular space between the brass rod and glasa tube was calculated from the mass rate of flow, the density a t the average pressure in the viscometer, and the cross-sectional area of the annular space. I n these tests average pressures from 25 to 90 pounds per square inch gage were used for a foam in which the volume ratio of air plus liquid t o liquid was 4.8. This ratio is usually called the expansion of the foam. At an average pressure of 33.5 pounds per square inch gage, tests were made on foams with expansions from 2 t o 14. T h e v e l o c i t y of f l o w t h r o u g h t h e annular opening was varied from 2 t o 19 feet per second. The results of these tests are presented in Table 11. The foam agent used in these tests was Mearlfoam, which is made by the
TABLE I. CALIBRATION OF FOAM VISCOMETER DenViscosity, Sugar, Temp., Lb./ Lefiu. Wt. % O F. Foot/Sec. Foot 70, 95 1063 83. 83.4 70.0 104 0.0765 65.0 86 0.0522 81 8 55.0 95 0,00951 78.0 55.0 86 0.01179 78.1 45.0 104 o,oo305 74,4 45.0 95 0.00366 74.6 35.0 104 0.001615 71.3 25.0 86 0.001254 68.6 0.0 77 0.000607 62.2 0.0 64.4 0.000712 62.3
VelooF%/ Sec. 4. 5.52 6 49 2.38 7.17 5,13 12.88 6.96 8.77 7.82 16.73
Force, Lb. 2,82 2.67 2.64 0.151 0.668 o,1651 0.722 0.1651 0,271 0.1580 0.658
Reynolds No. 16,
Friction Factor
47 0.25 0.181 0.081 0.039 o,0199 0.0138 0.0113 0.0121 0.0098 0.0089
31 53
102 250 650 1360 1600 2500 4200 7600
TABLE 11. FLOW OF FOAM IN VISCOMETER Pressure Density Lb./&. Temp., Ex: Lb./Cu.' Velocity Inch ' F. pansion Foot Feet/&:. 14 1 25 82 4.8 25.8 25 84 4.8 26.0 4.76
Force, Lb. 0.826 0.236
Friction Lb./ Factor Foot/Sec. 0,0378 1.90 0.0945 0,645
D VP,
'
Foam
Reynolds Viscositya, No. Lb./ (Fig. 3) Foot/Sec. 286 0 0073 92.5
33.5 33.5 33.5
84 84 84
4.8 4.8 4.8
29.0 28.9 28.9
17.5 14.4 2.53
0.887 0.630 0.087
0.0236 0.0235 0.1114
264 2 16 0 381
490 445 79
0I0052
40.5 40.5 40.5 40.5
82 82 82 84
4.8 4.8 4.8 4.8
31.2 31.2 31.2 31.2
17 8 13.5 9.28 1.83
0.788 0.512 0.316 0.0448
0.0188 0.0211 0.0278 0.1013
2.89 2.20 1.51 0.279
710 580 384 87
0.0040
55.0 55.0 55.0
82 82 82
4.8 4.8 4.8
34.6 34.7 34.7
14.20 7.00 2.70
0,465 0.1722 0.0519
0.0157 0.0239 0.0485
2.56 1.26 0.488
990 480 188
0.0026
70.0 70.0 70.0 70.0
82 82 82 82
4.8 4.8 4.8 4.8
37.8 37.9 37.6 37.6
15.10 11.53 9.16 4.75
0.434 0.300 0.210 0.0661
0.01190 0,01570 0.01407
2010 1270 1000 730
0.00165
0.01837
2.97 2.27 1.79 0.930
90.0 90.0 90.0 90.0
82 82 82 82
4.8 40.8 4.8 ' 40.8 4.8 40.6 4.8 40.7
13.55 10.84 8.21 3.88
0.373 0.260 0.151 0.0377
0.01175 0.01279 0.01303 0.01452
2.88 2.31 1.74 0.822
2200 1630 1530 1190
0.00128
33.5 33.5
83 83
7.0 7.0
21.9 21.8
14.08 3.57
0.895 0.1959
0,0477 0.1665
1.60 0.405
192 52
0.0082
33.5 33.5
83 83
2.1 2.1
46.6 46.6
12.53 10.34
0.342 0.220
0.01102 0.01042
3.04 2.51
2600 3200
0.00092
33.5 33.5 33.5
83 83 83
3.2 3.2 3.2
37.6 37.6 38.1
15.88 11.10 6.62
0.519 0.314 0.1392
0.01293 0.01600 0.01970
3.10 2.17 1.31
1600 960 650
0.0021
33.5 33.5 33.5
83 83 83
4.8 4.8 4.8
29.0 29.0 29.0
17.14 12.26 4.05
0.852 0.563 0.1558
0.0236 0.0305 0.0773
2.59 1.85 0.611
440 340 114
0.0056
65.0 55.0
83 83
13.9 13.9
16.5 17.8
6.43 9.03
0.567 0.817
0.1960 0.1328
0.554 0.834
42 65
0.0126
(I
From slope of line in Figure 4.
INDUSTRIAL AND ENGINEERING CHEMISTRY
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Figure 4.
Calculation of Foam Viscosity Pressure
Line
Sym- Expan- Lb./SG. bo1 sion Inch
0
L
13.9 7.0 4.8
3
2
5
8A
6
X
3 4
4.8 4.8 4.8
Vol. 43, No. 5
55.0 33.5 25.0 33.5 33.5 40.5
Pressure.,
Line
7 8
9 10
11
Symbo1
p
40
@
Expan- Lb./Sq. sion Inch 4.8 55.0 3.2 33.5 4.8 70.0 4.8 90.0 2.1 33.5
shear ( 2 , 6, 7). Previous work has been done at relatively low velocities and rates of shear where the viscosities are high and an increase in velocity reduces the viscosity markedly. Values as high as 108 poises for low rates of shear and 100 cp. for flowing foam have been reported by Blackman ( 2 ) . EFFECT O F PRESSURE ON FOAM VISCOSITY
An increase in pressure on a foam decreases the viscosity, as illustrated by the data in Table 11. For a foam of 4.8 expansion an increase in pressure from 25 to 90 pounds per square inch gage reduces the viscosity from 0.00733 (10.9 cp.) to 0.001285 pounds per foot per second (1.9 cp.). Such a decrease in resistance t o flow should be expected, as an increase in pressure reduces the volume of air relative to the volume of water. This foam is equivalent to a foam containing less air or one of lower expansion. Increasing pressure is equivalent to reducing the air content of foam in its effect on viscosity. This is shown by Figure 5 , in which viscosity is plotted against foam density in pounds per cubic foot. One line can be drawn through all points which include foams with expansions from 2 to 14 and pressures 25 to 90 pounds per square inch gage. The foam viscositv is determined, then, b y the volume ratio of air and water under the particular flow conditions. ACKNOWLEDGRSENT
~
~~
Figure 5.
Effect of Pressure on Foam Viscosity
best lines drawn through the points. In Table I1 are presented the results of the calculations of the viscosity. EFFECT O F RATE O F SHEAR ON FOAM VISCOSITY
The only variable which is changed for any line in Figure 4 is the rate of flow of foam. A single viscosity can be used for a foam over a range of velocities from 2 to 19 feet per second. Thus it is found that a foam behaves like many other non-Newtonian fluids in turbulent flow. The apparent viscosity is constant (1). This result is not inconsistent with observations in the literature that the viscosity of foam varies appreciably with the rate of
This investigation was carried out under the sponsorship of the Naval Research Laboratory, Washington, D. C., under Contract N6-ONR 248-09. The helpful suggestions of members of the staff of the Chemistry Division during its progress are gratefully acknowledged and greatly appreciated. LITERATURE CITED
(1) Alves, G. E., Chem. Eng., 56, No. 5, 107-9 (1949). (2) Blackman, M., Trans. Faraday Soc., 44, 205-6 (1948) (3) Clark, N. O., Chemistry & Industry, 1948, 22-5. (4) Clark, N. O., Dept. Sci. Ind. Research (Brit.), Chemistry Research, SpeciaE Rept. 6 (1947). ( 5 ) Natl. Bur. Standards, Circ. C 440 (1942). (6) Penney, W. G., and Blackman, M., Ministry of Home Security (Brit.),Note 282 (1943). (7) Sibree. J. 0..Trans. Faradau Soc.. 30,325 (1934). (8) Squires, L., and Dockendorff; R. L., I k . ExG. CHEM., ANAL.ED., 8, 295-7 (1936). RECEIVED January 27, 1960.
