Falling Ball Viscometry. Practical and Theoretical Aspects of the Development of a Rapid Routine Instrument
SIR: I n a previous paper (5) an instrument was described which is capable of the precise measurement of viscosity by timing the fall of a small sphere through the liquid. This paper describes modifications t o the instrument and discusses the effects of the proximity of the container walls and of turbulence, which are important over portions of the extended TTiscosity range.
r a w o f f Tube ith Collar
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-
Tube Holder
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L
EXPERIMENTAL
The sample handling system of the apparatus previously described (5) was redesigned to hold 12 sample tubes, which could be precisely and rapidly positioned, and provide for rapid adj ustment of sample height and positive control of ball position. These features are illustrated in Figure 1. The level of sample in each tube is adjusted, after equilibration, by drawing off the excess to a constant level which is below the surface of the bath liquid, thereby minimizing temperature gradients in the sample. A guide is inserted into each tube to ensure free axial fall. The sensing coils are encased in mumetal shields and mounted 15 cm. apart on a square tubular post, which can be raised and lowered through closely fitted guide blocks by a handdriven pinion and rack assembly. Thus, when the post is lowered, the next sample tube can be brought into place and the sensing coils can be raised around it to the precise position for measurement. The bridge resistors are mounted inside the post for mechanical protection, and connections are made through the post to a receptacle at the top. The entire system, which is shown in Figure 2, is exposed to free circulation of the bath liquid providing maxiniuni heat transfer and minimum equilibration time. I t was necessary to increase the depth of the constant temperature bath to 18 inches to accommodate this assembly. Satisfactory results were obtained a t temperatures from 25" to 150' C. RESULTS AND DISCUSSION
Study of Ball Characteristics. The balls used should meet t h e following requirements: They should be small (to minimize wall effects), yet large enough for ease of handling; the diaiiieter variation should not exceed 0.01 %; the surface must be free of defects; the material must be suitable for triggering the electronic timing device; the cost should be small; and the balls should be available in quantities of 1000 or more.
Sample Tub
r
Figure 1.
Sample tube holder
On the basis of these considerations, 440-stainless steel balls in I/%-, l/32-, and l/la-inch sizes were chosen for use. As the precision of the instrument is affected by the precision of the ball parameters, it was necessary to test the latter. Ten balls were selected a t random from a batch of 1/32-inch stainless steel balls, which had a tolerance of i10 micro-inches. They were dropped repetitively in the same oil; the average fall time for each ball correlated well with its weight, as shown in Table I. It is not possible to determine the diameter of the balls directly with sufficient precision to get a n accurate value for their density. However, since the weight is known, one can calculate ball diameter assuming uniform density and vice versa. When uniform density is assumed the diameter varies between 0.03118 to 0.03128 inch. When uniform size is assumed, the density varies between 7.5351 and 7.6054. Since a variation in depth of case hardening is not
unlikely, a variation of 1% in density may be considered more probable than a range of a t least five times the guaranteed size tolerance. Consequently, balls should be selected by weight, and the precision obtained with the method will be largely determined by the weight range of the balls used. The high degree of uniformity and low price of the balls justify discarding them after use ( 5 ) . Suitable large lots of balls car! be selected by weighing with a fast microbalance, the weight range of the balls being determined by precision requirements. Steel balls having a density of about 8 can be used over the entire viscosity range described. However, materials of higher density (such as tungsten carbide) would permit the use of smaller balls to reduce the effect of the container walls. Balls of substantially lower density would give increased fall times, diminishing the effect of turbulence in liquids of low VOL. 37, NO. 4, APRIL 1965
613
Table I.
Ball No. (wt. sequence)
Correlotion of Fall Time with Ball Weight
Ball wt.,
Av. fall time,
mg.
see.
viscosity. Hollow steel halls did not prove sufficiently different from solid steel halls to warrant further investigs, tion. Aluminum halls were more uniform in weight than any of the steel balls examined, but preliminary tests indicate that the precision of viscosity determinations with these halls does not differ from that found for steel halls. Wall Effect. I n operating over wide ranges of viscosities, the instrument described here uses different hall sizes in relatively narrow tubes, and consequently we must take the wall effect into account. The appropriate calculations were experimentally verified by making fall time measurements of stainless steel spheres of different sizes in liquids of widely differing viscosities, and comparing the known values of the viscosities with those calculated by applying the Haberman correction to the Stokes' function
(1-4).
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Fall time sequence, hall No.
Generally, we can write:
q/(d.
dJt = K , 2r2g/91 where q is the
absolute viscosity of the liquid, d, the density and r the radius of the sphere, d Lthe density of the liquid, 1 the distance between coils, t the fall time, and K , the Haberman correction to the Stokes' Figure 2. Impedance bridge-sample function. We can obtain values for the holder assembly term on the left side of the equation (kJOund) by making the fall time measurements on oils of known viscosity and density, and can then compare these correction does suggest efforts to ensure values with those calculated from the reasonable centricity of the path of the right hand side of the equation (!G~~~~.). falling sphere. Table I1 shows the values klDundand Turbulence. I n the preceding we kroltd.for steel halls having diameters of assumed streamlined flow, where the I/M, '/=, and '/,a inch. fall time of a hall is proportional to The values of kl...a are averages from the viscosity of the liquid, At high oils that varied in viscosity over a tenhall velocities, the flow becomes turhufold range; the values for each hall size lent, and the relationship between varied only over a range of 0.5'%, and viscosity and ball fall time becomes the average value of kl,,,d differed from nonlinear. The drag caused by turthe calculated value by only 1% or less. bulence is related to hall velocity and is Table I1 shows, in addition, the Haherrepeatable, so satisfactory results can man correction K , , which indicates the he obtained in this region by use of a dem q n i t u d e of the deviation from Stokes' tailed calibration curve. law for each hall size. Thus, for a To demonstrate the departure from Table 11. Wall Effect Corrections '/,Finch hall falling in a test tube of the linearity, the viscosities of a series of oils Diameter of halls, inches size used in our experiments (12-mm. were measured by using '/=inch 'Jm '/a2 'Jn 0.d.) one would calculate a viscosity stainless steel balls, and calculated by 50YGgreater than the true viscosity if kl.d use of the calibration constant derived one neglected the drag on the hall from the linear portion of the fall time 0 . 5 1 5 2 1 . 9 0 2 3 6.0959 ((d. _" d d t> caused by the proximity of the container vu. viscosity curve. Data for the kcazad. walls. calibration constant were obtained on 0.5206 1.8926 6 . 0 7 6 5 Although small deviations from cooils ranging from about 100 to 1000 axiality of the hall path with respect to centipoises and at temperatures from K I (Haberman the tube did not cause significant error correction) 1 . 0 9 1.20 1.50 25" to 100' C. The calculated values for (6),the magnitude of the Haberman the low viscosity oils are compared with values obtained from capillary viscorneter data (see Table 111). The ratio of these two quantities for each oil, Table 111. Effect of Turbulence also shown, indicates the departure from linearity. In addition, the velocViscosity, Visc. (caled.) Viscosity, Ball velocity, ity of the ball it falls through the Visc. (actual) cm./sec. cp., calcd.m ep., actualb liquid is shown. 93.7 1.00 2.05 93.6 Performance. T o obtain direct in58.0 1.01 3.27 58.6 formation for the proposed routine 30.0 1.07 6.0 32.0 14.0 1.38 10.6 18.0 operation, determinations of the pre1.72 15.2 7.4 12.7 cision obtainable by using groups of 2.5 22.2 3.4 8.7 halls dropped in sequence without 25.2 2.0 3.8 7.6 retrieval were made. A group of 10 Conditions: 'llrineh halls, 25" C soheres was taken from a hatch of inch spheres selected by weight ' & From linear function, n = k(d. - di)l. b From capillary viscometer data. described previously, and these 10 halls were dropped successively five
(.,'+)
0
614
ANALYTICAL CHEMISTRY
Table IV. Summary of Precision Tests with a Group of 10 ’/32-ln. Balls
Av. time, see.
Rel. std. dev.,
13.5559 13.5445 13.5543 13.5392 13.5187
0 164
5%
0 i35
0 121 0 097 0 139 Pooled std. dev. 0.133 Rel. std. dev. of av. 0.111
times in the same oil under identical circumstances. The relative standard deviations obtained in each of the five series were pooled to give a pooled value of 0.133y0, The relative standard deviation of the averages was O . l l l ~ o . The data are summarized in Table IV. To illustrate the application of the instrument over a range of viscosities and temperatures we showv,in Table V, the results of determinations made to obtain a calibration constant, k, for l:le-inch balls in the c.alculation of the wall effects as discussed above. The oil densities, d r , were determined in pycnometers, and the kinematic viscosities, Y , were determined in capillary viscometers according to AIST,llmethod D-445. Reverse flow capillary viscometers, which are less precise, had to be used for the last five oils and these data were not used in the calibration. Absolute viscosities were calculated from 7 = vdi. The k-value was calculated for each oil from k = 7 / ( d a -
Table V.
Temp.,
Calibration Data for ‘/l,Jnch
capillary CP.
Balls
A?, Fall time, c see. Liquid O F . /c Oil blend 77 421.2 422.1 - 0 21 10.220 Bright stock 100 541.1 540 2 0.17 13.095 Polybutene-1 210 546.4 552.7 -0.97 13 327 Oil-PBc blend 1 100 680.0 680.9 - 0 13 16.501 Oil-PB blend 2 100 984 985 -0.10 23.869 Bright stock 77 1438 1438 0.00 34 887 Oil-PB blend 3 100 1546 1544 0.13 37.400 Oil-PB blend 1 77 1846 1847 - 0 05 44.818 Oil-PB blend 2 77 2697 2670 1.00 65 703 Oil-PB blend 4 100 3789 3774 0.40 91.357 Oil-PB blend 3 77 4405 4414 -0.20 107 . 0 21 Polybutene 2 100 6641 * 6801 -2.41 164,571 Oil-PB blend 4 77 ll,094b 11,140 -0.41 269,94 Polybutene 2 77 20,534b 20,512 0.11 496,87 Polybutene 1 100 24,260* 24,295 -0.14 588 74 Polybutene 1 77 73,445b 74,711 -1.72 1812.2 a Calcd. from 7 = k ( d , - d,)t, where k = 6.0959. 6 Detd. in reverse flow capillary viscometers; data not used in calibration. c Polybutene. 1)
d i ) t , and the 12-values were averaged to obtain the calibration constant. The calibration constant includes the wall correction factor, K l . The “falling ball viscosity” was then calculated for each oil from the fall time and the calibration constant. The variations between the viscosities so determined and those obtained by means of capillary viscometers are shown in terms of per cent difference. In the last column the fall time is shown, and this can be compared with the minimum of 200 seconds required for capillary viscometry. In viev; of the wide range of viscosities studied, the agreement is considered satisfactory.
7
falling ballje CP.
LITERATURE CITED
( 1 ) FaxCn, H., Arkiv Mat. Astron. Fysik 17, 1 (1922). ( 2 ) Faxkn, 0. H., Ing. Vetenskaps Akad. Handl.. No. 187 11946). ( 3 ) Haberman, W: L., Sayre, R. XI.,
Rept. 1143, Hydromechanics Lab., Dept. of Navy, October 1958. ( 4 ) Ladenburg, I{., Ann. Phystk, 4th Series 2 3 , 447 (1907). (5) Lim, W. K., Johnson, H. W., Jr., Wilhelmsen, P. C., Stross, F. H., ANAL.CHEM.36, 2482 (1964).
E. E. SEIBERT JR. H. W. JOHXSON, F. H. STROSS Shell Development Co. Emeryville, Calif.
Liquid Alpha-Gamma Counter for Simultaneous Determination of Plutonium and Americium SIR: Alpha counting is the most rapid method for analyzing plutonium in low concentrations. Americium may be determined by either alpha or gamma counting. A technique for directly counting alpha emissions from plutonium-containing solutions has previously been proposed by Byrne and Rost (1).
Plutonium solutions usually contain minute quantities of americium-241. The americium has a specific activity of about 50 times that of the plutonium; therefore, it will interfere with the radioassay of plutonium. Fortunately, the americium has an abundant 60k.e.v. gamma emission, while the plutonium has a very low gamma activity. This difference in gamma activity perinits the determination of both the plutonium and americium
in a solution by simultaneously counting the alpha and gamma emissions using two independent counting systems. For the purpose of brevity, the liquid alpha-gamma counter will be referred to as the LAG counter through this paper. EXPERIMENTAL
The LAG counter consists of two vertical opposed scintillation detectors and related electronic compohents. The upper detector assembly contains the alpha detector and lower assembly contains the gamma detector. The alpha and gamma sections of the L.IG counter each contain all the electronic components for independent operation. Each section also contains a ratemeter for the iinmedinte estimation of the count rate of the sample. For reasons of safety, the alpha de-
tector, which is moveable to allow introduction of the sample, and the sample holder are enclosed. The alpha detector is raised and lowered by compressed air which is activated by opening and closing the door of the enclosure. Figure 1 illustrates the physical relationship of the detectors and the sample. When the sample is counted, the alpha detector assembly is lowered to form a light-tight unit. The alpha detector phototube is protected from ewessive light by a switch-operated relay which turns off the high voltage to the phototube as the alpha detector assembly begins to rise. The voltage is turned on again when the assembly is closed. The alpha detector is a silver activated zinc sulfide phosphor which is secured to a lucite light pipe. The gamma detector is a commercial sodium iodide crystal, 2 mm. thick and 1 3 i 4 VOL. 37, NO. 4, APRIL 1965
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