V O L U M E 26, NO. 10, O C T O B E R 1 9 5 4 Table 11. Comparison of Titrator and Potentiometric Results Mercaptan Sulfur, 7/Ml. of Distillate Fuel Automatic titrator Potentiometric 2.8 2.8 8,s 8.4 14.2 14.3 23.2 22.8 34.2 33.2 46.5 45.6 57.0 57,O 112 111 166 163 270 277
1609 the coulometric current, are minimized. This interference is especially important a t high coulometric currents, but it is negligible below 5 ma. Currents as high as 10 ma. have been used without difficulty. The automatic mercaptan titrator has proved adequate for routine laboratory use. Samples containing as little as 2 y of mercaptan sulfur can be titrated. Further work is being directed toward combining the coulometric generation and detection systems into a continuous-recording titrator. This instrument could titrate a flowing plant stream, automatically monitor instantaneous changes, and directly control mercaptan-treating operations. LITERATURE CITED
sample is introduced, silver ions are generated in the electrolyte until an arbitrary deflection of approximately 0.2 pa. is reached, such as point P. This corresponds to a blank run. The sample is then introduced and the mixture is again automatically titrated to this point. This method minimizes the titration error and eliminates the effects of different initial detector currents due to variations in the electrolyte. \\ hen the electrolyte will no longer hold the sample in solution as evidenced by a milky two-phase system, the electrolyte is discarded. Approximately 15 to 20 samples of 1 ml. each can be titrated before this condition occurs. The detecting electrodes may become sluggish after long use, especially when large amounts of mercaptans are titrated. Sensitivity can be restored by polishing the electrodes with steel wool. Several titrations with mercaptans are then necessary to condition the electrodes. A sulfided silver electrode can be used in place of the gold electrode; however, its characteristics changr in the presence of hydrogen sulfide. The electrodes are Dositioned in the titration cell so that transient currents, induced in the detecting electrodes by starting
Rergatrom, P., and Reid, E. E., IND.ENG.CHmr., X V ~ LED., . 1, 186 (1929). Carson, W.W., Jr., ANAL.CHEM.,25, 226 (1953). Cooke, W.D., and Furman, S . H., I b i d . , 22, 896 (1950). Cooke, W. D., Reilley, C. K.,and Furman, S.H., Ibid., 23, 1662 (1951).
DeFord, D. D., Johns, C. J., and Pitts, J. S . , I b i d . , 23, 941 (1951).
DeFord, D. D., Pitts, J. X., and Johns, C. J., I b i d . , 23, 938 (1951).
Kolthoff, I. AI., and Harris, IT. E., ISD.EXG.CHEX.,ASAL.ED., 18, 161 (1946).
Lykken, L., and Tuemmler, F. D., I h i d . , 14, 67 (1942). Pompeo, D. J., Penther, C. J., and Hallikainen, K. E., Instruments, 1 6 , 4 0 2 (1943).
Sease, J. W., Siemann, C., and Swift, E. H., ANAL.CHEM., 19, 197 (1947).
EKG.CHEM.,ANAL.ED., Tamele, 31. W., and Ryland, L. B., IND. 8, 16 (1936). R E C E I V Efor D r e n e w Sovember 27, 1933. Accepted July 1 3 , 1954
A Ball and Cup Absolute Microviscometer P. D.GARN and W. E. CAMPBELL' Bell Telephone laboratories, M u r r a y Hill,
N. J.
The need for a convenient method of determination of the viscosity of oils from bearing greases or from other sources, where only a small sample is obtainable, led to the study of the ball and cup viscometer. This viscometer was originally designed as a test for lubricants in the shop. The results show that the ball and cup viscometer is capable of reasonable accuracy and precision w-hen used with either an inversion or a balance technique. The drop or pull-up time is proportional to the absolute viscosity. The sample may be as little as 0.035 ml. This viscometer permits quick and convenient determination of viscosity using a very small sample and permitting complete recovery of the sample. The standard deviation of a set of data is general13 less than 2%.
I
S T H E anal)-sis of used oil the viscosity is generally an im-
portant characteristic, but frequently only a fraction of a drop of oil is obtainable for test. h-o simple, rapid, precise method for determination of viscosity on very small samples appears to be available. A convenient method for the rough de-
' Present address, T h e Brush Laboratories
Co , Cleveland, Ohio
termination of the absolute viscosity of small amounts of lubricant in the shop has been discussed by hIichell ( 8 ) , using an ingenious cup and ball device. The experiments described in the present paper were carried out with this device modified to minimize the quantity of oil needed for test, and operated with much closer control of the experimental conditions than described by Michell. The results obtained show that satisfactory precision is obtainable over a wide range of viscosities. INVERSION ,METHOD
The ball and the inner surface of the cup should be accurately spherical and should be polished to a high surface finish; an ordinary bearing ball will do for the ball. The cup is fitted with three pins as illustrated in Figure 1, to support the ball, so that there is a uniform clearance of the order of 1 mil between the ball and cup surfaces. In operation, the sample is placed in the cup and the ball is set into the cup, displacing the oil into a reservoir surrounding the cup. The cup is then inverted, so that a deficit in pressure due to movement of the ball will draw the oil back into the cup against the viscous drag of the oil. After an interval of time determined by the viscosity of the oil and the dimensions of the cup and ball, the ball drops from the
ANALYTICAL CHEMISTRY
1610 cup. The time interval during which the ball is held in the cup is a measure of the viscosity of the oil. -4 mathematical derivation of the relation between the “drop time” and the dimensions of the cup has been performed by Bosivall(1). The final relationships applicable to this viscometer are
9?R 2gCh
t = - 1[ 2 In cos
+ sin* pol
pFo
sample breaks, and the ball falls free of the cup. A typical plot is shown in Figure 2. Apparatus. The apparatus consists of a cup on a peg as designed by Michell, a ball fitted with a peg, and a support. The support with the ball and cup in place is shown in Figure 3. The support is designed for quick inversion of the cup and ball around an axis through the ball. This design minimizes the effect of shock during inversion of the assembly. Stops are provided, so that the cup peg is vertical both before and after ~nversion. The peg on the ball fives a reprodurible portion of the
and (2)
t = l- be made by allon-ing the oil to settle in the cup for several seconds before setting in the ball. Cleaning of the ball and cup between determinations on t,he same oil is not necessary. However. a fen- seconds should be allowed between determinations for the sample to settle into the cup. For high viscosity oils an additional weight may he attached to the peg. Results. Preliminary results showed a high degree of reproducibility even a t very low drop times and ambient room temperature. Twenty measurements wit,h a medicinal white oil yielded a drop time of 5.4 with a shndard deviation of 0.2 second. For longer times standard deviations of 2 to 3Cr, were normal. The precision depends, to some degree, on the period of time the hall is allowed to settle in the cup. This period must be s u l ~ stantially greater than the drop time. LIeaeurements using sample RD-382-51 and an ambient room temperature near 36” C. showed that by increasing the settling time more precise data were obtained. For settling period:, of 60, 90, 120, and 180 seconds, the drop times n-ere 60.4, 84.2, 85.2, and 85.5 seconds, with standard deviations of 1.9, 2.7, 2.6, and 1.1 seconds, respectively . o=it!- stmdards obtained =Z number of oils, including three from the Sational Bureau of Standard?, were used to calibrate the instrument. The absolute viscosities of the oils were calculated from densities found by the sink-float method ( 2 ) , and from kinematic viscosities determined by means of Cannon-Fenske (3) viscometers, which were calibrated using viscosity standards of the Sational Bureau of Standards. The drop times and viscosities are tabulated in Table I and plotted in Figure 4 as time
1611
V O L U M E 26, N O . 10, O C T O B E R 1 9 5 4 T a b l e I.
Drop Times and viscosities (For lubricating oils and viseositu standard at 25" C.) Dron Time, Sec. ~ i Weighted l only ball (11.43 E.) (45.96 g.) 6.8 10.1 22.3 43.4 40.9 11.0 G5.7 14.2 27.8 ~
viscosity. Poisea
Sample Univis 90
1.59
M-22
Univis 200 N-20 RD-383-51 univis 445 RD-382-51 RD-381-51
OB-€
2.23 4.94 9.26 10.05 13.80
27.74
58.80
200.7
.
Std. Der.. Sea. Ball only 0.1 0.3 0.9
Weighted ball
0.4 1.5
0.1
1.1
60.2
211.4
0.4
0.7 1.4 1.9
ancc painter was about 2 mm. below the top of the scale. T h e apparatus is shown in Figure 5. Procedure. The bdance point is determined by adding sufficient weight to the weight hook t o raise the balance arm, then adjusting the weights on the balance arm until the pointer is a t zero. The weights on the balance arm are then adjusted to the desired excess weight. A s a m d e of the fluid is then nlaced in the CUD. The balance arm is raised manually and held for a sufficient time to permit the
before another determiZiatian is performed Results. I n order to calibrate the instrument, the lower limit of exes8 or effective weight was determined. Preliminary experiments showed that as the effective weight was diminished, the time required to pull up the ball increased nonlinearly and became highly irreproducible. For this reason, a study of "pull-up" time us. effective weight was performed. Three oils of different viscosities were observed. The pull-up times for 220 200 180
160 y1
0
140
0
:120 5 100
Figure 3.
Ball and Cup Mi-viscometer
I r
80 60
The ball and peg used in these determinationt weighed 11.43 grams. For the higher viscosity oils a weight waz added. The total weight of the weighted ball and peg was 45.9f grams. (The sets of data are plotted together for camparisor only. The data for the ball should be plotted on an expanded viscosity scale for use as a calibration curve.) Ten determinations were made on each oil except OB-8, on which only three determinations sere made. T h e Univis and RD-oils are Essc oil8 supplied by the Standard Oil Development Co. and thf Colonial Beacon Oil Co. The samples M-22, N-20, and OB-f are the viscosity standards. T h e cup has a nominal pin clearance of 0.005 cni. The slopes of the plots of data obtained for the ball and the weighted ball are 0.94 and 0.21 poise per second, respectively The ratio of the slopes (4.5) agrees fairly well with the ratio 01 the --eights of the two balls used (4.0). us. viscosity.
40
20
00
20
Figure 4.
40
60
80 100 izo 140 V l S C O S l T I iN POISES
160
180
200 a20
Dropping Time Related to Viscosity of Oil
BALA-CE METHOD
Subsequent reference to Michell's patent (7) indicated that 2 balance method would be useful for extending the range of tht instrument to lower viscosities. By this method a force can bt applied which is independent of the weight of the ball and whict can be varied over a considerable range. A lower applied force yields greater release times for viscosity of a given sample and permits extension of the range to lower viscosities for a giver hall and cup sample. T h e method was tried with a cup havinp 0.0012 cm. in clearance.
Apparatus. The apparatus consists of a Ceneo triple bean balance, a ball on a peg, a cup, and a support to hold the cup in
r""."."... nnoi+inn
The balance pan was removed, and the cup mounted below the pan hook. The auxiliary weight hook N&S fitted to support the ball and nee as Tell as counterbalance weiehts. A flexible support was ;sea to hold the ball. The height d t h e cup was adjusted so that, n-hen the cup was supporting the ball, the bal-
Figure 5.
Ball and Cup Mieroviseometer Using Balance T e e h h i q u e
ANALYTICAL CHEMISTRY
1612 effective weights of 1.00, 1.05, 1.11, 1.18, 1.25, 1.33, 1.43, 1.54, 1.67, 1.82, 2.00, 2.22, 2.50, 2.86, 3.33, 4.00, and 5.00 grams were determined. The data were plotted as time DS. the reciprocal of the effective weight in Figure 6. These weights were selected to give equally spaced points on the graph. The radius of the circle for each point is a measure of the standard deviation of the data.
22 20
18 I6
Z
14
0
I5 12 z 10 w
z 6 4
2 0
0
10
20
30 40 50 60 70 80 V I S C O S I T Y IrJ C E N T I P O I S E S
90
100
Figure 7. Pull-up Time of Ball Related to \-iscosity of Oil for Applied Forces I.
11.
5.00-gram v i s c o s i t v 2.50-gram v i s c o s i t y
Table 11. Pull-up Times and \-iscosities
Figure 6.
Pull-up Time of Ball Related to dpplied Force I.
11.
111.
5-7 K-11 L-20 (plotted as time/3)
The data show a nonlinear relationship for effective weights below 2.22 grams, probably due to effects of surface tension. For those aeights greater than 2.22 grams the plot of drop time vs. weight-' is linear, and the data are generally more reproducible than for lesser effective weights. An oil series of instrument oil range was used as calibration standards. The S/V samples were supplied by the Socony Vacuum Laboratories. The absolute viscosities of these samples were calculated from the kinematic viscosity data supplied by that laboratory and densities determined by the sink-float method ( 2 ) . These data are given in Table I1 and plotted in Figure 7 . The cup has a nominal pin clearance of 0.001 em. Wherever an insufficient quantity of sample is used, the pullup time is excessively long and data are not reproducible. The results may also be due to the effect of surface tension. When small increments were added successively, the weight of sample K-11 was found to be 0.030 gram or about 0.035 ml. in order to obtain reproducible data. The minimum sample is sufficient to form a film rising in a meniscus above the reservoir. Both the balance and inversion techniques w x e used to verify the assumption that the viscosities determined are the absolute viscosities. Glycerol and an arochlor (a chlorinated diphenyl) were selected because their densities are significantly different from the densities of the oil used in calibration. The kinematic viscosities were determined using a Cannon-Fenske viscometer (3) and the densities were determined by the sink-float method ( 2 ) . The absolute viscosities xere calculated from these data and
a
(For risrosity standards a t 2 5 O C 0 ) Excess Weight 3.0 g , 2~ S t d . Dev . See. Yiscosity. Sample Centipoises pull-up tirne. set. 3.0 g. 2.5 6. 0 17 20.23 10 64 S/V-D 88.9 0 18 8 ?2 17.47 L-20 74.1 0.14 10.28 42.7 5 23 S/V-c 0 06 4 18 8.15 K-11 33.6 0 04 2 32 4.53 5-7 17.4 0 08 3.72 1 87 14.0 S/V-B 0 01 1 40 10.2 1-9 2.8.5 0 OF 1 02 2.03 H- 8 6.5 Data a r e average of ten determinations on each sample.
compared with the viscosities determined using the ball and cup microviscometer. The cup used was equipped with force-fit pins. The pin clearance was nominally 0.005 em. An effective weight of 25.00 grams as used n ith the halance technique. The data are shown in Table 111. DISCL SSIOY
The ball and cup viscometer is a simple, quick, and convenient device for determination of absolute viscosities of small samples. The equation relating drop or pull-up time to viscosity is 7 = Xt c, where 7 is the viscosity in poiseP, t is thc time in seconds, and k and c are constants characteristic of the apparatus. The constant c i s a small correction, possibly the result of small deviation of the pin clearances from the nominal clearances, or possibly an intrinsic correction which does not appear in Equation 1 because of the assumptions necessary to accomplish derivation of the equation. The value of c is about 0.3 poise for the cup used in the inversion apparatus and about -0 2 centipoise in the cup used with the balance technique. The effect of the constant c indicates that calibration of the instrument is required. The important advantages of this instrument are the small size of sample, the convenience of operation, and direct determination of the absolute viscosity. Detepminations may be made on as little as 0.035 ml. of sample. The solution form of a sample may be placed in the cup, when necessary, and the solvent evaporated. When desired, the sample may be recovered completely. The instrument is readily cleaned by washing with a solvent.
+
V O L U M E 2 6 , NO. 10, O C T O B E R 1 9 5 4 Table 111. .4bsolute and Kinematic Viscosities (Related t o drop or pull-up time) Viscosity D r o p Time, Density, Kinematic, -4bsolute3 Poises Sample Sec. G./C.3 stokes Calcd. Exptl. LI-22 9.4 0.87 2.56 2.23 PI‘-20 37.6 0.88 10.48 9.26 Glycerol 15.1 1.25 2.96 3.70 3.66 Pull-up Time, Sea. RD-382-51 30.4 0.91 30.5 27.7 RD-381-51 63.2 0.94 62.5 58.8 Arochlor 56.7 1.53 34.5 52.8 52.6
With the dropping ball device, the need for a settling time substantially in excess of the drop time is obvious, for the same forces are applied before and after inversion of the cup. While the ball is settling, gravitational forces, due to the weight of the ball, act to displace the oil upward and into the reservoir around the cup. The viscosity of the oil determines the time required for the ball to settle against the supporting pins. When the cup is inverted, gravitational forces due to the weight of the ball cause a deficit of pressure above the ball. Oil is displaced upward into the spherical shell segment by atmospheric pressure. The oil must return to essentially the condition existing before the ball was set in the cup in order for the ball to drop. Therefore, if a long enough settling period has not elapsed before inversion, and the excess oil has not been forced into the reservoir, the time required for the viscous flow inward after inversion should and would be approximately equal to the time allowed for the viscous flow outward. A settling time of about 1.5 times the drop time is sufficient, although the results show that somewhat greater precision is obtained by extending the settling period. Occasional stray data nere observed, but, in each case, they were coexistent with dirt or bubbles in the cup. These stray data are invariably low and are usually a t least 20% lower than the average. The effect of dirt or bubbles in causing low data is readily deduced. If a dirt particle should settle on one of the supporting pins, the effective clearance between cup and ball would be increased. Because the time required for the viscous flow inward is dependent on the second power of the pin clearance, a particle, 1 micron in diameter, settling on a 0.001-cm. pin, would cause a 10% change in the thickness of that portion of the spherical shell and, hence, a 20% increase in the rate of f l o ~in that region. The effect of a bubble expands the fluid, so that the ball travels farther to produce the required difference in pressure. The greater travel of the ball increases the clearance between the cup and ball, permitting the oil to flow in a t a greater rate. The balance method shows the greatest promise as a laboratory method. The range may be extended to higher viscosities simply by using a greater excess weight. The cup and ball may be designed for use a t the lowest anticipated viscosities. According to Equation 1, the drop time is proportional to the viscosity of the sample and the radius of the cup and ball, and inversely proportional to the square of the sample layer-i.e., the pin clearance. The dependence of the drop time on the pin clearance was confirmed by one set of data using pin clearances of 0.0012 j=0.0002 and 0.0025 Z!Z 0.0002 cm. Using the same oil, the drop time for the cup nith the small clearance was about five times that for the cup with the larger clearance. The deviation from theory is well within that permitted by the tolerances. The cup size and required clearance may then be calculated for a cup having the desired lower limit of viscosity. I n order to achieve reasonable precision the dimensions should be calculated for a drop or pull-up time of a t least 10 seconds for the least viscous fluid. If the ball size is to be changed, the dependence of the mass on the third power of the radius must be taken into ac-
1613
count, unless the balance technique is used. The use of a larger radius would be practical, if a spherical segment with a sufficiently accurate surface is available. Otherwise, the gain is not large. The device will also require a much larger sample. The use of a narrower reqervoir would diminish the sample size required without impairment of accuracy or precision. The balance method lends itself readily to the use of an air bath thermostat. The thermostat could surround the cup and ball and a portion of the supporting chain. The use of a thermostat should permit even better precision than that obtained in this work. The ball and cup viscometer has been used in Great Britain as a convenient field test method for the viscosities of lubricating oils. There have been no reports of its use in the United States. The utility and convenience of the device require some further study. A number of microviscometers have been described for samples from 5 to 100 g. (4-6). A higher degree of precision is claimed for these viscometers than can be attributed to the ball and cup viscometer a t this stage of development. Each of these requires, of course, close control of temperature. The effort required to obtain data is considerably greater. In many cases of analytical importance, knowledge of the viscosity within 5% is sufficient. For these determinations a simple and convenient viscometer is desirable. The ball and cup viscometer permits direct determination of absolute viscosity with a minimum of effort yet with a useful degree of accuracy. ACKNOW L E D G M E 3 T
The authors are grateful to Irving L. Hopkins for his aid in clarifying t’he theory of operation of the instrument,. LITER4TURE CITED
(1) Boswall, R. O., Phil. Mag., 3, 994-1006 (1927). ( 2 ) Campbell, W. E., and Vincent, S. hl., Bell Telephone Laboratories Analytical Procedure 200458, June 3, 1952; Proc. Am.
Wood-Preserters’ Assoc., 49, 62-3 (1953). (3) Cannon, 31. R., and Fenske, A I , R., IND.EXG.Cmar., ANAL. ED.,10,297-301 (1935). (4) Glynn, E., and Grunberg, L., J . Inst. Petroleum, 34, 331-8 (1948). (5) Levin, H., IND.ENG.CHEM.,~ ~ N A ED., L. 9, 147-9 (1937). (6) Lidstone, F. LI.,J . Soc. Chem. Ind. (London), 54, 189-90T (1935). (7) llichell, A. G. AI., Brit. Patent 117, 234 (July 11, 1918). (8) Alichell, A. G. ll.,“Lubrication, Its Principles and Practices,” pp. 46-7, London and Glasgow, Blackie B. Son, Ltd., 1950. RECEIVED for review April 27, 1954. Accepted July 15, i954. Presented before t h e Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Pittsburgh, P a . , M a r c h 1931.
Spectrographic Determination of Impurities in Zirconium and Hafnium-Correction The following references should have been included in the literature cited for the article entitled “Spectrographic Determination of Impurities in Zirconium and Hafnium” [ANAL. CHEM.,25, 1605 (1953)3 Fassel, V. A . , and Anderson, C. H., J . Opt. Soc. Amer., 40, 742 (1950). Fassel, V. A , Howard, 9.II.,and ilnderson, Darlene, ANAL. CHEM.,25, 760 (1953). hlortimore, D. lI.,and Koble, L. A., Ibid., 25, 296 (1953). Smith, D. D., and Spitzer, E. J., “Spectrographic Analysis for Hafnium in Zirconium Oxide,” U. 8. Atomic Energy Commission, AECD-2342 (March 1950). These references are all contributions on the spectrographic analysis of zirconium and hafnium and all discuss methods of analysis. SEIL E. GORDOZT, JR. RALPHhf. JACOBS
