Modified Method for Viscosity Measurement of Small Samples J. G. LILLARD Humble Oil and Refining Co., Baytown, Ter. ODIFICATIOX of a small scale viscometer recently de-
the viscometer over a wide range of angles of indination resulted in a curvilinear relationship between the angle of inclination and flow time when plotted on log-log paper as prescribed in the original procedure.
NI scribed ( 2 ) has resulted in improved accuracy, extension
of temperature range, and reduction in operating time requirements. The viscometer was designed for use with sample volumes of leea than 0.1 ml. In principle, the apparatus is based upon the rate of flow of a drop or slug of liquid between two fixed points in an inclined capillary tube. To obtain a suitable efflux time, the angle of inclination of the tube may be varied in accordance with the viscosity of the sample. 4PPARATUS
The basic design of the original viscometer and support were not altered, except that a 0.2-ml. capillary was employed. However, because operating temperatures as high as 210' F. were desired, the constant-temperature bath shown in Figure 1 was built to replace the custom unit used in the original procedure. A 50-50 mixture of r a t e r and glycerol was employed as a circulating medium in this bath to avoid excessive boiling and vapor locking difficulties. Ethylene glycol-water mixture has also been used for this purpose, but rapid discoloration makes it less satisfactory than the glycerol-water mixture. The backpressure regulator valve shown serves the dual purpose of preventing vapor locking in the centrifugal pump and as a fine control (&O.l' F.) for the temperature of the viscometer. At el+ vated temperatures water vapor interfered with the operation of the thermoregulator shown in Figure 1, necessitating replacement wit,h a Thermoswitch inserted through the wall of the bath, such that the regulator unit was locat'ed near the feed to the circulating pump. Improved control of the temperature ( k O . 1 ' F.) resulted. The viscometer tube support was modified by the addition to the protractor plate of a circular slot provided with adjustable angle stops as shown in Figure 2. Srtting these stops to the same angle for opposite inclinations from horizontal permits rapid replicate readings. An obvious improvement over the original protractor design would be the addit,ion of a vernier scale for precision of reading to 0. l o or lese. OPERATION
The operation of the microviscometer was essentially the same as the original, except that time measurements \Tei-e made for the complete passage of 0.04 ml. of sample through the calibrated zone rather than for the passage of the forward meniscus; errors due to small deviations in sample volume are thus reduced. The necessity for thorough cleaning of the tube between samples is emphasized.
1 CONNECTION 10 VISCOME.IR
Ill COPPER i U B l H C I R L O P E C Wll&ASEtSTOS CORD
R E Y O Y A B L E COVER --
Figure 1. Constant-Temperature Circiilating Bath for Viscometer
Hence, in order to determine the best relationship of variables,
a study of the function of flow in the inclined tube was made on the basis of the fundamental Poiseuille equation:
for liquid with absolute viscosity 7,and volume VI flon-ing under pressure PI through a capillary of radius T , and length I , in time e, all variables in consistent units. For a vertical capillary, the pressure may be expressed as
P = hpg for height h, of liquid of density
p,
(2 1
under acceleration of grarity
STANDARDIZATION
Standardization is c a r r i e d out with samples of known viscosity, covering the desired viscosity range (usually 3 to 1000 centistokes a t 100" F.). Primary or secondary viscosity standards are preferred, but oils may be used on which reliable average values from a number of determinations by conventional procedures ( 1 ) h a v e been established. Attempts to employ standardization data obtained with
Table I. Typical Ratios of Viscosity to Flow Time at Several Angles for Several Viscosities Viscosity, Cs. Temperature 210' F. Viscosity, Cs. Temperature looo F. .%nel~, _____--
6 5 , 8 5 E 78 49 E J l i . 9 S 2 . 1 7 7 s 3.1570 5 . 6 1 a 8 . 5 0 6 s 7 . 8 2 S 0 . 0 6 6 4 0 . 0 7 1 0 0 . 0 6 7 3 0 . 0 6 5 6 0.0652 0 . 1 3 5 6 0 . 1 4 2 0 0.1436 0.1502 0.1434 . . . . . . . 2 0 . 2 1 0 1 0.2241 0 . 2 2 1 9 0.2319 0 . 2 2 1 8 . . . . . . . . 3 . , . _ 0.3996 0 , 4 0 5 6 0.3991 .... . . . . . . . . 0 . 4 9 5 1 0:4986 0:5&3 0 . 4 8 1 4 6 . . . . . . . . 0 . 7 7 1 1 0.7775 0.7797 0.7536 0 : 7 i 7 3 0.7658 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.8597 0.8491 0.8671 10 ,,. 1.079 , , . . . . . . . . . 1.053 1.043 1.042 12 , . , . 1 060 . . 1.394 . . . . . . . . . . . . 1.347 1.349 1.328 1.355 15 . . . . . . . . . . . . . . . . . . . .... . . . 1.830 1.819 1.858 1.809 20 ,., ..,. , . , . . . . . . . . . . . . . . . . 2 . 8 2 5 2 . 7 9 0 2 . 8 3 8 2 786 30 . . . . . . . . . . ........ .... . . . 3 . 3 1 4 3 . 2 5 3 3 . 3 0 5 3 2'26 35 . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . 7 4 0 3 . 6 9 3 3 . 7 7 0 3 698 40 . . . . . . . . . . . . . . . . . . . . . . . 4.464 4.577 4.528 . . . . . . . . 50 . . . . . . . . . . . . . . . . . . . . . . . 5 . 1 3 3 5.275 5 212 . . . . . . . . 60 . . . . . . . . . . . . . . . . . . 5 707 . . . . 5.566 5.759 . . . . . . . . 70 Average \-slues b y t-bbelohde viscometer ( I ) . Letter S following 'I iecosity value indicates standard. 1
a
7.413 S 0 0699 0 1419 0 2224 0 3922 0 4851
l5.62n 0 0687 0 1453 0 2258 0 4003 0 4918 0 7657
36.02a
. . . . . . . .
....
1042
1043
V O L U M E 24, NO. 6, J U N E 1 9 5 2
tempted. Typical tabulation of the v/O ratios a t various angles for the several standards employed is shown in Table I. For any angle, values of v / O which deviated by more than 3t2% from the average were omitted. The observed data did not result in a linear relationship as expected, but were found t o be exponential of the form
Table 11. Typical Viscosity Measurements at Various Angles Observation .4v. time, Angle a .
90.25 74.25 47.80 41.90 34.53 26.70 19.68 12.75 10.87 9.63
6 9 10 12
15 20 30 3 ;7 40 a
Log t 1 9554 1 ,8740 1.6794 1.6222 1.5382 1.4268 1 2940
t
O
J
Calihration, R - 0 3994 -0.3112 -0,1155 -0.0648 0 0226 0,1289 0.2643 0.4486
1.1055
0.515'2
1,0362 0.9836
0.5705
Kinematic Viscosity, Cs. Log UO UQ (Assigned, 35.97 1,5560 3 6 . 6 4 1.5628 36.63 1 ,5839 36.09 1 ,5574 36.37 1.5608 35.93 1.5554 36.17 1,5583 35.82 1.5541 35.60 1.5514 35.82 1,5641 36.02" 36.09
Deviations from Mean
cs.
%
-0.12 +0.45 + O , 54 0.00 + O , 28 -0.16
+O.W -0.21 -0.49 -0.27 f0.26
Log
+0.7
(vie)
= A
+
B log sin
h\-erage of four valuesobtained b y ( 1 ) .
Table 111. Statistical Summary of Viscosity Measurements ~ n g i R ~ ~ T ~~ ~ Kinematic ~ ~ . ~ , Viscosity. , Cs. So. O F. Observed Assigned 7.41317 7 500 4 2-6 100 15.60 1.5.62b 6 3-15 100 3 6 . 0 2b 36.09 100 10 5-40 11 6 6 , b6 6.5. 100 9-70 11 i7.80 78.49a 9-70 100 417.4 417.9" 0 30-70 100 43.03 43.11c 12 4-35 100 120.5 120.6c 8 100 15-60 9-5 3.253 3.157b 210 3 "-9 5.61b d , 69F( 210 4 7,86" 7.971 4 2-9 210 8 306a 8.512 .j 3-15 210 2 8 , 73 29.17" J b -3 5 210
Accuracy (Error) Maximum Average
Precision Cs. % h0.3 T O .024 250.2 10.04 =to. i 10.26 10.2 =!=0.16 10.4 10.33 f0.5 x2.0 k0.4 10.16 10.7 h0.8 10.5 3 Z O . 015 10.6 3Z0.034 11.4 kO.115 k0.6 hO.049 10.8 10.22 Av. 1 0 . 6
cs. +0.087 -0.02 +O.Oi +0.71 -0.69 0.0
-0.08 -0 1 +0.096 f0.089 + O . 151 +0.006 -0.44
w
/o
cs.
7%
+1.2 -0.1
+o.122 -0.11
+1.6
+0.5
+1.1 -0.9 0.0 -0.2 -0.1 4-3.0 +1.6 fl.9 +0.1 -1.5 L0.9
+ O 61
+0.96 -1.39 +3 J +0.38 4-1.4 +0.113 + O . 136 + O 328 CO.094
-0.75
-0.7
+1.7 +1.4
-1.8 +0.8 +0.9 f1.2 1-3.6 f2.4 +4.2 +1.1 -2.6
a
(5)
The small deviation of the exponential constant, B, from unity ( B = 1.1177) is attributed to secondary film effects, such as surface tension. The calibration constant, A , is influenced by temperature, and empirical correction has been made according to the equation
At =
'4100
+
o.oO0 l(t
-
loo) (6)
where 1 is the temperature of measurement in O F. For con+vr ndary viscosity standard; p:ircha>ed from .Standard Inspection . S . I ; I ! , ~ ~ . venience, speed, and accuracy, 7 Avcrape of four values obtained by ' 1 . a table of factors may be comC SB? Srsndard3 (certified). d e d from the calibration constants a t the severel temperatures for all angles from 0" t o 90°, such that multiplication of the mean flow time by the proper factor results in kinematic y TVhrn t,he capillary is inclined, however, the equation for presviscosity in centistokcs. suw become>: 2
P=hXsinaXpg
(3)
for an inclination from horizontal of angle a.
Substitution of Equation 3 in Equation I, eliminating h and V ( V = d h ) , and dividing by p, the equation in t e r m of kine-
matic viqeosity, v , becomes (4)
In consideration of the indicated linear relationship between u/O and sin a, evaluation of the calibration constant, k , was at-
RESULTS
The reliability of the modified procedure wa.a checked by making replicate measurements of several primary and secondary standards a t various angle settings. The data from the measurements of a typical secondary standard are shown in Table 11, where the reproducibility a t the various angle settings is apparent. In Table I11 a summary of the viscosity measurements of several primary and secondary standards is shon n. These results indicate that the modified procedure will enable the determination of viscosities within the lubricating oil range a t temperatures from 100" to 210" F. with an average accuracy of i l . O % , and nil1 permit the calculation of viscosity indices u ith an average accuracy of 3t3 unite. K i t h the modifipd procedures savings in time requirements are realized through use of the angle stops and through reduction of the number of angles of measurement. As a result, quadruplicate determinations (four angles) may be made in 30 to 40 minutes, including cleaning apparatus and charging sample, with a sample requirement of 1%. than 0.1 ml. 4CKNOW LEDG \I EYT
-
L
w
LITERATURE CITED
(1) Am. Soc. Testing Materials, Philadelphia, Designation D 445-
A
t
~ b ,
L S T I T ONART E A S E SOPPORT IRIARJ
Figure 2.
--
YIRI!CAL SUPPORT
i '
