June, 1931
INDUSTRIAL A N D ENGINEERING CHEMISTRY
were not included in the calculation of the mean values plotted in Figure 6. Presumably the velocity-constant curve for crystallization of sucrose is typical of what may be expected for sugars when isomeric changes are not involved. The curves for lactose and galactose appear to involve mainly the effects of isomerism. In the case of glucose, some additional influence evidently comes into play, as manifested by the difference in slope of the curve above and below 20' C. It should be mentioned that additional runs on glucose a t 20" C. were made in an effort to discover possible errors in the earlier runs. The earlier results were confirmed.
673
Literature Cited (1) Hudson, J . A m . Chem. Soc., 26, 1065 (1994). (2) Jenkins, Ibid., 47, 903 (1925). (3) Kucharenko and Kartashev, Nauch. Zapiski Sakharnoi Prom., 5, 177 (1927); C. A . , 22, 1490 (1928). (4) Kucharenko and Nachmanowitsch, Nnuch. Zapiski Sakharnoi Prom., 2, 173 (1924); Cenlr. Zuckerind., 33, 1609 (1925). (5) Noyes and Whitney, Z . p h y s i k . Chem., 83, 689 (1897). (6) Parisi, Giorn. chim. ind. a p p l i c a f a , 12, 225 (193G). (7) Rahn and Sharp, "Physik der hlilkwirtschaft," pp. 151-4, Paul Parey, Berlin, 1928. ( 8 ) Savinov, Nauch. Zapiski Sakharnoi Prom., 7, 416 (1929); C. A . , 23, 3825 (1929).
Viscosity-Tempera ture Relationship of Lubricating Oils' R. G. Sloane and Carl Winning STANDARD 0x1.DEVELOPMENT COMPANY, ELIZABETII, N. J.
T IS standard practice in this country to determine viscosities of lubricating oils a t temperatures of loo", 130", and 210' F. (37.8",51.4",and 98.9" C.) However, the viscosity at some other temperature is often required. Pumping effort and fluid-film friction are functions of the viscosity a t the temperature in question, and this temperature may be such as to make viscosity determination inconvenient or impossible with the usual Saybolt viscometer. I n such cases it is very helpful to be able to obtain the viscosities mathematically or graphically by extrapolation from known values. Most of the graphical methods devised comprise plotting viscosity versus temperature on such a system of coordinates that a straight line is obtained. Since no mathematical expression has yet been given to these coordinate systems, they are not easily reproduced and a market has consequently developed for such ready printed forms as those of MacCoull ( I O ) and Herschel ( 7 ) ,which permit the desired linear plotting. Naturally the forms have not always covered the desired range and they have on occasion been extended, as by Larson
I
(9)
Extrapolation on such charts over wide temperature ranges based on viscosities a t 100" and 210" F. (37.8' and 98.9" C.) may give viscosity data greatly in error and figures so obtained can be considered approximations of only a low order. This misfortune cannot be avoided. The charts are more valuable for coordinating viscosity data secured over a wide range of temperatures by special instruments, and it is in this service that most of the published accounts have appeared
plot could be obtained. If such a relation could be found it would free the worker from printed forms, which are often either not available or not adapted to the particular problem. Many equations have been written to express the variation of viscosity with temperature, such as:
++ +
log q = A log (t B) C (5, 6 ) log log 9 = At B (14)
(1) (2)
but they are generally applicable only t o a limited temperature range. The relation (3)
has been shown by Bingham ( 2 ) to possess a high degree of accuracy, but it is too involved for graphical representation. The writers finally turned to a modification of the Vogel equation (7, I S ) : (log q k - A ) ( t
-
B)
=
c
(4)
(3, Q l 15).
where q k is the kinematic viscosity. \Then tested on a number of oils over a wide temperature range, calculated values in good accord with the experimental data were obtained. Unfortunately, the equation contains three constants, and since a method of linear plotting was desired, only two constants, which vary from oil to oil, could be tolerated. A , B , and C were therefore calculated for ten oils on which very accurate viscosity data were available, in the hope that one of them might be common to all oils.
Since to set up a chart based on this information requires accurate viscosity-temperature data on a number of oils besides considerable time and patience, an attempt was made t o find a simple mathematical expression by which a linear
ivote-Three different types of viscometers were used in obtaining the above data, the choice being based on convenience in handling. At moderate temperatures a Saybolt Universal viscometer was used. For viscosities at high temperatures a capillary viscometer as described by Upton (12) was used. This instrument permits of easy and rapid determinations with increasing temperatures. The specific gravities required to compute the viscosities were calculated from the gravities at 60" F. using the Bureau of Standards formula ( I ) . For the high viscosities obtained at low temperatures it was necessary to employ greater pressures than could he applied to the Upton viscometer; a special instrument was therefore designed for this work. This viscometer, resembling somewhat a Saybolt instrument, was closed at the top to permit the application of pressure and was provided with a long glass capillary at the bottom through which the oil was forced. The viscosities were calculated from constants of the capillary together with the amount of oil discharged in a given time.
1 Received March 17, 1931 Presented before the Division of Petroleum Chemistry at the 81st Meeting of the American Chemical Society, Indianapolis, Ind March 30 to April 3 1931.
The least variation was found in B, but, as Table I shows, even this leaves much to be desired. However, the average
The coordinate systems in common use are apparently based on the observations of Porter (11) that if the temperatures a t which two oils have identical viscosities are plotted against each other a straight line will result. From this relation it follows that if the coordinates are so adjusted that one oil appears as a straight line all others will also give linear relationships. Proposed Method
INDUSTRIAL A N D ENGINEERING CHEMISTRY
674
5
!
TEMPERATURE
‘F
value of -135 was chosen and Table I1 indicates the magnitude of the errors introduced when viscosities for oils 22, 25, and 29 are calculated by the formula: (5)
Some of the errors may seem rather large, for example, that between 5.0 and 7.7 million a t -20’ F. (-28.9” C.) on oil 29, but it should be observed that this difference could be accounted for by an error of 3 ” F. (1.7” C.) in temperature which is not far from the limits of temperature control a t this point. Again, oil 25 is a wax-containing oil and its experimentally determined “viscosity” a t 0” F. (-17.8’ C.) decreases with increasing rates of shear (16). This effect is responsible, at least in part, for the difference between the experimental and calculated viscosities. It appears, therefore, that Formula 5 can be used for most practical purposes. T a b l e I-Constant
OIL
ORIGIN
A T 210’
F.
(98.90 C.)
Seconds 20 21 22 24 25 28 29 31 32 33 34 35
Coastal Pennsylvania Coastal Peruvian Pennsylvania Colombian Midcontinent Coastal Midcontinent Pennsylvania Coastal Pennsylvania
4.1 ._
43 49 49 49 62 62 7 ti 75 75 95 95
B
- 132 -~~ - 148
- 132 - 135 - 130
- 160 - 140
- 120 - 148 - 133 - 113
Av.
- 124
135
place of the logarithm of kinematic viscosity. Such a chart can be prepared with little effort and made to fit any desired range, an advantage not common to the various fixed charts now on the market. The wax-free oils 20, 31, and 32 plot quite accurately as straight lines over the whole range from -40’ to 400” F, (-40” to 204.4’ C.). Wax containing oil 21, on the other hand, shows too high an apparent viscosity a t low temperatures, which is in keeping with the observations of previous investigators of this field (8, 9 ) . Conclusion
A comparison of this chart with those of MacCoull and Larson does not show perfect agreement, yet the data for oil K , which was presented as a straight line on Larson’s chart, yields a wholly s a t i s f a c t o r y linear plot in Figure 1. On the whole the divergence is surprisingly slight considering the complexity of the relation represented here by a comparatively simple equation. Since these s h o r t c o m i n g s are so small in m a g n i t u d e , the e q u a t i o n presented 140 200 280 400 s h o u l d p r o v e equal in value to the Calingaert-Davis (4) vapor pressuretemperature formula, viz. :
+A
- log p = & 2t
(6)
without which the oil industry would feel itself badly handicapped. Table 11-Comparison of Experimentally D e t e r m i n e d Viscosities w i t h T h o s e Calculated b y E q u a t i o n 5 OIL 22 OIL 25 OIL 29 Calcd. Expt. Calcd. Expt. Calcd. Expt. 1, O F. Sec. Sec. Sec. Sec. Sec. Sec.
...
- 35
- 20
0 50 100 150 200 210 250 300
8,450,000 7,000,000 ... 845,000 900,000 88 700 88,000 35;3kO 50;OOO 2:730 2,800 1,635 1,600 275 270 363 363 95 90 100 106 55 54 52 54 50 48 49 50 41 40 40 40 36 35 33 36
B as D e t e r m i n e d on Various Oils SAYBOLT VIscosrrY
Vol. 23, No. 6
45 37
45 37
Literature Cited
DEVIATIOX FROM
MEAN
70 - 2
10
- 2 0 - 3 19 4
-11 10 2 17 - 8
* 7
The particular merit of this relationship is that i t lends itself readily to graphical representation, as shown in Figure 1, where log 7]k is plotted against -1/(i! f 135). Corresponding values of Saybolt viscosity could be inserted in
(1) Bearce and Pesser, Bur. Standards, Tech. Paper I? (1916). (2) Bingham, “Fluidity and Plasticity,” p. 137 (1922). (3) Blackwood and Rickles, J . SOC.Aulomolioe Eng., 28, 234 (1931). (4) Calingaert and Davis, IND ENG.CHSM.,15, 592 (1923). (5) Eckhart, “Handbook of Petroleum Industry,” by Day, Val. I , p. 390 (1922). (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)
Hatschek, “Viscosity of Liquids,” p. 7 0 (1928). Herschel, Oil Gas J., 25, No. 28, 146 (1926). Herschel, J. IND. ENQ.CHEX.,14, 715 (19223. Larson, J . SOC.Aufomotive Eng., 2 8 , 321 (1931). MacCoull, “Lubrication,” p. 5 (The Texas Co., 1921). Porter, Phil. Mag., 161, 23, 458 (1912). Upton, Cornel1 Eng. Expt. Station, Bull. 6 (Oct., 1925). Vogel, Physik. Z . , 22, 645 (1921). Walther, Ed62 T e n , 1, 510; 2, 526; 4, 29 (1928). Wilkin, Oak, and Barnard, J . SOC.Aulomolivc Eng., 11, 213 (1928). Wilson and Barnard, J. IND.ENG.CHBM.,14, 682 (1922); 1. SOC. A U W motive EM.,11, 49 (1922).
