Aug., 1922
T H E JOURNAL OF I N D U S T R I A L A N D ENGINEERING CHEMISTRY
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T h e Change in Viscosity of Oils with t h e Temperature’*’ By Winslow H. Herschel U. S. BURZAUOF STANDARDS. WASHINGTON, D. C .
There is no satisfactory theoretical equation for change of viscosity with the temperature. Of the empirical equations which have been used, the four-constant equation of Bingham has been found most suitable for definite chemical compounds of low viscosity. The three-constant equation of Slotfe, in various forms, has prooed most serviceable for oils of comparatively high viscosity, The graphical method of Oelschlager may be considered as based on a two-constant equation, simplified f r o m Slotte’s equation, and which gives straight lines on a logarithmic diagram. Oelschldger should have used absolute viscosity instead of the “viscosity factor” calculated from the incorrect Ubbelohde formula. Oelschlager’s assumption that logarithmic viscosity-temperature graphs are straight lines is sufficiently accurate for practical pur-
poses, or within the limits of accuracy of commercial viscosimetry, if only oils of medium viscosity are considered, excluding spindle and airplane motor oils, as well as fatty, compounded and unrefined oils. The viscosity-temperature graphs meet approximately at a point, provided all oils are of the same base, and that the oils are limited as j u s t mentioned. I f is preferable to calculate the point of intersection with the help of a diagram in which the slope of the logarithmic graph is plotted against the logarithm of the absolute viscosity at a standard femperalure. The equation for change of viscosity with the temperature may be used to calculate the temperature of average viscosity, but it is sufficiently accurate to take this temperature as equal to the highest temperature minus one-third the range of temperatures.
IMPORTANCE OF SMALL TEMPERATURE COEFFICIENT OF
which have been used elsewhere will indicate the basis of the method of estimation finally used.
VISCOSITYFOR LUBRICATING OILS
T is well known that an oil will “thin out,” or grow less
I
viscous, as the temperature increases, but the theoretical law for the change of viscosity with the temperature is unknown and empirical methods must be employed. The change of viscosity with the temperature, or temperature coefficient of viscosity, is different for different oils. It is less for paraffin than for naphtliene base oils and less for fatty than for petroleum oils from any crude, castor oil however being an exception to this rule. From a practical point of view, a small coefficient is desirable for a lubricating oil because it lessens the danger of seizure when the temperature of a bearing is accidentally increased above its normal running value. It is noteworthy that the one characteristic emphasized by German engineers, in discussing possible substitute lubricants, was the temperature coefficient of vis~osity.~ CHANGEOF VISCOSITYWITH NEED OF ESTIMATING TEMPERATURE
THE
Standard temperatures4 have been adopted in commercial viscosimetry, and estimates would be avoided by their use, but nevertheless it is often necessary to efitimate the viscosity of an oil at one! temperature from the known viscosity a t another. The word estimate is used advisedly, because the relation between viscosity and temperature is not accurately known, two deliveries of oil are seldom identical , and there is always a possibility that impurities will be present which exert an influence upon the temperature coefficient of viscosity. Thus there is need of the method of estimation suggested in this paper, rather than of a table, equation or diagram for each oil. An examination of the equations 1 Received March 2, 1922. Presented before the Section of Petroleum Chemistry at the 63rd Meeting of the American Chemical Society, Birmingham, Ala., April 3 to 7, 1922. * Published by permission of the Director, U. S. Bureau of Standards. 8 Z. Ver. deut. Ing., 59 (1915),478. 4 The standard temperatures in the United States are looo, 130°, and 210’ F. (37.8’, 54.4’, and 98.9’ C.),but use is also made of 104”, 131”, and 212’ F. (20°,55’, and 100’ C.)which has the advantage of avoiding decimals. , SeeProc. A m . SOC.Test. Malerzals, 15, I(1915). 280;19, I (1919),
730.
EQUATIONS EXPRESSING FLUIDITY-TEMPERATURE EMPIRICAL
RELATIONS If Saybolt viscosity (the time of flow of oil when measured by means of the Saybolt Universal viscosimeter) is plotted against temperature, as in Fig. 1, a series of more or less hyperbolic curves is obtained, which are inconvenient for extrapolation. Little is gained by using viscosity in poises, the c. g. s. unit of viscosity, as in Fig. 2. It is desirable to adopt a method of plotting, or form of equation, which will give fairly straight lines with as great a variety of liquids as possible. EQUATION WITH TWO CONSTANTSl USING FLUIDITY-The range in viscosity between the most fluid and the most viscous petroleum products is so great that equations which are suitable for showing the viscosity-temperature relation of lubricants are not equally convenient for gasolines. For the latter, petroleum products with a viscosity less than that of water, it is most convenient to use the equation Fluidity =
-P1
=A
f Bt
(1)
Dean and Lane5 suggest a somewhat similar formula, but use kinematic viscosity (absolute viscosity in poises, divided by the density in g. per cc.) instead of absolute viscosity, with temperatures presumably in ’C., and find that “if the reciprocals of the kinematic viscosities as ordinates are plotted against the temperatures as abscissas, the resulting lines are straight for the lighter fractions and only slightly curved for the heavier fractions.” Fig. 3, partly from data of Thorpe and Rodger,O shows fluidity-temperature graphs for some of the aliphatic hydrocarbons and other very fluid liquids. Graphs for commercial gasoline and its substitutes lie between those for water and octane, while aviation gasolines lie between heptane and hexane. It will be noted that the graphs are much straighter 6
THISJOURNAL, 18 (19211, 779.
E. C . Bingham and J. P. Harrison, 2. physik. Chem., 66 (1909). 12; calculated from data of T. E. Thorpe and J. W. Rodgqr, Tvans. Roy. SOG. London, 185 (1894), 397; Winslow H. Herschel, Bur. Stds., Technologic Pafieu 185 (1919),17. 8
THE JOURNAL OF INDUXTRIAL A N D ENGINEERING CHEMISTRY
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than in Figs. 1 and 2, and that their curvature decreases as the viscosity decreases. Yet even with pentane there is a slight divergence from the straight-line relation indicated by Equation 1.
Vol. 14, No. 8
equation for water9 is a four constant equation of somewhat similar form to Equation 2: 8676.8 (4) t = 0.23275 (9 120) 8.435- 4 120 According to Dunstan and Thole, the form of Equation 3 has been found more accurate than that of Equation 2 to reproduce fluidity data obtained by experiment, but it is not as accurate as the form of Equation 4 which also contains four constants. It is generally considered that the more constants there are in an empirical equation the more accurately it may be made to fit a series of observed points, but Karl Pearson has remarked that a curve based on too great a number of constants may follow the undulations due to experimental error, instead of taking a course which is both smoother and more nearly correct. However, the excessive amount of labor involved is ordinarily a sufficient guard against the use of too many constants. I n the case of petroleum oils, where constants would have to be determined for every brand, it is evident that the uniformity of a given brand is not sufficient to warrant cxcessive accuracy. There is also considerable doubt as to what form of equation best applies to oils of high viscosity, as the equations above referred to have never been used for very viscous liquids. SLOTTE’S FORMULA-Thorpe and Rodger,lo after a thorough examination of available formulas, concluded that Slotte’s formula
+
+
+
gives the best results. Equation 5, when expanded on the /00
/I0
I20
130
/40
/50
I60
/70
/BO
/90 20U
210
Tempero fure, F FIG. 1-SAYBOLT
VISCOSITY-TEMPSRATURE DIAGRAM
It is convenient to use diagrams of the form of Fig. 3 for extrapolation, but care should be taken not to extrapolate beyond the boiling point of the liquid in question. In estimating fluidities a t temperatures which are too low to be conveniently reached in testing, it is assumed that the fluidity a t the point of solidification, or “pour test,” is zero, and then the graph is extended to pass through this point, as shown for one of the samples of kerosene. Water is an exception, because it undergoes a sudden change in consistency when it freezes, instead of gradually growing more viscous, as is the case with mineral oils. BINGHAM’S
EQUATIONS FOR FLUIDITY-TEMPERATURE RELA-
TION-Bingham’s belief that fluidities are additive naturally led to his use of fluidity-temperature equations, which have proved applicable to definite chemical compounds of low viscosity.’ Of special interest are his equations for three of the liquids shown on Fig. 3, hexane, octane, and water. For hexane he found the equation t = 0.218929
- 9137’8 + 254.03 9
where t is the temperature in for octanela he found
T
0.190749
O
(2)
C., and 4 is the fluidity;
4 - 343.42 - 23193 4
1325100
(3)
4s
Temperafure,
+
where T is the absolute temperature (“C. 273). The 7 A. E. Dunstan and F. B. Thole, “The Viscosity of Liquids,’’ 1914, 27. 8 E. C . Bingham, Am. Chcm. J., 40 (1908).279;48 (1910),292. Other equations for octane and other aliphatic hydrocarbons are given by Dunstan and Thole, LOC.cd., 5.
“E
FIO. ABSOLUTE VISCOSITY-TEMPERATURE DIAGRAM
E. C . Bingham, Bur. Slds., Sci. Paper 398 (1917),75. Trans. Roy. SOC.London, 186, I1 (1894). 438;R. F. Slotte, Beibl. Ann. Physik, 18 (1892),182. 0
10
Aug., 1922
T H E JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
assumption that the temperature coefficient is small, simplifies to
’
A
=
1
+ at + bt2
I
I
I
I
I
I
I
500 450
II
I50
- -$
JOO
-
.Er
3
B
50
0 --x -50
Temperahre, FIQ. 3-FLWlDITY-TEMPERATVRE
SIMPLIFIEDSLOTTEEQUATION WITH Two CONSTANTS If A in Equation 7 is zero,
(6)
0 = Binqham andNarr/son X = Bureau of Standards
550
717
“C
which represents a straight line on a logarithmic diagram. Since such straight-line diagrams have been used by Oelschliiger’s it is of interest to examine his work and to determine what justification there is for thus simplifying the Slotte equation. OELSCHLAGER’S METHoD-Oelschlager has given equations and diagrams for estimating the viscosity of oils at different temperatures, but his whole work is based on the unfortunate assumption that Ubbelohde’s equation for the Engler viscosimeter is reliable. In reality the error in this equation is about 20 per cent a t certain viscosities.16 Oelschlager, following Ubbelohde, uses Z to denote the “viscosity factor” which is equal to the kinematic viscosity of the oil, divided by the absolute viscosity of water, in poises, a t O o C. Using a logarithmic diagram, he plots 8, as obtained from Ubbelohde’s equation, against the temperature in “C., and obtains a series of straight lines, one for each oil, which intersect the axis of abscissas (where Z = 1, the viscosity factor of water) within a fairly narrow range of temperatures. Taking the average temperature, tl, at the point of intersection as 185’ C. (365” F.), he says that for most 02s deviations from this value may be regarded as within the experimental error. Then in order to find the viscosity of an oil a t any temperature, t, when its viscosity a t 20” C. (68” F.) is known
-log log -2 z 20
DIAGRAM
The work of Dean and Lane is based on Equation 6, modified by substituting kinematic for absolute viscosity. They say, “This is in effect the Slotte equation, which is usually employed to indicate the relation between absolute viscosity and temperature, but which the authors have found equally useful as applied to kinematic viscosity.” This method has the advantage that kinematic viscosity is obtained directly from readings of most efflux viscosimeters, while to obtain absolute viscosity it is necessary to determine density (by a hydrometer or otherwise) and make a further calculation.
logtl11--log log20 t log
(9)
from which
If Equation 5 is written /*=-
(t
K
- A)“
(7)
where K, A, and n are constants for a given oil, and t is the temperature, it is equivalent to several of the simpler equations which have been proposed. If n = 3, t is taken in O C., and A = -273, Equation 7 is equivalent to Batschinski’s formula.11 If n = 1, Equation 7 takes the form of Hersey7s12 Equation 49, where “A is the apparent solidifying temperature.” A similar equation was found by Ellis,la who found that, “if temperatures be taken above the point of solidification of the oil, and viscosities be taken with reference to the viscosity of water, then (representing temperature by T and viscosity by V) TV” = constant.” Bingham14 also makes the viscosity-temperature equation depend upon the solidifying temperature, since he regards fluidity as a function of the “free volume,” i. e., the volume in excess of that a t the temperature a t which the fluidity is zero. Proc. Am. SOC.Test. MQW~UZS, 14, I1 (1914), 583. D. Hersey, Truns. Am. SOC.Mech. Eng., 37 (1915), 190. 1’ R. L. Ellis, paper presented before the Alabama Light & Traction Aasociation, November 1913. Met. Chem. Eng., 10 (1912). 546. 1‘ J . A m . Chem. SOC., 86 (19141, 1391. 11
I*M.
11
2. Ver. deul. Ing., 63 (19181, 422.
16
Window H. Herschel, Bur. Slds., Technologic P u p a 100 (1917). 9, 27.
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T H E JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
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According to Oelschlager, if viscosities are expressed in poises and temperatures in a C., logarithmic graphs drawn as before will intersect on the line parallel to the axis of abscissas, where the viscosity is 0.0162 poise. As seen from Fig. 4,plotted from data of Archbutt and Deeleyl' the graphs are not straight, except for a few steam engine cyIinder oils, and they do not intersect at a point. It is believed that the approximate straightness of Oelschlager's graphs is due to his use of a shorter range of temperatures, and to an entirely accidental balancing of the errors due to the use of the Centigrade scale and of the inaccurate formula of Ubbelohde. As d l be shown later, the graphs are approximately straight when the solidification point of the oil is near the zero of the temperature scale which is used in plotting. Thus the Fahrenheit scale gives straighter graphs for the lighter oils, but as shown in Fig. 4, the Centigrade scale gives straighter graphs for very heavy oils. Changing the temperature scale is equivalent to changing the value of A in Equation 7. It will be noted in Fig. 4 that the curvature of the graphs for rapeseed and sperm oil is greater than for the mineral oils, which is in accordance with Oelschlager's tests. THE LOGARITHMIC VISCOSITY-TEMPERATURE DIAGRAM, USI N G FAHRENHEIT DEGREES-Fig. 5 is similar to Fig. 4 but
temperatures are in O F. instead of O C. It will be noted that a practically straight-line diagram for oils of medium viscosity has been obtained simply by changing the temperature scale. Excluding spindle oils, and those of lower viscosity, and also steam engine cylinder, or airplane motor oils, the graphs for the other oils meet approximately a t a point. The accuracy of the assumption that the graphs of Fig. 5 are straight was investigated as follows. If the viscosities A
Log,, Temperafure, F I G . &-LOGARITHMIC
O f
VISCOSITY-TEMPERATURE DIAGRAM, FAHRENaEIT SCALE, FOR PARAPBIN BASEOILS
log 2 = log
220
-
2.267 log t 0.966
(10)
where ZZois the viscosity factor at 20" C. (68" F.). Oelschlager warns his reader that his method should be used only within the range of temperatures covered by his tests, 20" to 100" C. (68" to 212O F.), and that the value of tl is only approximate. One steam engine oil gave 210" C. (410" F.) and another lubricating oil gave 200" C. (392" F.). According to his diagram, the lowest value of tl obtained with any mineral lubricating oil was about 175" C. (347" F.). Both the well-refined oils procured before the war, and the "present deliveries of badly refined oils," showed the strdightline relation, which was also found to hold good for rosin oil. On the other hand, "Oils such as paraffin oil, linseed oil, rapeseed, castor, and sperm, of which only the last two come under consideration as lubricants, act similarly to mineral oils, but the lines are not entirely straight, curving downward somewhat a t the higher temperatures. This is especially the case with rapeseed oil, which shows a strongly curved line which is considerably flatter than those for mineral oils a t low temperatures." Two tar oils and three other substitutes for lubricating oils showed straight graphs and low values of tl. The lowest value, 54" C. (129" F.), was obtained with a transformer oil, supposed to be pine oil, which gave a slightly curved graph, and was the least viscous oil which Oelschlager investigated.
FIG. 6-LOGARITRMIC
17
VI~COSITY-TEMPERATURB DIAGRAM POR NAPBTHBNE BASBOILS
''Lubrication and Lubricants," 1912, 190.
THE JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
Aug., 1922
pl p 2 ps.. p x of a given liquid are known for three or more temperatures tl t2 ta. .tr the value of n in Equation 7 may
be obtained from the equation
log Pi3 - log P4 etc. 1%(ta -A) -log(& -A)'
(11)
719
Table I1 shows the ratio between viscosities as found by experiment and as calculated from the constants of Table I, and shows that the percentage error in Equation 7 is much greater than woidd be concluded from an inspection of Fig. 5. The oils are in the same order as in Table I, omitting castor oil and the last two petroleum oils. Assuming no error in viscosimetry, the tables show that n in Equation 7 is slightly greater a t low temperatures than
9\ O = Before
x = After
7
anLi freafmenf If
11
I
I
I
I
I
I
/.9
20
2.1
2.2
2.3
2.4
I
3.6
17
18
L oq,* Temperature, FIG.
7-OILS
BEFORE AND AFTER
2.5
26
2.7
2.8
'E FIQ. RUSSIAN,
ACID TREATMENT
which may be abbreviated to n = B = C = D. From the data of Archbutt and Deeley, for fatty and for American petroleum oils, values of the constants of Equation 7 were obtained, as given in Table I. Temperatures were taken in " C., and A was chosen by trial so as to give the same value for B and C or for C and D. The temperatures were tl = l5,6', tz = 37.8', ta = 65.6', and t 4 = 100" C. (eo", loo", 150°, and 212' F., respectively). TABLE I-CONSTANTSIN EQUATION ~r=
ma FATTY K
FOR
AND
AMI~RICAN PETROLEUM 011,s
VISCOSITIES TAKEN AT TEMPERATURES O C. 15.6, 37.8, and 65.6 n R 2.88 78000 2.97 162000 2.72 50000
KINDOF O I L A Sperm -52 Olive -41 Raueseed -36 Castor. . . . . . . . . . . . . . . . . . . Spindle 886.. ........... -31 Spindle 860/70.. ........ -37 Light machinery 900/7 -40 Solar red engine -34 Bayonne engine.. ....... -37 Medium (dark) machinery -23 Valvoline filtered cvl. Dark cylinder A . .
................. .................. .............. .. ........
.... 2.64
3.19 3.57 3.65 3.78 3.22
...... 11500
224000 1930000 2950000 6920000 391000
. . ... ..... .. ... .. ... .. ... . . ....... .
37.8, 65.6, and 100
A
-4 -25 -36 -16
N
K
1.53 2.44 2.72
57 9180 50800
2.94
190000
- 1
- 3 - 3 - 5 -16 -14 -17 0
The average of the fourteen values of A for the petroleum oils is found to be -18.6" C. (-1.5" F.). Using the Fahrenheit scale is therefore equivalent to using almost, exactly the correct value of A, since it is the same as using the Centigrade scale with A equal to -18'.
SCOTCH, A N D OTHER O I L S
TABLS11-RATIO CUI,ATBD --VISCOSITY
BETWEEN EXPERIMENTALLY DETERMINED AND OF ARCHBUTT AND DEBLEY AT 100' -VISCOSITY AT 15.6'
VISCOSITIES, FROM DITA
Calculated from Viscosity a t Lower TemB Y TEST peratures 0.046 0.041 0.067 0.070 0.080 0.080 0.033 0.030 0.039 0.033 0.049 0.041 0.068
0.063 0.076
0.050 0.058 0.073
c.-
Ratio 1.12 1.04 1.00 1.10 1.18 1.20 1.16 1.09 1.04
CAL-
c.-
Calculated from Viscosity at Higher TemRatio B Y TEST peratures 0.59 0.71 0.42 1.10 0.92 1.008 1.118 1.12 1.00 0.67 0.68 0.453 1.09 0.67 0.727 1.138 1.79 0.64 1.915 2.85 0.67 2.66 0.82 2.172 3.046 3.48 0.88
a t high, except in the case of rapeseed oil, and that it is better to estimate viscosities a t high temperature from known viscosities a t low temperatures than vice versa. It is not certain whether there is a definite temperature at which there is a change in the viscosity-temperature relation, or whether the apparent change is due to error in the form of equation. Hurstia expresses the opinion that "there is what may be called a 'critical point' a t which temperature the oil begins to lose its viscosity more rapidly, and below which point the loss of viscosity on heating is very slow; this critical point varies with different oils, but the author has not been able to do more than make a few tentative experiments on the subject." As Hurst does not give even 1s
"Lubricating Oils, Fats, and Greases," 1911, 243.
THE JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
720
Vol. 14. No. 8
graphs for oils of this base. As will be seen later, there is a different point of intersection for each other class of oils, as observed by Dean and Lane but disregarded by Oelschlager NAPHTHENE BASE oms-Fig. 6 shows testslg upon American oils of naphthene base, together with some foreign oils. Most of the graphs are fairly straight, the most marked exceptions being the fuel oils from Mexico and Persia. The Mexican fuel oil showed marked viscosity hysteresis, and according to Dunstan and Tholez0 this phenomenon “is one eminently characteristic of colloids.” Thus it would appear that the curvature of the graphs for fuel oils is probably due to the presence of colloids, a conclusion which has some support from the work of Beaton, Probeck and Sawyer,21 who found, with varnishes, that the shape of the viscositytemperature graph is determined by the amount of colloids. Fig. 7, from data of Dunstan and Thole, does not show any marked relation between the amount of acid treatment and the form of graph, although colloids are removed by acid treatment. This may, however, merely prove that colloids were not present in large quantities in the oils as received by Dunstan and Thole, which is quite possible, since the phenomenon of viscosity hysteresis is comparatively rare. The data concerning Russian and Scotch oils, Fig. 8, are not sufficient to locate points of intersection, for oils of moderate viscosity, as in Figs. 5 and 9. The only curved graph is for one of the Scotch oils; it has been found that oils of such low viscosity always show curved graphs. 1’ Thus it may be concluded that the great majority of mineral oils of moderate viscosity will show approximately straight graphs, but there is more uncertainty in assuming a straight
.
/.2
-
40 0.8
__
0.6 -
0.4 0.2
0.0 -
/IS -
3 a i.4 - q 16-
.c,
4
62
-3 G
/To -.$0
2 f.8
-& 0
26 --
24 2.2 -
to 3.8Z 6 L T FIG. FRACTIONS OF SINGLE SAMPLE OF NAPHTHENE BASEOn,
There is some evidence that Equation 7, with A equal to the solidification temperature, is more accurate and covers a wider range of oils than Equation 8. Ellis found that some of the more viscous oils did not give a straight logarithmic graph, but if the temperature above the point of complete solidification was used instead of temperature in O F., substantially straight lines were obtained even with these oils. Fig. 4 also shows fairly straight graphs for the most viscous oils. There is, however, some objection to the introduction of the solidification temperature into an equation, as the laboratory method for exactly determining this temperature is doubtful, and Equation 8, with temperatures in O F . , has therefore been adopted, as sufficiently accurate for practical purposes for the majority of oils most frequently used, and as most convenient for graphical methods.
APPLICATIONS OF THE LOGARITHMIC VISCOSITY-TEMPERATURE DIAGRAM
OILS-All the American mineral oils tested by Archbutt and Deeley appear to have been of paraffin base, with the exception of the two oils of lowest viscosity, so that Fig. 5 may be taken as the diagram for paraffin base oils, which indicates the approximate intersection of the PARAFFIN BASE
16
/.7 f.8
L 9
2.0
2.1
2.2
2.3
2.4
25
26
2.7
Log,, Temperafur% PIG. IO-ANIMAL
AND
VEGETABLE OILS
1) W.F. Parish, J . Am. SOC.Naval Eng., S2 (1920).45; W.F. Higgin., Nut. Phys. Lab. Collected Researches, 11 (1914),10; 18 (Isle),281. 10 J . Inst. Petroleum Tech., 4 (1917-18), 201. *I THISJOURNAL, Q (1917).35.
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T H E JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
graph for an unrefined than for a refined lubricating oil of the same viscosity. RIIacCoul122has devised a special crosssection paper which gives straight lines when Saybolt viscosity, in seconds, is plotted against temperature in F., but this diagram gives curved lines for the same oils which appear curved on the ordinary logarithmic diagram. THE EFFECT OF NARROW cum-In order to determine whether the range of boiling point influences the shape or slope of the graph, a sample of naphthene base lubricating oil was subjected to a fractional distillation, without steam, a t 1.5 mm. absolute pressure, so as to avoid cracking.23 Of the resulting ten fractions, Fraction 8 was selected for a second distillation, after having been discolored with part of the residue from the first distillation. It was due to this contamination that the original oil of the second distillation had, as shown by Fig. 9, a slightly higher viscosity than Fraction 8 of the first distillation. Fraction 5 of the first distillation has practically the same viscosities a t all temperatures as the original oil. I n the second distillation the same is true of Fraction 6, so that the evidence appears to be that narrowness of cut does not influence the slope of the logarithmic graphs; in other words, the value of n in Equation 8 depends upon the viscosity of the oil a t a given temperature, but not upon the boiling point range. It will be noted that all the oils on Fig. 9 are strictly from one crude, being in fact all fractions of the same sample, O
Lubrication, June 1921, 5. *a It was found b y J. E. Schulze, formerly of the Bureau of Standards, who developed this method, that it suitable precautions were taken to prevent leakage, the distillation could he carried t o 300° C. (572O F.) without cracking. 22
72 1
and it would therefore be expected that the point of intersection would be more clearly defined than in Fig. 5 where the oils were probably from different localities. FATTY OILS-AS already indicated by Fig. 4, the graphs of fatty oils are more curved, but not so steep on the average, as those for mineral oils. Fig. 10 also shows that with fatty oils, as with mineral oils, the curvature is most for the lighter oils a t the lower temperatures. The graph for castor oil, from data of Kahlbaum and RaberZ4and others, and the two graphs for rapeseed oil, show that there is considerable error in the assumption that two samples of a given kind of fatty oil will have the same viscosity. Such oils cannot therefore be regarded as liquids of “known viscosity” for use in calibrating viscosimeters, unless the viscosity of the particular sample in question has been determined.25
I
METHODOF CALCULATING POINTOF INTERSECTION OF LOGARITHMIC GRAPHS DIAGRAM FOR DETERMINING THE VALUE OF
p =
K
-It t”
n I N EQUATION
may be seen in Figs. 5 to 9 that the steepness
of the slopes of the graphs increases with the viscosity of an oil a t a given temperature. If as in Fig. 11, n, which is a measure of the slope, is plotted against the logarithm of the viscosity a t a standard temperature, the data can be Quoted in Bur. Stds., Technologic Paper 112 (1919),24. The Bingham viscometer (Bur. Stds., Sci. Paper 298) was used for determining the viscosity of the fractions shown in Fig. 9. It is used to determine the viscosity of calibrating liquids, having a kinematic viscosity not over 0.5, but is not considered accurate for more viscous liquids on account of drainage error. 24
26
T H E JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
722
fairly well represented by three straight lines, for naphthene base, paraffin base, and fatty oils, respectively. The greater scattering of the points for naphthene base oils is probably due to a large extent to the natural tendency
Vol. 14, No. 8
EQUATIONS CONNECTING THE n DIAGRAM WITH THE LOGARITHMIC VISCOSITY-TEMPERATURE DIAGRAM-A straight
line on Fig. 11may be represented by an equation of the form 1~
= H (log PI
+ E)
(14)
where H is the tangent of slope and E is the value of - log pl where the line intersects the axis of abscissas. By a modification of Oelschlager's method, using absolute viscosity a t 100" F. (37.8" C.) instead of the viscosity factor a t 20" C. (68" F.), and assuming that logarithmic graphs meet a t a point, log log fil
- log P D - log
-
PD
log to - log t log t D log 100
-
(15)
where t o and po are the coordinates of the point of intersection of the logarithmic graphs for oils of the crude under consideration, and p is the viscosity a t any temperature, t. It should of course be kept in mind that there is no certainty that logarithmic graphs should be straight above 100" C. (212" F.), so that t o should be regarded as a means of calculation rather than as the temperature a t which all oils of a certain class would actually have the same viscosity. There is some evidence, however, that the viscosity-temperature relation follows the same law for a considerable range above the boiling point of water, as below it, for Dean and Lane made two tests a t 180" C. (356" F.) and found close agreement between the observed and extrapolated viscosities.
45
40
c 3s B 30
.?
By combining Equations 14 and 15,
and
E FIG.~~-VISCOSITY-TEMPERATURE GRAPHS FOR Two MEXICANCRUDEOns
to regard any oil, not of paraffin base, as a naphthene base oil. Thus oils from mid-continent crudes, or blends of paraffin with naphthene base oils, may have been classed and plotted with the naphthene base oils. However, the upper limit of points in Fig. 11, as determined by oils of Fig. 9, is clearly defined. It will be noted that castor oil is an exception to other fatty oils, and that the commonly accepted belief that it "thins out less with the heat" than do paraffin base oils, is a delusion. In order to get a definite value of n from the curved graphs of Fig. 10, it was necessary to assume straight lines between certain temperatures. These temperatures were taken, as for the mineral oils also, as 100" and 212" F. (37.8"and 100" C.). Since tallow and wool fat are solid a t the lower temperature, it was necessary to find the slope from a shorter range of temperatures. The oils marked "compounded" were mineral oils containing a blown fatty oil, which indicates a convenient way to decrease the temperature coefficient of viscosity. Blown oils, however, increase in viscosity with time. Fig. 11 gives all the data necessary for finding the constants in Equation 8 if the viscosity has been determined a t the standard temperature of 100" F. (37.8' C.). Then log K = 2%
+ log
(12)
PI
where pl is the viscosity a t 100" F., in poises. Entering Fig. 11 with log pl the ordinate n may be read, and K calculated from Equation 12. Then for any other temperature log
p=
log K--n. log t =
1~
(2-log t )
+ log
Pi
which is about equal in simplicity to Equation 10.
(13)
= -log
(17)
PO
by means of which a point of intersection may be calculated on Figs. 5, 9, and 10, corresponding to the full lines on Fig. 11. The calculated as well as the graphically determined points are given in Table 111, the calculated points being shown on Figs. 5 and 9 by double circles. TABLEIII-cO6RDINATES
O F POINTS O F
CLASS O F OILS Paraffin base, Fig. 5 . . . . . . . Xaphthene base, Fig. 9 . . , . . . F a t t y oils, Fig. 1 0 . . . . . . . , . Paraffin base, calculated.. . . . . Naphthene base, calculated.. F a t t y oils, calculated.. . . .
.. . . . . ..
GRAPHS log PO 2.00 8.78
2.35
3.58 8,88 2.75
INTERSECTION PO 0.010 0.006 0,022 0.0038 0,0076 0.0056
OR
LOGARITHMIC
log t Q 2.60 2.59 2.66 2.77 2.57 2.82
fQ
398 389 363 589 371 661
Conversely, a line on Fig. 11 may be found corresponding
to a certain point of intersection obtained graphically. The values of H and E are given in Table IV, both as obtained graphically and by calculation. FOR LOCATING GRAPHSON THE n DIAGRAM CALCULATED----OBTAINED GRAPHICALLYIntersection Intersection CLASSOB with Axis of Tangent with Axis of Tangent E of Slope Abscissas E of Slope OILS Abscissas 1.67 5.00 2.00 2.42 1.30 Paraffin base 3.58 2.22 1.70 1 . 7 5 8 . 7 8 3.88 2.12 Naphthenebase 1.65 1.79 1.22 2.35 3.75 2.25 F a t t y oils
TABLE IV-DATA
----
The dotted lines on Fig. 11 were IocaOed by the calculated values in Table IV. It will be seen that these lines do not agree a t all well with the experimentally determined graphs, shown in full lines. On the other hand, the calculated point's of intersection, on Figs. 5 and 9, agree with the graphs as well or better than the points obtained graphically, so that it is preferable to calculate the point of intersection. Before considering the temperature of average viscosity (which is a related but distinct subject) it may be well to summarize the practical applications of the method developed for estimating viscosities. It should be remembered that
