I ,
H. H. HOROWITZ Products Research Division, Esso Research and Engineering Co., Esso Research Center, Linden, N. J.
Predicting Effects of Temperature and Shear Rate on Viscosity of Viscosity Index-Improved Lubricants ,
This investigation makes possible a realistic appraisal of the behavior of multiviscosity grade lubricating oils under actual operating conditions in an engine at high rates of shear. The data might be used immediately in redefining the SAE winter grade motor oil classification system
T m most significant development in the passenger car lubricant field in the
tion on the flow properties of viscosity index improver formulations now being used commercially. I n this article, past few years is the rapid growth of reduced variable flow curves are prethe multiviscosity grade oils. These oils, typified by the SAE ~OW-~O’S, sented, from which the viscosity-shear curves of almost all currently used combine the performance of a light viscosity index-improved oils can be winter grade oil and a heavier summer obtained. grade oil in one year-round lubricant. Correlations permit calculation of low To achieve these desirable characteristemperature viscosities and flow curves tics, these oils are formulated with polyof polymer oils from low shear viscosity meric additives known as viscosity index measurements made a t higher tempera(V.I.) improvers (7). Thus, they repretures (100’ and 210’ F.). There is little sent dilute solutions (1 to 3%) of high published information relating to the polymers and their viscosity behavior specific polymer-oil systems currently differs from that of conventional mineral used. Actual low temperature viscosity lubricants in two important respects. measurements are difficult, because waxy The method used for many years to materials in the oil impart a transient predict the viscosity of mineral oils at gel structure to the oils, which the autodifferent temperatures does not hold for mobile engine during cold cranking oils containing significant concentrations apparently does not see. Because of of viscosity index improvers; and polylack of meaningful data at low temperamer-thickened oils show decreasing vistures, the SAE winter grades of motor oils cosity as shear rates are increased. This are still determined by viscosities obis a “temporary” loss in viscosity, not tained by extrapolation on the ASTM to be confused with the permanent visWalther chart. This is fairly accurate cosity loss caused by polymer degradafor mineral oils, but extrapolations for tion under highly turbulent conditions. polymer oils can be in error by a factor While the behavior of viscosity indeximproved oils is typical of polymer soluof 2 (6). tions, the literature does not give informaViscosity-Temperature Correlations Table
l.
Viscosity Index,lmprover Concentrates Intrinsia Poly- Vis. of mer Polymer Concn., in Polymer Type Wt. % Toluene5 Polyisobutylene 20 0.48 Poly(alky1 methacrylate)
A1 A2 A3 A4
46 38 30 25
0.46 0.60 0.81 1.05
Poly(alky1 methacrylate) Type B 30 0.88 a Measure of polymer molecular weight, fractional increase in viscosity of 100 ml. of solvent per gram addition of polymer at infinite dilution.
As the ASTM Walther chart fairly well predicts viscosity-temperature relationship of mineral-base oils, it is necessary only to develop correlations to predict the change in the specific viscosity of the polymer solution with temperature. I t is expedient to use empirical quadratic equations, as the familiar relationships between the logarithm of the viscosity or specific viscosity and the reciprocal absolute temperature are not accurate enough (8). Despite their empirical nature, these quadratics apply to all commercially used viscosity index improvers and all experimental ones looted at, in all types of base oils examined. The study is based on measurements made in Ubbelohde capillary viscometers at temperatures from 210’ F.
to just above the “cloud point” in the case of paraffinic oils (15’ to 20’ F.) and a t 0’ F. in a few highly dewaxed stocks. Base oils ranging in viscosity from 3 to 12 cs. a t 210’ F. and in viscosity index from 30 to 113 were used. The viscosity index improvers studied are available as concentrates in oil having the characteristics shown in Table I. Type A polymethacrylates all have the same composition and differ only in molecular weight. Type B material differs in the nature of its alkyl group side chains. The specific viscosity, asp, used here is based on centistoke viscosities. llsp
=
-
vis. base oil vis. base oil
vis. blend
vis. blend -1 vis. base oil T o express the variation of qaP with temperature, it is convenient to use the ratio, S,of vsp a t any temperature to Vap a t 210’ F. The standard temperature is taken as 210’ F. because all petroleum industry laboratories make routine viscosity measurements a t this temperature, and it is the standard temperature for the SAE summer grade motor oil classification system, and one of the standard temperatures of the viscosity index system. For a given base oil and viscosity index improver, S varies very little with concentration over a fairly wide range (Table 11).
Table II.
S
Varies Very Little with Concentration (Polymethacrylate V.I. improver Type A-3 100 V.I. neutral oil)
Concn., Wt. 7 0 2 4 6 8
VOL. 5 0 ,
%PV
210OF. 0.270 0.569 0.918 1.30
NO. 7
8100
0.823 0.831 0.828 0.832
0
JULY 1 9 5 8
820
0.563 0.579 0.578 0.587
1089
40t
I
1
I
I
I
I
I
1
I
,
I
PETROLEUM BRIGHT STOCK (DOES NOT IMPROVE VI1
'11
0 POLYISOBUTYLENE 8 POLYMETHACRYLATE TYPE A 0 POLYMETHACRYLATE TYPE B E X P E R I M E N T A L V I IMPROVER BASE O I L TYPES
0 COLUMBIAN
LOW COLD TEST ( 3 2 VI) COASTAL LOW COLD TEST ( 3 8 VI 1 0 55 VI PHENOL EXTRACTED COASTAL l o o t V I SOLVENT EXTRACTED NEUTRAL(4.3 C S / 2 1 0 1 -0-l O O t VI SOLVENT EXTRACTED NEUTRAL ( 5 5 C S / 2 1 0 ) l o o t VI SOLVENT EXTRACTED NEUTRAL (MISCELLANEOUS VISCOSITIES) ,d SOLVENT NEUTRAL BRIGHT STOCK MIXTURES U P TO 11.8 C S / Z l O
b
d
/
FITTED
@-
I 210
I I00
T E M P E RAT U R E (*E )
Figure 1, Variation of specific viscosity with temperature depends on polymer type Bright stock and V.I. improvers, 100 V.I. neutral base oils 6'100 is useful for constructing viscosity index improver blending charts, because it is relatively constant in base oils of about the same viscosity index. The change in S with temperature depends on the polymer type, as shown in Figure 1, where points represent the average of four values obtained at different concentrations. Type A methacrylate is represented only by A-3, as molecular weight has little effect on these curves. The different slopes are merely a reflection of the differing viscosity index potencies of the polymers. All these curves, however, are considerably flatter than the curve for a petroleum bright stock, which does not improve the viscosity index significantly. The use of base oils of different solvency to make blends with these and other polymers increases the number of curves possible in Figure 1, until an infinite fan-shaped family of curves is obtained. Most of the low temperature data available in this study were obtained at 20' F.-the lowest temperature at which wax precipitation does not interfere with capillary viscometer measurements for most light dewaxed paraffinic lubricating oil stocks. In Figure 2, $20 is plotted against SI00 for all polymers, base oils, and concentrations investigated. A total of 65 points represents viscosity index improver concentrations of up to 15% (57, active ingredient) and base oils ranging from 3 to 12 cs. at 210' F. and 30 to 113 viscosity index. The polyisobutylene blends are at the upper end of the curve, while the two types of polymethacrylate blends in different base oils are intermingled a t the lower end of the curve. To show that the relationship is continuous, a series of blends of an experimental viscosity index improver of an entirely different type, a poly(viny1 ether), has been included. This polymer is of intermediate viscosity index potency and occupies the
1090
zone between the polybutene and polymethacrylate polymers. There is a unique, continuous relationship between Szo and SIOO.Considering that the coordinates of each point represent two sets of quotients of four numbers each, and that the viscosities at 20' F. are not always measurable with the usual viscometric accuracy because of incipient wax gelation, the scatter of the points is very small indeed. This curve can be fitted by the following parabola : Szo = 2.00
-
(Si00)~
1.82 (Sioo)
INDUSTRIAL A N D ENGINEERING CHEMISTRY
= aOZ -I- be
+1
(1 1
Coefficients A and B are changed to a and b because of the change of variables, from T to 0. Introducing the value of SZOabove, we can solve for a and b and obtain: a =
+'
1.316 (5'100)~ - 2,334 (SIOO)0.962 10,000 (2)
and b
=
4- 0.735
This equation enables the calculation of vSp a t 20' F., given vsp at 100" and 210' F. Knowing vaPat three temperatures it is possible to set up an empirical parabolic relationship for calculating S at other temperatures. The curves of vsp or S us. temperature are so smooth and gradual that there is little doubt that a parabola of the form S = A T 2 BT Cwill fit every one of them (Figure 1). I t is possible to define the entire family of curves if A , €3, and C are ex. is not pressed as functions of S ~ O OThis difficult, using the relation for Sa0 given above. I t is then possible to calculate S at any temperature within the range studied, knowing only &'loo. To simplify the arithmetic the quantity 0 = 210 - T has been substituted for the temperature in the general form of the parabola. When T = 210°, 0 = 0 and S by definition equals 1. Therefore, using 0 instead of T , C is automatically equal to 1.
+
So
+
(3)
where subscript 100 still refers to the value of S at 100' F. (not 0). These expressions for a and b when introduced into Equation 1, give the expression for all viscosity index improvers in all base oils studied a t all temperatures between 20' and 210' F. This can be extended to 0 ' F. to test other limited data at this temperature in low pour point stocks by substituting 0 = 2.10 in Equation 1 to obtain :
+
Sa = 2.760 ( S I O O - )2.992 ~ (SIOO) 1.114
(4)
A plot of actual us. calculated S values at 0 ' F. is shown for a number of blends in Figure 3. The close proximity of the points to the curve indicates that Equation 4 is valid and that the general empirical formula given by Equations 1, 2, and 3 can be extended somewhat below 20' F. because of the smoothness of the curves. From Equations 1, 2
and 3 one can also calculate: At + l o " Si0 = 2.366 X ( S ~ O O -) ~ 2.384 X (Sioo) 0.914
+
At -10" S-ic
3.182 X (SIOO)~ 3.694 (SIOO) -I- 1.329
At -20" S,SS = 3.628 X (SIOO)~ 4.352 X (Sioo) f 1.565
'
Figure 3. Actual and calculated S values agree very well at 0" F.
These equations are applicable to all the viscosity index improvers and in all base oils and concentrations so far studied. Limited data on commercial oil formulations indicate that detergent inhibitor additives do not affect the correlations. They are not believed to be applicable to blends whose SIOO values are less than 0.6, however, as the minima of many of the empirical parabolas occur shortly below this value. By using the above equations, the S value of any polymer blend can be calculated at any temperature and vSp determined from it. The over-all viscosity can be obtained by multiplying the base oil viscosity at that temperature by 1 vBP.The base oil viscosity can be found fairly well by extrapolation (or interpolation) on the ASTM chart. This method is far more accurate than using the ASTM chart directly for polymer oils (Table 111).
I
I 10
09
I
I
/.I
I 2
100
5
+
Variation of Specific Viscosity with Shear
Once the specific viscosity at low shear is known, a "flow curve" is necessary to determine the true viscosity under the high shear conditions prevailing in the engine or engine part under consideration. Ferry's reduced variable technique ( 5 ) , with slight modifications, is convenient for plotting a generalized flow curve for each polymer type, that takes into account temperature, viscosity, concentration, and polymer molecular weight. Similar techniques have been often used in polymer solution studies ( 3 ' 9 ) . The measurements were carried out using two capillary pressure viscometers. A simple instrument covering only about one decade of shearing stresses (from 18,000 to 160,000 dynes per sq. cm.) and operated at room temperature was used to study the effects of concentration and molecular weight. Effects of temperature were studied in a more refined instrument in W. Philippoff's laboratories at the Franklin Institute. The temperature range extended from 14" to 200" F. and the shear stress from less than 100 to more than 400,000 dynes per sq. cm., achieved by using a variety of pressuring means and capillaries of varying radii. Experimental conditions were chosen so that temperature rises were negligible or easily corrected for. Kinetic energy correc-
\ '
_ I
V
-
I
198 F ' 0 - 99 O F 0 14 'F
j
04
tions were made when the flow rates where high enough to make them necessary. In all experiments the pressure and flow rate were the measured quantities. The shearing stress at the wall was calculated as Pr/2L, where r is the radius of the capillary and L is its length. The shearing rate at the wall was taken to be 4V/nra, where V is the flow rate. This is strictly true only for Newtonian fluids, but by using the well known method for obtaining the true shear rate (70)it was found that the error due to this oversimplification is small (1 to 2% of the over-all viscosity) for these blends. The effect was therefore neglected. In Figure 4 are presented the results for a 1570 solution of the polyisobutylene viscosity index improver concentrate
j
I
(about 3% active ingredient) in a light mineral oil at three temperatures, obtained in the Franklin Institute viscometer. The ordinate is similar to Ferry's
Table 111. Viscosity a t 0" F. Is Determined More Accurately Than by ASTM Method 6% polymethacrylate Type B V.I. improver Blend vis. = 6.95 os. at 210' F., 30.22 cs. at looo F. (167 V.I.) Base oil vis. = 3.10 cs. at 210' F., 15.15 cs. at looo F. (55 V.I.) ASTM
Calcd.
Measwed
Extrapolated
819
450 45
Vis. at ' 0 F., c8.
% error
82 1
0.3
VOL. 50, NO. 7
...
JULY 1 9 5 8
1091
V
\
15 W T % BLEUD POLYMETHACRYLATE -YPE A V 1 IMPROVER ( 4 5 % ACTIVE INGREDIEDIENT CONCENTRATlOh)
I
I
Figure
6. Viscosity
reduced viscosity, the specific viscosity expressed as a fraction of the specific viscosity at zero shear. For the abscissa Ferry uses the product of the shear rate and the low shear viscosity, but here simply the shear stress has been used. The two have the same units and are numerically very similar in these cases, because the base oil represents about 40y0 of the total viscosity. The curves are virtually superimposable a t all three temperatures, without including temperature as a part of the reduced variable. If shear rate were used as the abscissa, the curves would be far apart. Thus, by using shear stress as abscissa, the effects of temperature and the varying viscosities of the blends
1092
1
1
\ O
I
vs. shear stress
are eliminated. The same results have been obtained for other types of viscosity index improvers (Figures 5 and 6). The results for the polymethacrylate Type A are not so good as those for the polyisobutylene. The results with the Type B polymethacrylate are very consistent at 14' and 198', but at 9 9 O and above about 1500 dynes per sq. cm. shear stress an anomaly occurs. This is believed to be a capillary entrance zone phenomenon, but is not clearly understood. Similar results are discussed by Bestul and Bryant (2). Pending further evidence, it is assumed that the anomaly does not invalidate the general correlations. The use of shear stress as abscissa in
INDUSTRIAL AND ENGINEERING CHEMISTRY
Figures 4, 5, and 6 has an interesting sidelight. Little viscosity change might be expected in an automobile engine under cold starting conditions, because the speeds and hence shear rates are low. Actually a considerable drop in viscosity occurs, because the high viscosity of the cold oil causes high shear stresses. Figure 7 verifies the usefulness of including concentration in the reduced variable. Here blends of the four molecular weight grades of Type A polymethacrylates at several concentrations show good superposition when the shear stress divided by the per cent of active ingredient in the blend (as obtained from Table I) is used as the abscissa. The points show a fair scatter, but these studies were carried out in the room temperature viscometer and at the low concentrations a 1% error in viscosity becomes as much as 37, error in specific viscosity. If concentration is not included in the abscissa, the curves spread far apart. Thus, by means of the reduced variable only one curve can be used to describe the behavior of a given polymer type in oil regardless of concentration, molecular weight (between 0.4 and 1.1 intrinsic viscosities), temperature, or viscosity. In the academic sense molecular weight has no real effect in the range of molecular weights currently used for viscosity index improvers. Equal concentrations of the same polymer type give identical 17 os. shear stress curves. In a practical sense, however, there is a real effect of molecular weight, as commercial motor oil blends containing a given polymer type are generally made to equivalent specific viscosities at 100' and 210' F. rather than equivalent active ingredient concentrations. The curves of qSp/[~7.~]o us. the shearing stress divided by the concentration for all three of the major viscosity index improver types, applicable for all temperatures from 14' to 200' F. and probably beyond, over a wide range of shearing stresses are compared in Figure 8. These curves were taken from the data given in Figures 4, 5, and 6. The measurements actually extended to about 400,000 dyes per sq. cm. shear stress. If the curves were applied to 2% blends, for example, they would extend to 200,000 dynes per sq. cm. With 1OW-30 oils having a viscosity near 10 centistokes at 210' this corresponds to a shear rate of about 2,000,000 reciprocal seconds at 210' F. These results then should be applicable to many practical situations where high viscosity index stocks are used. Whether they can be applied to lower viscosity index stocks remains to be investigated. The curves in Figure 8 are spaced in roughly the same order as the viscosity-temperature slopes of the polymers (Figure I). In fact, there appears to be a
LUBRICANT V I S C O S I T Y linear relationship between the SIOO values of the blends used to obtain Figure 8 and the logarithm of the value of the shear stress divided by the concentration at the point where reduction in viscosity begins :
r
I
I
I
I
I
I
ROOM TEMPERATURE I C A 7 7 O F ) BLEND VISC=130-150 c s I I I
I
v
Polymer Type Polyisobutplene Polymethacrylate A-3 Polymethacrylate B
8100
Logarithm of Shear Stress + Concn. (Wt. %) at Incipient Viscosity Loss
1.236
1.81
0.807
1.04
0.689
0.83
I
I
l
l
l
i
l
v
CONCENTRATION OF ADDITIVE CONCENTRATE
-\
V: 04-
40%A-3 o'llo%A-3 0 :15 0 % A- 3 I
I
1
I
I
l
I
l
I
"
I
An approximately linear relation also exists at all other values of qsp/(qSp)~. Whether this is a n inherent relationship or merely fortuitous is to be investigated further, with base oils of varying viscosity index. If there is a fundamental relationship, it will be possible to predict both viscosity temperature behavior and loss in viscosity at high shear stress of any blend from its S100,regardless of polymer type. Application to
Cold Starting Tests
An example of the use of the correlations presented is prediction of the "cold starting" viscosities of viscosity index-improved oils a t 0' F. The data for this example have been taken from the previous paper on cold starting (6). Three 1OW-30 oils having approximately the same viscosities at 100' and 210' F. were blended, using the three different viscosity index improver types in base oils of the same viscosity index. The viscosity of the base oils differed, as did the amount of polymer required for each blend. An outline of the calculation of the viscosities a t 0' F. during cranking is given in Table IV. The only measurements needed to predict the cold cranking viscosity are the viscosities of the blend and the base oil at 100' and 210' F. All calculations are based on the centistoke viscosities, but the Saybolt viscosities are also given for the convenience of many accustomed to this viscosity scale. (The SAE motor oil grading system is based on this system.) From the measurements, the specific viscosities are calculated a t each is determined as temperature. S ~ O O qsp a t 100°/qsp at 210'. Next, Equation 4 is used to calculate SO. This quantity multiplied by qBp a t 210' gives qaP a t 0' F. The viscosity of the base oil at 0' F. is determined by extrapolation on the ASTM chart from the base oil viscosities at 100' and 210' F. This is
\
01 I 100
010
SHEAR STRESS
I
1000
- WT
10,000
POLYMER IN BLEND (DYNES/CMZ/%
100.000
1,000,000
ACTIVE INGREDIENT)
Figure 8. Master viscosity shear curves for different V.I. improvers are applicable to many practical situations
+
multiplied by (1 qBP)to give the low shear viscosity of the blend at 0' F. This viscosity is probably not measurable in a capillary instrument, because of the interferepce of wax, but nevertheless has a real meaning. I t represents the viscosity measured a t a shear stress high enough to break any weak wax gel structure that might exist at 0' F. but low enough to be below the point where polymer temporary viscosity loss becomes noticeable. The average shearing stress in the recent model V-8 engine used during cold starting a t 0' to -20° F. has been estimated a t about 500,000 dynes per sq. cm., on the basis of a comparison of curves similar to Figure 4 with the viscosities observed with several polyisobutylene oils a t three temperatures in an engine, as determined by calibrating the engine as a viscometer with Newtonian oils. Using this value and Figure 8, qBPa t 0' F. under shear is determined, by extrapolation in the case of the pdy-
methacrylates. The viscosity of the blend during cranking again equals the base oil viscosity times (1 qep),where qBPis the high shear value. The results thus calculated are in good agreement with the experimental values, when it is remembered that viscosities measured by means of cold cranking tests may be in error by as much as 10% (Table V). Similar cranking test results obtained by Wood (72) confirm this method of approach. The above example points up the different means of formulating multiviscosity-graded motor oils. I t shows how oils of essentially the same viscositytemperature slope between 100' and 210' F. may be prepared using polymers of varying specific viscosity-temperature slopes by using different base oils. These oils do not continue to be the same a t 0' F., where the viscosity of the base oil dominates. Furthermore, the percentage of the viscosity due to the polymer a t different
+
VOL. 50, NO. 7
JULY 1958
1093
Table IV.
of of of of
Vis./210 Vis./210 Vis./lOO Vis./lOO
Correlations Are Used for Calculation of Cold Starting Viscosities of 1 OW-30 Oils with Different V.I. Improvers (At 500,000 dynes per sq. cin. shearing stress)O V.I. Imorover Tvoe Polymethacrylate Polymethacrylate Polybutene, % of Con- 8 - 3 , % of ConcenB, % of Concentrate in Oil, 4.9 centrate in Oil, 12.9 trate in Oil, 5.5 cs. sus Cs. sus cs SUS Determined Values blend 11.29 63.9 10.79 62.1 11.31 64.0 base oil 4.40 40.7 5.85 45.1 6.66 48.0 blend 71.2 330 67.8 3 14 719 333 base oil 24.7 118 40.2 187.2 50.0 232 Calculated Values
at 210' qBpat 100'
1.566 1.883 1.202 1.505 2.357
?sp
8100
so
at 0 Vis./Oo of base oil (ASTM
?8p
0.844 0.687 0.814 0.507 0.427
chart) 1040 4800 shear blend vis./On 3500 16,100 Shear stress X concn. active ingredient 194,000
Low
?sa/ (TSP) 0
vsp at high shear
Calcd. engine vis./Om
and
0.50 1.179 2260
10,500
2560 3670
0.698 0.438 0.627 0.323 0.225 11,800 16,800
303,000 0.22 0.094 2800 12,900
3910 4780
18,000 22,000
340,000 0.10 0.023 4000 18,400
Value assumed on basis of several cranking tests with several polybutene oils at Oo, - l o o , -ZOO F.
Table V. Calculated vs. Actual Cold Cranking Viscosities at 0" F. (low-30 oils of Table IV) Calculated and experimental results a g r e e well
17. 1. Improver Type
Viscosity, PolyO", SUS butene Calculated 10,500 Observed 9,500 ASTM extrap. 11,000
Polymeth- Polymethacrylate acrylate A-3
n
12,900 14,000
18,400 20,000
10,500
11,500
temperatures varies considerably for the three blends used (Table VI). The polybutene oil owes far more of its viscosity to the polymer than the other oils, especially at 0" F. The calculated effect of the loss in viscosity at 500,000 dynes per sq. cm. shearing stress on the over-all viscosity of the blends is least for the polybutene blend a t 210' but greatest for the polybutene blend at 0" F. (Table VII). The loss in viscosity of polymer-
Table VI.
% Viscosity At 210'F. At 1OOOF. At Oo F.
1094
Viscosity Due to Polymer in 1OW-30 Blends Polymer Type Polymeth- PolsmethPolyacrylate acrylate butene A-3 B 61 65 70
46 41 30
41 31 18
thickened oils results in easier cold starting and lower fuel consumption than would be predicted on the basis of their low shear viscosities. However, this does not mean that load-carrying ability will be lost under hydrodynamic lubrication conditions. In fact, there are some advantages in load-carrying ability for polymer oils over mineral oils of the same nominal viscosities (4, 7, 7 7 ) . These may be due not only to variable viscosity but also to little understood phenomena such as Weissenberg or normal stress effects, the time dependence of viscosity and "anisotropic" viscosity, or viscosity differing in different directions. This area requires considerable further investigation.
0" to 210' and shear rates up to 2 X IO6 sec.-l, when only the low shear viscosities at 100" and 210' F. are known. The temperature effects are calculated from an empirical quadratic relationship. The viscosity-shear curves are slight modifications of the reduced variable curves used by Ferry. There is indication that the viscosity-shear curves of a series of polymers are related to their viscosity-temperature behavior, but this needs to be checked further. By using these correlations it is shown that for blends of equal viscosity and viscosity index, those made with polybutene give easier cold starting at 0' F. and yet less loss in viscosity due to shear at higher temperatures than those made with polymethacrylates. The data presented might be used immediately in redefining the SAE winter grade motor oil classification system. In many other instances they could be used in engine design and oil formulation work, if the shearing stresses were accurately known. Acknowledgment
The author wishes to acknowledge the work done for him by Wladimir Philippoff, Franklin Institute of Philadelphia, who carried out pressure viscometer measurements at 1 4 O , 99",and 198' F. Literature Cited
(1) Am. SOC. Testing Materials, Philadelphia, Pa., Designation D 56741.
(5) (6)
Conclusion
Correlations are presented whereby it is possible to calculate the viscosity of any commercially used viscosity index improver blend at any temperature from
(7)
18) j
,
(9)
Table VII. Calculated Effect of Shear on Viscosity of 1OW-30 Blends at 500,000 Dynes per Sq. Cm. Shearing Stress
(10)
% . . Loss in
(12)
Over-all Blend Viscositv Due toShear At210'F. At 0' F.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Polymer Type Pohmeth- PolvmethPolyacrylate acrylate butene -4-3 E 31 35
36 23
37 16
(11)
Be&, A. B., Bryant, C. B., J . Polymer Sci. 19, 255 (1956). DeWitt, T. W., Markovitz, H., Padden, F. J., Jr., Zapas, L. J., J . ColloidSci. 10, 174 (1955). DuBois, G. B., Ocvirk, F. W., Wehe, R. L.. Natl. Advisorv Committee for Aeronaut. Contract NO. NAW6197, Progress Report 9 (revised) August 1953. Ferry, J. D., J . Am. Chem. Soc. 72, 3746 (1950). Fischl, F. B., Horowitz, H. H., Tutwiler, T. S., "Cold Starting with V. I. Improved Multigrade Oils," SAE Annual Meeting, Detrqit, Jan. 9-13, 1956. Harrison, V. Q., "Proceedings of Second International Congress on Rheology," Academic Press, New York, 1954. Johnson. M. F.. Evans. W. W.. Jordan, I., Ferry, J. D.: J . Colloii Sci. 7. 498 (1952). Padden: F. J., JY:, DeWitt, T. W., J . Appl. Phys. 25,1086 (1954). Philippoff, W., "Viscositat der Kolloide," Theodor Steinkopf, Dresden, Germany, 1942; Edwards Bros., Ann Arbor, Mich., 1944. Umstatter, H., Automobiltech. Z. 59, 35 (February 1957). Wood, F. S., Discussion. SAE Annual Meeting, Detroit, Jan. 9-13, 1956.
RECEIVED for review October 10, 1956 ACCEPTED January 2, 1958 Division of Petroleum Chemistry, Symposium on Additives in Lubricants, 130th Meeting, ACS, Atlantic City, N. J., September 1956.
