Consistency and Temperature of Oils and Printing Inks at High Shearing Stresses RUTH N. WELTRIAIVY Interchemical Corporation, A'ew York, N. Y .
material, attempts were inade to maintain the temperature of the material under investigation constant by placing the rotating part-the cup-of the viscometer in a constant temperature bath. Since controlling the temperature of the cup might not be sufficient to keep the oil temperature down at points away from the cup wall, the question rras raised whether it would be possible experimentally to separate to a higher degree the temperature from the molecular alignment effect.
T h e reversible breakdown in consistency of oils and other materials at high rates of shear is shown to result mostly from thixotropic behavior and not from temperature increases due to shear in the viscometer. In the case of oils the thixotropic behavior is assumed to be caused by molecular shear alignment. Calculated data taken from the literature, for the decrease in the viscosity of oils with an increase i n rate of shear, are found t o be of the same order of magnitude as the experimentally obtained results. The consistency of plastic and thixotropic materials in shown to decrease with increasing temperature.
3IEASL'RIhG PROCEDURE
T
HE behavior of oils at high rates of shear has been a debatable subject for years. Some investigators ( 1 , 9, 10, 11, 14, 16, 17, 19) believe that the observed reversible decrease in viscosity during a viscometric measurement results from an increase in temperature caused by the energy absorbed in the oil. Others IB, 3, 18, 15, 20) consider molecular alignment as at least a contributing factor. It is difficult to separate the teniperature and other breakdoxn effects; therefore it is hard to determine whether the rising teniperature or the thixotropic breakdon-n is causing the reduction in viscosit,y or how much of each is responsible for the effect. Practically all suspensions exhibit thixotropic hrcalido~w Green and Keltniann (7, 8) have shown that the thixotropic characteristics of the materials are determined by the hysteresis flow curve when the viscometric measurements are performed YT-ith a rotational viscometer. I n 1943 the author reported (20) that even oils subjected to shearing above a certain rate of shear show hysteresis f l o ~curves similar t o those of suspensions. Because of this striking similarity it was concluded that oils have the behavior of thixotropic materials and this Jyas assumed to be caused by niolecular shear aligiiment. Because the author realized that a rising temperature of the oil during the viscometric measurement n-ould causc a reduction in viscosity, \Thicli could conceivably be interpreted as the thixotropic breakdom of the 1
Present address, r a z e Institute of Technology, Cleveland, Ohio.
r;
WESTON GALVANOMETER
l,l ' I
This necessitated more specific information on the temperature increase in the oil during measurement. All measurements reported here xere performed with a rotational viscometer of essentially the construction desciibed by Green (6). The cup, the outer cylinder, was located in a cons t a n t temperatuie bath. The bob, the inner cylinder, vi as equipped v,ith a sensitive thermocouple, 'f so that the effective c region of the therniocouple was located at F 5 the outer surface of 0, the bob, to have the LT 9 same temperature as t h e bob surface B which is in diicct conW tact with the oil. To k P obtain a temperature distribution as unif o r m a s possible 0 TA throughout the metal TORQUE parts of the bob, Figure 2. Schematic Oil Flow copper bobs x e r e Curre used for most experiments. T h e high thermal conductivity of copper Kas considered important when water cooling 11-as employed. Two different galvanometers TTere used, necessit,ating two thermocouples of suitable sensitivity. In one set a Leeds & Xorthrup mirror galvanometer of 18ohm critical damping resistance and of 15.1-ohm internal resistance i ~ a sused in connection TTith a feed-back amplifier described by Vchlister, Matheson and Bn-eeney (13). The csternal resistance was arranged t o hive the desired sensitivity with the copper-nickel thermocouple employed. I n this particular circuit arrangement t,he temperature mas read on a scale of a milliampere-meter. The meter scale had 100 divisions. Each degree centigrade was equal to two divisions or about 1.5 mni., so that it was possible to read the temperature within 0.2" C. This galvanometer arrangement, unfortunately, was available for only a limited tiine and it became necessary t o set up sonirthing equally sensitive but less elaborate. For this purpose a Keston galvanometer having a resistance of 49.7 ohms and requiring an external resistance for critical damping of 190 ohms was selected. This instrument has a scale of 1 3 0 divisions, each equal to approxima,tely 0.5 X 10-6 ampere. In conjunction with the copper-constantan thermocouple used with this instrument, each scale division of about 1 mm. equaled approximatelv 0.9" C .
Figure 1. Cup, Bob, and Cooling System of Rotational Viscometer
212
. February 1948
INDUSTRIAL AND ENGINEERING CHEMISTRY
273 representing the rate of shear as function of the distance
from the bob, each for a given cup and bob diameter. In all experimenta, the bob diameter 2.6 was cm. while the cup diameter varied in four equal steps from 2.7 to 3.0 cm., providing clearances of 0.5, 1.0, 1.5, and 2.0 mm. The four curves are plotted to have the same mid-point rate of shear (290.3 sec.-l), which is also considered to be the average rate of shear, since the rate of shear function even for the largest clear, ance does not deviate sub5 I 1.5 stantially from linearity. RADIAL DIFFERENCE ( r - 4 ) in m m In all cams the outside Figure 3. Calculated Rates of Shear between Cup-and Bob for Four Different diameter of the bronze cup Clearances and Same Mid-point Rate of Shear was 3.5 cm. To obtain comparable data the test material Therefore, with this instrument it was again possible to read the wm subjected to the same average rates of h e a r for the temperature within about 0.2' C. In both arrangements the M e r e n t clearances. zero junction of the thermocouple was plawd in an oil contaiiier hung in the constant temperature bath of the viscometer (Figure 30 I). Thus temperature increases were measured directly. Satisfactory checks were obtained with both arrangements. All experiments described were conducted so that certain parameters were maintained to permit comparison of results,
POLYWTENE OIL 33 OOPPER-SLEEVED LUClTE BOB
FLOW CURVE
In Figure 2 a typical oil flow curve is shown. In accordance with established measuring procedure, the rate of shear is increased in distinct steps of a predetermined value and the torque measurement is taken for each step after the same time interval. If, for example, the material is to be measured to a top rate of shear, A , the time required for the run is n X t, 1 being the time used for the torque reading at each step and n the number of steps betwcen zero rate of shear and the top value, A . Below the limiting rate of shear (Figure 2) the oil behaves like a true liquid and its flow curve is a straight l i e through the origin. The Newtonian viscosity in ths region is obtained from the cotangent of angle TLOL. The plastic viscosity for the rate of shear which exceeds the limiting rate of shear A is obtained from the cotangent of angle T A T I A . The yield value is calculated from the intercept, TI. The apparent viscosity is obtained from the cotangent of angle TAOA for the rate of shear A . All viscosities and yield values are calculated according to equations given in the literature (6, 18). To permit comparison with results of other investigators, the discussion is related to both plastic and apparent viscosities.
CLEARANCE (Rc-Rb)
hl
mm.
Figure 4. Temperature Increase at Bob Wall As a function qf olearanoe between cup and bob for different top rate4 of qhear.
a8
obtamed for a polybutene oil m t h copper-sleeved Lucite bob
CLEARANCES BETWEEN BOB AND CUP
STAINLESS STEEL SWAFT
-
I t seemed significant to determine the shear-produced temperature increase for different clearances between cup and bob. The relationship between the cup revolutions per minute and the rates of shear a t the mid-point of the clearance (dv/dr), in reciprocal seconds is:
where Rc and Rb are the radii of the cup and bob, respectively. AI1 the top r.p.m. given in the paper are based on a 2-mm. clearance between cup and bob. In a rotational viscometer the rate of shear increases in the direction from cup to bob. In Figure 3 four curves are shown
COPPER SLEEVE
SOB
I
Figure 5.
Three Types of Bobs Used with Rotatioad Viscometer
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
214
Figure 4 shows plots obtained experimentally for a polybutene oil of 675 poises Newtonian viscosity Tvith a copper-sleeved Lucite bob (Figure 5). This is a typical family of curves, when the temperature increase measured a t the bob surface is plotted against the width of the clearance for different top rates of shear. The experimental procedure followed to establish these data consisted in running flow curves for different clearances as shown in Figure 2 up t o various top rates of shear and in making temperature measurements simultaneously r i t h each torque reading. In all experiments the cup was located in a controlled constant temperature bath of 30" i. 0.1 O C. Care was taken to subject the material for an equal length of time t o each average rate of shear.
CLEARANCL (R,-RD)
in mm
Figure 6. T e m p e r a t u r e Increase a t Bob Wall As a function of clearance between cup and bob for bobs of different material, as obtained for a polybutene oil a t a constant top rate of shear
Figure 7.
Vol. 40, No. 2
BOBS O F DIFFERENT MATERIALS
Five different sets of experiments were conducted, using bobs of materials with varying heat condu,ctivities. Flow curve and temperature measurements mere made with:
A Lucite bob (Figure 5 ) having a I-mm. copper ~leeve. Thr thermocouple was wcdgcd under the copper slcevc in direct contact with the copper and Lucite. A solid stainless steel bob (Figure 5 ) . The thermocouple wab soldered in a slot along the side of the bob. A hollow copper bob (Figure 5 ) with an air volume of about 10 cc. The t,hermocouple again was soldered in a slot directly a,t the surface of the bob. The same hollow copper bob filled with \Tater. The same hollow copper bob cooled by pumpingmntcr from the constant tempersture bat,h by way of surgical rubber tubings through the bob during the measurement (Figu1.e 1). The rubber tubings w r e so arranged as not to introduce any torque or frictional resistance. The bobs r e r e selected to provide different heat conductivitieb and heat capacities. In Figure 6 the bob wall temperature w function of clearance is shown for the same top rate of shear and for the five differcrit bobs for a polybbtcnc oil of 675 poises Newtonian viscosity at 30" C. As expected, the highest temperature increase is noticed for the Lucitc bob, and the smallest for tho water-cooled copper bob. The curves remained essentially the same as shown in Figure 4, approximating straight lines whose slopes seem to depend upon the conductivity of the bob. Witb different oils and printing inks the same results were obtained, but in addition the slope of the lines changed with the type of test material. It might be assumed in all cases that the cooling and heat conductivity of the cup is such that the tempcmture of the material in the viscometer a t the n d l of the cup is about the same as the temperature of the constant temperature \rat,er bath. It seems reasonable to expect that the temperature \Till increase with the distance from the cup and should reach its maxiinurn at
Flow Curves, E a c h for Three Top Rates of Shear f o r a Polybutene Oil, Using Bobs of
Different Materials
275
INDUSTRIAL AND ENGINEERING CHEMISTRY
February 1948 24
P S
F
5
16
!i
Kz W
s
h W
4c
8
POLYBUTENE OIL 32
300 RPM, 400 R m 2-
0
4
0
200
400
600
000
1000
TIME ( t ) tn seconds
Figure 8.
Temperature Increase a t Bob Wall
AB 8 funotion of time during which a constant rate of shear is applied as obtained for a polybutene oil with two different bobs and at two rates of shear
have been obtained. This might be taken as good evidence that the bob wall, particularly if the bob material has a low heat the temperature effect due to shear in the viscometer is of second capacity and a poor thermal conductivity and is not cooled. order and that the hysteresis flow curve obtained is due mostly to Such conditions do exist to some extent for the Lucite bob where the thixotropic behavior of the polybutene oil above the limiting the greatest temperature increases were found. rate of shear. Similar results were found for other oils and Although the temperature increase as a function of clearance printing inks. seems to be essentially a linear relationship and dependent on the test material of the thermal characteristics of the bobs, one cannot conclude that the temperature increase in the direction from cup to bob also follows a linear law. Let us msume that because of excellent thermal conductivity and aomplete heat removal, no temperature increase occurs at the bob and cup surfaces; a higher temperature should nevcrtheless be found somewhere between cup and bob. These conditions yere simulated with the water-cooled copper bob, E' 200 RpM. which had sufficient conductivity to remove most of the shear-produced temperature. In Figure 7 five flow curves are shown, d l obtained for the same polybutene oil and a 2-mm. clearance, but using five different bobs. Considering experimental errors and variations, these flow curves, obtained for three different top rates of shear, practically coincide. Thus it can be concluded that, though in each of these five cases the temperature at the bob surface was substantially different and thus the average temperature of the material must have varied somewhat during each run of the experiment, this difference in itself was not great enough to affect the flow characteristics and consistencies of the material. 15 225 30 37 Even with the Lucite bob, where the temTORWE x 10-5 in dynes crn. perature increases a t the bob surface are the highest, about the same flow curves Figure 9. Flow Curve of a Silicone Fluid at Three Top Rates of Shear 1
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
276 IOOC
TIME
900
Pigurt 8 dhows the teniperature m crease as a function of time a t a constant rate of shear. Four typical curves are shown as experimentall\ obtained for a polybutene oil with thc stainless steel and the water-filled copper bobs using a 2.0-mm. clearancc and rates of shear of 217.6 and 290.3 see.-'. Although only four curves arc shoa ri, experiments have been con ducted with the various clearancea bobs, and rates of shear for a numbrr of materials. I n all cases, the teniperature increases fast a t first and thw more gradually until a temperature equilibrium is established, when tht temperature increase produced in the material a g a result of the shearingwork is equal to the heat loss. Although no definite data have beel established for the heat equilibrium time for the various mateiiuls and kindb of bobs used, there is sufficicnt evidena to show that the time after ahich the heat equilibrium is reached depends or the bob material (see Table I). With the water-cooled copper bob it takeb about 0.5 to 1 minute, ahile with the Lucite bob the heat equilibrium is o b tained only after about 10 to 15 minuteb Since even for the highest rates of shear used in this investigation, a maximun of only about 100 seconds was re quired to complete a run, the equilihriurn is not always reached during flow curve measurements. Thereforr the time during which the experiment is performed is an important element when comparative data are being estab Iished and hence all flow curves, inde pendent of clearance, were taken in such a manner as to allow a definite time interval for each distinct rate of shear step (about 13 seconds for e a c t 100 r.p.q*)e At higher rates of shear, it IY dw sirable to complete a run in as short a time as possible in order to keep the temperature down to a minimum, SLE that its effect will interfere the leaai with the flow characteristics of the material resulting from thixotropic behavior. For the lower shearing forces, the temperature increase during even a longer time period is inconsequential, With the Lucite b o t although it has the lowest heat conduction, due to the efficient cooling of the cup in the water bath, the temperature increase in oils a t the limib ing shearing stress of about 70OC dynes per sq. em. (20)and somewhat higher, is still so small during and at completion of the test that the temperature-indicating equipment we.& not sensitive enough to register 8 change.
BOO
700 600
f 500
'E
s
g
400
t
t
cn
8
300
F I-
6 a 4
2
Vol. 40, No. 2
200
4
----Bo8
LSmm
150
KK,
1
BOB CLEARANCE
CLEARANCE
0
9
i
4
4
0
4
*
5
0
0
5
.
25
Llmm
20rnm
LOmm
3
30
r
l &
.
40
35
1
50
45
BATH TEMPERATURE (T) in *C. Figure 10. Apparent Viscosity as a Function'of 'Bath Temperature For various boba and clearance8 between c u p and bob, as obtained for a polybutene ail and a eilicontl fluid, each at three top rates of shear
100
I20
25
30
35
.
40
BATH TEMPFRATURE (T) n
45
5
OC.
Figure 11. Plastic Viscosity as a Function of Bath Temperature Far various bobs and clearancea between cup and bob, as obtained for a polybutene oil and a silicone fluid, each a t three different top rates of shear
INDUSTRIAL A N D ENGINEERING CHEMISTRY
February 1948
TABLE I. HEATEQUILIBRIUM TIME AND SPIWJFIC POWER INPUTVALUEFOR BOBSAND CLEARANCES Clearanoe, Mm.
Oil
Specifio Power Input Value DynedSq. Cm.'Sec.
Heat. Equilibnum
1.0 2.0
Polybutene oil 32
1.0 1.6 2.0 2.0
Polybutene oil 24
1.0 2.0 1.0 1.0 2.0
3ilioone fluid 6101C I,inpParl
nil
2.9X106 2 . 9 x 106 2 . 7 X 106 a.7X106 2 . 7 X 106 2.6XlOs 2 . OX 106 2.6XlOfi 2 . 9 x 106 2.9X106 2.9X106 Av. 2.7X106
SILICONE FLUID 900 900 900 600 600
800 600 800
200 000 600 700
Bob 2 H w v b rriiueral
oil
2 . 9 X 106 2.9x10a 3 . 4 X 106 3.4XIOS 2.8XlOb 3.4X106 3. OX 106 3.1XlO6 3.1X106 hv. 3.1Xl06
1.0
2.0 Polvhiltrne
oil 32
Polybutene oil 24 I,l"RP.Pd
oil
-
1.0 1.5 2.0
1.0 2.0 1.0 2.0
700 700 400
500 400 700
800 300 600 660
Bob 3 Haavy
mineral oil
Polybutene oil 32 Polybutene oil 24 dilioone fluid 5101B
5.4XIOfi 4.4X106 4.3X106 4.3Xl06 6 . 5 X 106 . 3 . 8 X 10s 3.9XIOfi 5.3X106 6.5XlOs hv. 4.8X106
1.0 2.0 1.0 2.0 1.0
2.0 1.0
Idmeed oil
2.0 1.0
Heavy mineral oil
1.0
400 600 400 500 400 500 200
800 300 450
2.0 Polybutene oil 32
1.0 1.5 2.0
30 20 70 70 60 60
With the Lucite bob the temperature increases above the 30" C. of the constant temperature bath became noticeable only when the power input per unit volume, P,,, exceeded about 3 X 106 dynes per sq. om. per second. This value seems to be
almost independent of the clearance and of the material tested, but is higher when a bob is used with better conductivity and better cooling. For the water-cooled copper bob the specific power input was of the order of 14 X 10' dynes per sq. cm. per *pmnd. The specific power input value was calculated as 'lo
($y
P., = 2 where
dV
To establish additional evidence that the temperature increase during viscometric measurements is a second-order effect, some silicone oils have been tested which are known to show an extremely small change in viscosity as function of temperature. Figure 9 shows a flow curve of such an oil, which is a true Newtonian liquid bclow the limiting rate of shear (Newtonian viscosity of 605 poises at 30"C.) but exhibits a hysteresis flow curve above this shearing rate value. On repeating the flow curve measurement on the same sample after sufficient rest, good checks were obtained, indicating that the change in consistency is completely reversible. If temperature increase is to be considered as the only cause of the reversible decrease in apparent and plastic viscosity, the temperature increase would have to be about 75" to 90" C., respectively, for a rate of shear of 290.3 sec.-l or 400 R.P.M., and about 60" and 75 C. for a rate of shew of 217.1 sec.-l or 300 R.P.M., when extrapolated from the semilogarithmic plot of the Newtonian viscosity as shown in Figures 10 and 11. Extrapolations from the A.S.T.M. chart yield still higher temperatures. The flow curve measurements on the silicone fluid were conducted with various bobs. The maximum measured temperature increase above the 30 " C. of the constant temperature bath at the wall of the water-cooled copper bob obtained a t 400 R.P.M. with a 2-mm. clearance was about 0.6" C. Even if one assumes a somewhat higher temperature a t the center of the clearance, the decrease in viscosity could not have been caused by the very moderate elevation in temperature. O
vi scowrY
Bob 5 13.9X 108 13.9X106 14.6Xl06 14.6 X 106 14.GXlO6 Av. 14.3X106
rate of shear waa obtained. The torque-time relationship was found to follow a logarithmic law as described previously (%I, fi) for thixotropic materials. Upon rest the material regained its original consistency.
Time,Seo.
Boh 1
Heavy mineral oil
277
All data given above were taken a t a bath temperature of 30" C. and the different bobs and clearances which resulted in various temperature increases a t the bob had little effect on the viscosity. To obtain a more complete picture of the effect of temperature increase, viscometric measurements were performed also at bath temperatures of about 25", 35", 40",and 45" C. In no case did the temperature increase a t the bob affect the consistency. In Figures 10 and 11 the logarithm of the apparent and plastic viscosity, respectively, is plotted against the bath temperature for various bobs and clearances. For each bath temperature, the viscosities for the same top rate of shear fall close together, so that it is possible to draw curves which are essentially straight lines within the limited temperature range tested. This indicates that the viscosity is only a function of bath temperature. Although this is shown only for one polybutene oil and one silicone fluid, the results are typical of other oils and printing inks. The average top rate of shear is the parameter of the different lincs. For completeness, the Newtonian viscosities are also plotted. YIELD VALUh
is the rate of shear a t which the first sign of temperature
hcrease is noticed and 'lois the apparent viscosity a t this speed. The specific power input value might depend on the heat capacity of the material tested. But since the specific power input measurements are not too accurate, and the heat capacities of the oils investigated are close, this could not be definitely established. [n Table I specific power inputs are given a t which the temperature increase becomes first noticeable undcr prevailing test conditions for different bob materials, clearances, and test wnples. Simultaneously with the temperature-time measurements the decrease in torque witJh time of application of a constant
Although no definite data have been established for the quantitative change in yield value intercept as function of bath temperature, the yield value intercept for the many oils and printing inks tested decreased with increasing bath temperature a t least within the limited temperature range from 25' to 45' C. Since the limiting shearing stress of oils (about 7000 dynes per sq. om.) is independent of temperature, it is conceivable that for oils the yield value intercept for any given applied rate of shear, but for a higher temperature, is smaller only because of less energy input due to a lower viscosity at the higher temperature. The energy input per unit volume or the shearing stress, the product of Newtonian viscosity and rate of shear, was calculated from
278
INDUSTRIAL AND ENGINEERING CHEMISTRY 50C
I
I
’
N
E
.ti 400 0. VI
0 RED
CYL OFFSET INK
Vol. 40,
No.
2
V SILICONE FLUID 510lC A SILICONE FLUID 5101 B
YELLOW OIL OFFSET HJK o L A C K OIL OFFSET INK 11
0 WLYBUTENE OIL MIXTURE 24,32
RED VAPOLITH INK
1
v YELLOW VAPOLITH INK
1
I BLACK VAPOLITH INK
v)
B -z.
~
1I
.5
d YELLOW VAWRIN INK X
BLACK VAPOSET INK
I
z
8 300 aw a
m Y
8 z 0 k
$
200
IU
0
5w 0
U U
0 w 0
100
0 BATH T E M P E R A N R E
Fipure 12.
(T) in
OC.
Coefficient of Thixotropic Breakdown ( M ) as a Function of Bath Temperature Left. Far various printing inks Right. For various oils
experimental flow curve8 obtained foi various oils at various temperatures and was found to be essentially constant for the same yield value intercept, indicating that the above assumption might be correct. Since the yield value intercept of oils, printing inks, and other pigment suspensions increases with increasing rates of shear (8, 20), the shcar-produced temperature could only have reduced this increase. Hence, the increase in yield value intercept caused by thixotropic behavior or shear alignment alone would be even greater than the measured value if shear-produced temperature increases had occurred during the measurement.
down M ( 7 ) , which represents the decrease in plastic viscosity per unit increase in rate of shear, is plotted against increasing temperature for oils and for printing inks in Figure 12. The fact that printing inks are less thixotpopic a t higher temperatures might be of practical value to the printer. When the thixotropic behavior of inks is decreased by preheating on the printing press, the consistency of the ink in the fountain (at a low rate of shear) and a t the point of application (at a higher rate of shear) will be more alike. The ink, if less thixotropic, will print almost equally well a t the beginning of a press run and after a longer time of press operation.
THIXOTROPY
EXPERIMEYTS AND THEORIES
It is known and also evidenced from Figures 10 and 11 that the change in viscosity of the silicone fluid with increase in temperature is much smaller than that of the polybutcnc oil. Inspection of the curves for the silicone fluid and the polybutene oil, representing the change in viscosity as function of bath temperature for different top rates of shear, shows that the curves for the silicone fluid are almost parallcl, while the oncs for the polybutene oil fan out, being farther apart at thc lower bath temperature. The difference in plastic viscosity obtained for any two rates of shear indicates the amount of thisotropy present In a material. Therefore, since the difference in viscosity change with rate of shear between thc low and the high bath temperature is small for the silicone oil but is rather substantial for the polybutene oil, the silicone fluid is only slightly less thixotropic while the polybutene oil becomes very much less thixotropic at higher bath temperatures. The coefficient of thixotropic break-
Bondi (a) and Dcutsch ( 4 ) evaluated theoretically tho change in apparent viscosity with increase in shearing force, each basing his theory on a somewhat different postulate. Bondi applied, the Eyring theory (5) and assumed molecular orientation under the influence of a stress field, whilc Deutsch bascd his calculations on Maxwell’s law of relaxation in connection with the pure elastic statc in a body and assumed shearing by jerks. I n Figure 13 both curves are plotted as the ratio of apparent t ( J Newtonian viscosity against the shearing stress of tho material, the product of Newtonian viscosity and rate of shear. Bondi’s curve has been plotted as it was published, while Deutsch’b curve, to bring it in the same order of magnitude, had to be recalculatc*d on an assumption that the rigidity of the oils is 50,000 instead of 8000 dynes per sq. em. as postulated in the papcr. This higher rigidity value is obtained from the equatiou given by Deutsch if one considers tho initial viscosit,y to be con-
INDUSTRIAL AND ENGINEERING CHEMISTRY
February 1948
279
measured a t the bob wall varied substantially for different bobs and for various clearances between cup and bob, dt h o u g h t h e s a m e test material was used and the same rate of shear was applied. This temperaEXPERIMENTAL ture increase seems to depend on the heat conductivity and the cooling of the bob and on the clearance width between cup and bob. But in spite of the different temperature increases a t the bob surface, the flow curves were CALCULATED practically identical. (LITERATURE) When the results of the different experiments were correlated, it was found that the temperature increase due to the energy 4dsorption in the mateSHEARING STRESS (qdv/dr) in dynes/&, rial is a s e c o n d - o r d e r Figure 13. Ratio of Apparent to Newtonian Viscosity as a Function of Shearing Stress effect upon the change in consistency compared to the effect due to thixotropic behavior or molecular shear alignment. Nevertheless, a stant within a variation of 1%, a t which point the breakdown in water-cooled copper bob should be used for smallest temperature viscosity becomes noticeable. In addition, Weltmann's (90) experimental curve for the heavy Bureau of Standards mineral increases during shear, if the most accurate consistency measureoil and more recently obtained data for two polybutene oils, two ments a t high shearing stress are desired. dicone fluids, and one linseed oil, most of them for two bath Curves from the litcrature which give a calculated decrease in oil viscosity with increasing shear stress are compared with temperatures, have been plotted in Figure 13 (see Table 11). In experimental data. The experimental and calculated results Figure 14 experimental plots are shown for the same materials, but instead of the apparent viscosities the plastic viscosities were are shown to be of the same order of magnitude. The plastic viscosity, apparent viscosity, yield value intercept, used. Both theoretical curves, although derived only for apand coefficient of thixotropic breakdown of oils and printing ink8 parent and not for plastic viscosities, are again added for comparison. In all experimental curves the data are plotted for the average or mid-point rates of shear (Equation 1). SUMMARY
Attempts have been made to separate thixotropic behavior effects of oils and other materials tLt high rates of shear from temperature effects due to shear in the viscometer. I n the case of oils the thixotropic behavior a t higher rates of shear is assumed to be caused by molecular shear dignment. Five bobs of various materials with built-in thermocouples were employed in a rotational viscometer to obtain information on the temperature rise of the material during me a s u r e me n t The temperature i n c r e w
I
EXPERIMENTAL I o 6 9
I
I
f '
CALCULATED (LITERATURE) I-
12
ti
.
-----
31 I I I
I
I P SHEARING STRESS (qdv/dr) in dynrdcm!
. Figure 14.
Ratio of Plastic to Newtonian Viscosity as a Function of Shearing Stress
INDUSTRIAL AND ENGINEERING CHEMISTRY
280
R,
T.4RIlE
TI.
3TTF'PI.EVEEST TO
Test Temp.. ' C. 30
Oil I 2 3 4
5
6
Polybutene oil 32
46
Polybutene oil 24 Silicone fluid 5 l O l C
30 30
Silicone fluid 5101H
30
46
7 8 Linseed oil
$5
30
9
45 30
LO Heavy mineral oil (eo)
Sewtoniaa Viscosity. 1 (Poisea) 675 187 180 605 ,503 213 179 118 39
:m
Bondi's theoretical aurve for 1200 mo!. wt. ( 8 ) 12 Deutsoh's theoretical curve recalculated ( 4 )
11
are found to decrease with an increase in bath temperature R ithin the range of 25" to 45" C for low as well a7 for high ratrs of qhear. \CKNOWLEDGME\II'
The author r\prabsrs thanks t o lntcrchemicai Corporation for permission t o publish this paper, to Henry Green for his valuable advice, and to Evelyn Berezin, LIarion Gallaglwr, and Vera Osman for their able assistancr.
R.P.hI W
75
=
P
=
U
=
T
=
AT
= = =
t M
radius of cup, cm. specific power, dynes/sq. o m sec apparent viscosity, poises Newtonian viscoeity, poises plastic vificosity, poises bath temperature, O C. temperature inrrease at hoh wall, ' (' time, PCC. coefficient of thixotropic breakdown
LITERATURE CITED
(7)
BjGrnstnhl, Y., 2. Physik, 119, 245 (1942). Bondi, A,, J . A p p l i e d Phys., 16, 539-44 (1945). Bondi, A., Petroleum, 32, 45 (1936). Deutsch, Walther, Phil. Mag., 36, Series 7 . 115-21 (1945). Glasstone, S., Laidler, I
