February, 1942
INDUSTRIAL AND ENGINEERING CHEMISTRY
( 5 ) Beattie, Sirnard, and Su, Ibid., 61, 26 (1939). (6) Beattie, Su, and Simard, Ibid., 61, 929 (1939). (7) Bridgeman, Ibid., 49, 1174 (1927). (8) Brooks, Howard, and Crafton, J . Research Nail. Bur. Standards, 24, 33 (1940). (9) Deschner and Brown, IND. ENG.CHBM., 32,836 (1940). (10) Kay, Ibid., 32,358 (1940). (11) Kelso and Felsing, J . Am. Chem. SOC.,62,3132 (1940). (12) Keyes and Burks, Ibid., 49, 1403 (1927). (13) Kvalnes and Gaddy, Ibid., 53, 394 (1931). ENG.CHEM.,28,257 (1936). (14) Lewis, IND. (15) Rose-Innes and Young. Phil. Mag., 151 47, 353 (1899).
163
Rotinjanz and Nagornow, 2. physik. Chem., A169, 20 (1934). Sage and Lacey, IND. ENG.CHEM.,30,673 (1938) Sage, Lacey, and Schaafsma, Ibid., 27, 48 (1935). Sage, SchaafRma, and Laoey, Ibid., 26, 1218 (1934). Sage, Webster, and Lacey, Ibid., 29,658 (1937). Ibid., 29, 1188 (1937). Smith, Beattie, and Kay, J. Am. Chem. SOC.,59, 1587 (1937). Thomas and Young, J . Chem. Soc., 67, 1071 (1895). Vaughn and Graves, IND. ENG.CHEM.,32,1252 (1940). Young, in International Critical Tables, Vol. 111, p. 345, New York, McGraw-Hill Book Co., 1928. (26) Young, 2.physik. Chem., 29, 193 (1899).
(16) (17) (18) (19) (20) (21) (22) (23) (24) (25)
Calculation of Viscosity from Stormer Viscometer Data J. A. GEDDES AND D. H. DAWSON Krebs Pigment & Color Corporation, Newport, Del.
B
ECAUSE of its simplicity of operation and ease of cleanbration of the Stormer viscometer in absolute units. We ing, the Stormer viscometer has long been used for realized that appreciable correction factors would need to be consistency measurements of paints and allied prodapplied, and that these might be valid only over a limited range. This difficulty was not considered too serious, howucts. Consistency is a measure of the flow of materials which exhibit permanent deformation ever, because present recomunder applied shearing stress. mendations on the Stormer visThis term will be used not only cometer hold the speed of the for plastic materials, but also rotating paddle between relaTo explore the possibility of describing the in cases where the viscous natively narrow limits. Krebs ture of a substance has not been units are measured only beconsistency of paints in more fundamental established. Consistency is tween times of 24 and 40 units, use of the modified Stormer viscomenot always a definite physical seconds per hundred revoluter on truly viscous oils has been studied. quantity, since its value may tions, while the American It has been found possible to correlate the depend upon the stress applied, Society for Testing Materials viscosity of these oils with Stormer data, or upon the previous history suggests a paddle speed of 200 of the sample. Viscosity is der.p.m., interpolated frommeasprovided a correction for kinetic energy fined in the usual manner (8’). urements varying over a range losses is made. I n spite of the extensive not greater than 27-33 seconds The fork-type paddle ordinarily used on use of the Stormer viscometer, per hundred revolutions (1, 2). the modified Stormer viscometer has been little effort has been made to replaced with a newer “submerged” paddle, express the results obtained in Apparatus and Materials absolute units. It has been which allows more reproducible readings. The modified Stormer viscomcustomary to present such data The formula developed for calculation of eter as described in Perry’s handby giving the weight-time relabook ( 5 )was used, with a further viscosity of truly viscous liquids is limited tion (9,B ) , or the Krebs units modification in the paddle emwith respect to several variables, including ployed. The old forked type (6, 6)read from a weight-time required calibration and marking temperature and container size (pint cans chart. of each individual paddle before These arbitrary methods are preferred). It is suggested that maximum use and, in addition, very careopen to criticism for several ful setting to ensure the proper tolerances of *O0.25O C. be imposed in all depth of immersion in the liquid reasons. The principal objecliquid and paint measurements. Although being measured. tion is that even in the case of The newer submerged paddle Containers from half-pint size upward may truly viscous liquids, a straight( 6 ) is not subject t o these limibe used, measurements made in containers line relation between weight tations, since it can be supplied already marked by the manuand reciprocal of time on the of different sizes cannot be intercompared facturer, and the depth of immermodified Stormer viscometer without correction. sion is determined on a relatively does not exist. A curve consmall center shaft. It is thereFurther application of the kinetic energy cave toward the weight axis is fore much easier to set, and the correction to measurements of yield value obtained, and the apparent viserrors from incorrect settinp are minimized. Paddles of this and mobility of paint systems with the cosity depends upon the stress type have been used for some applied. Stormer viscometer is under consideration. years in this laboratory withcomIt was therefore considered plete success. A recent compariadvisable to attempt a calison of the forked and submerged
164
Vol. 34. No. 2
INDUSTRIAL AND ENGINEERING CHEMISTRY
paddles by several laboratories ( I ) likewise indicated the usefulness of the newer type. A scale drawing of the submerged paddle is presented in Figure 1. As true viscous liquids, five oils comparable t o paints in consistency vere available. The viscosity of one of these (oil C) had been recently measured at the Pu’ationalBureau of Standards, and the viscosity of the others was determined by direct comparison.
TABLE11. STORMER VISCOMETERMEASUREMENTS AND CORRECTIOSS ON VISCOUSOILS hp p 1i ed Weight F , Grams
Observed ~ ~ Seconds
50 100 150 200
250
83.3 43.2 30.7 24.5 20.2
50 100 150 200 250 300
115.0 55.9 39.2 30.3 24.9 21.4
60 100
117.7 58.3 39.6 30.9 25.9 22.0
K. E,
Correction, ~ ~ 27,5000 t2
Corrected Weight, t 2 7 , 5,0 0 ~ t2
Reci rocal of &me, l/t
Oil A, 6.03 Poises 3.4 12.8 25.3 39.7 58.4
46.6 87.2 124.7 169.3 191.6
0.0120 0.0232 0.0326 0 0408 0.0495
48.0 90.3 132.7 171.2 207.5 242.3
0 00867 0.0179 0.0256 0.0330 0.0402 0.0467
48.3 92.8 134.8 174.7 213.9 250.0
0.0171 0.00860
Oil B, 8.14 Poises 2.0 9.7 17.3 28.8 42.5 67.7
Oil C, 9.08 Poises
1.50
200 250 300
1.7 7.2 15.2 25.3 36.1 50.0
0.0252 0.0324 0.0386 0.0451
Oil D, 10.59 Poises 50 100 150 200 260 300 350
0 00716 0.0144 0.0216 0.0283 0.0352 0.0407 0.0461
Oil E, 33.7 Poises
FIGURE 1. SUBMERGED P~DDLE
These comparisons were made in an Ostwald viscometer, selected t o require several minutes for the thinnest oil to flow through the capillary. Temperature was kept at 25‘ =t0.05’ C. by means of a water bath. Results are listed in Table I. TABLEI. Oil
VISCOSITY O F
OILS
-4s LIEASURED BY AN OSTWALD
VISCOMETER Time of Flow t , Seconds
Densit Gram/gc.
Viscosity, Poises
100 200 300 400 500 600 700 800 900 1000
203.8 100.1 68.7 60.6 40.2 34.1 29.3 25.8 22.9 21.0
0.00491 0,00999 0.0146 0.0198 0.0249 0.0293 0.0341 0.0388 0.0437 0.0476
terms and, for the purposes of our approximate calculations, will be neglected or thrown in with the kinetic energy. The error involved here is insignificant with regard t o measurements in the paint consistency range, as will be shown later. Consideration of the capillary-tube kinetic energy correction factor (4), (-mp
a Standard used f o r calibration.
Kinetic Energy Correction Stormer measurements mere obtained on the five oils mentioned above, over a range of applied weight sufficient t o vary the time for 100 revolutions from 20 t o above 100 seconds. Temperature was maintained a t 25-25.5O C. in a constanttemperature room. These data are listed in Table I1 and plotted in Figure 2. The curves show a definite concavity toward the weight axis, except that of the most viscous (33.7poise) oil. This increase in apparent viscosity under increased stress obviously is caused by greater loss of energy or, we might say, the employment of the applied force in some manner other than the production of viscous flow. The general viscosity equation for instruments of the Stormer type (v = F t / A ) may then be altered to read Ft + f ’ +f”+f”’ . .. (1) 7J =
+
where the added functions f’,f”,f”’ . . . represent corrections for the kinetic energy losses, friction in the instrument, slippage on the walls and blades of the rotor, etc. AI1 of these factors except the kinetic energy correction are second-order
V / 8 T It),
indicates that only the density p and the time t are variable; the other terms may be grouped as a constant. Equation 1 is therefore modified to read:
This can be further rearranged t o the form (3)
which shows more clearly the influence of the typical kinetic energy term on the applied force. By selection of several pairs of points from the upper graph of Figure 2, the value of K’ can be estimated quite closely t o be 27,500. Substituting this value in the equation, and plotting the corrected applied force against the reciprocal of time, as listed in Table 11, we obtain a series of straight lines through the origin, with slopes corresponding closely to the fluidity ( 1 / ~ )of the various oils (Figure 2, lower graph). It is then a simple matter t o calculate A in Equation 3 from these slopes, and the completed equation for obtaining the approximate viscosity of liquids in poises on the Stormer viscometer becomes:
INDUSTRIAL AND ENGINEERING CHEMISTRY
February, 1942
, (4) This is found to be valid within approximately 5 per cent over the range of variables covered during this study (Table 111). OF CORRECTED STORMER AND OSTWALD TABLE 111. COMPARISON VISCOSITIES
Oil
Viscosity, Poises Ostwald Cor. Stormer
Range of Krebs Units
Specifically, these variables and their limits may be listed as follows:
Although this treatment obviously does not fully compensate for losses in friction or kinetic energy, slippage, etc., it is believed that simplified Equation 4 is suitable for all purposes for which the Stormer is normally employed in the paint trade. To illustrate, a consistency range of 73 to 130 Krebs units is covered, which would include lightly pigmented enamels to heavy flat paints. Below this range, the increased influence of kinetic energy and turbulent flow limits the application of Equation 4, but a t higher viscosity this equation will probably be suitable. I n the more restricted consideration of materials having the same weight per gallon, it is possible to modify Equation 4 further by combining the density with the kinetic energy constant K' to obtain the simplified equation,
'
+-$) 610
=
where K = K'p
=
165
Since it would obviously be beneficial to supplant such arbitrary methods with a determination of actual yield value and mobility, the application of a kinetic energy correction to modified Stormer measurements on paint systems is under consideration. Elimination of the concavity toward the weight axis a t high shearing rates for plastic materials, in a manner similar to that described above for viscous substances, would make this possible.
Determination of Krebs-Unit Values Since Krebs units are available in the literature only in the form of a family of curves (6),Table IV gives those values of most interest to the paint trade. This table plots the driving weight against the time in seconds required for 100 revolutions of the paddle, and the number of Krebs units is found simply by reading in the appropriate line and column. Thus, if 400 grams caused the paddle to make 100 revolutions in 28 seconds, the material being tested would have a consistency of 102 Krebs units. The curves from which these arbitrary units are taken were derived from a series of measurements on heavily pigmented lithopone-tung oil-soybean oil flat paints. A paint considered to be of proper brushing consistency by several competent observers was given-an arbitrary value of 100 Krebs units. Additional paints, both thicker and thinner than this standard, were then prepared, and members were selected by these same observers to differ in consistency by successive steps
(5 )
27,500~
Since the density enters only into a correction term, it is possible to use Equation 5 even though minor differences in density may exist. It is common knowledge that paints are not viscous but plastic and therefore require two parameters to describe their flow properties (yield value and mobility). At least two points on the stress-strain curve must be obtained in order to calculate these values. However, this is seldom done in practice, because of the difficulties involved in measurement. Instruments which give satisfactory values are too difficult to handle for ordinary purposes, while those which are simple to operate do not provide results capable of interpretation as yield value and mobility factors. The usual trade practice, therefore, is to measure the consistency of a paint under specified conditions and report the result in arbitrary units which are a combination of the two parameters outlined above. It is quite possible under such a system to describe paints of widely differing flow properties in identical values.
400 5 0 0 GOO 7 0 0 APPLIED F (GRAMS)
100
200
300
800
900
100
200
300
800
900
400 SO0 600 700 CORRECTED F (GRAMS)
FIGURE 2. WEIGHT-TIME CURVES OF VISCOUS LIQUIDS
INDUSTRIAL AND ENGINEERING CHEMISTRY
166
Vol. 34, No. 2
TABLE IV. KREBSUNITSFOR STORYER CONSISTENCY Sec. j100 Revolutions
24 25 26 27 28 29 30 31 32 33 34 33 36 37 38 39 40
-
75 42 45 4i 49 31 53
j+ ai)
56 57 58 j9
60 61 62 62 63
100 52 54 56 57 99 60 61 62 63 64 64 65 66 67 68 68
69
150 65
66 68 69 70
71
72 73 74 75 75 76 76 77
78 78 79
200 75 76 78 79 80 81 82 82 83
84 84 85 85
86 87 88 88
250 83 84
300 90 90 91 92 93 94 95 95 96 96 97 98 BY 99 99 100 100
85
86 87 88 89 90 90 91 91 92 92 93
93 94 94
350 95 95 96 97 98 99
400 99 100 101 102 102
103 104 104 10;
106 107
Grams 500 550 I08 111 109 112 110 113 111 111 112 115
107
I12
11.5
112 113
116
115
450 103 104 105
101 102
10:
102
106
103 103 104 104 104
107
108 108 109 109 110 110 111
107
111
100
100 101
106
108 108 10s
112 112 112
arbitrarily given values of 10 Krebs units. Modified Stormer viscometer measurements were then made on paints ranging in consistency from 60 t o 160 Krebs unite. A sufficient number of different weights was used to vary the time required for 100 revolutions of the paddle from 24 t o 40 seconds. Table IV was then derived by interpolation from these results. The flat paints in question were considered t o be of constant Krebs-unit consistency over a wide range of applied stress. Consequently, Krebs units represent an attempt a t a practical combination of yield value and mobility factors. Only in the case of flat, paints similar in type t o the original standard mill the consistency measured by these units he independent of the stress applied.
Influence of Temperature
It is well k n o m that slight changes in temperature will cause definite changes in the viscosity of liquids, particularly the more viscous types. The effect on plastic systems is less marked, probably beeawe the yield value is little aff ectetl, and only the mobility is influenced by temperature. HOT\ever, the necessity of temperature control in paint consistency measurements is recognized, and the A. S. T. M. test for enamels ( 2 ) limits temperature variations to *0.5" C. To determine the magnitude of the temperature effect. measurements were made on oil A and a light enamel paint at two temperatures (Table V). Using Equation 4, the viscosity was calculated a t each temperature. Since the viscosity of tlie oil decreases 9 per cent per O C., it is evident that a temperature range of *0.5" C. ~ ~ o uresult l d in almost 5 per cent error from this factor alone. As heavier oils would show even greater effects, a temperature deviation of only 1 0 . 2 5 ' C. would be preferred for viscous materials. A similar limitation should be considered on paint consistency measurements, in vie\\- of the 7 per cent change in apparent viscosity per C. observed. TABLEV.
INFLUENCE OF TEMPERATURE ON STORMER CONSISTENCY OF OIL AND PAINT
Temp.,
Applied Weight, Grams
21.0 25.0
100 100
21.0 25.0
100
C.
Obsvd. Time, Seo.
57.1 43.9
Cor. Weight Oil A4
92.7 87.6
Liaht Enamel P a i n t ,
a
100
48.0 40.4
Viscosity, Poises
85.3 79.2
P
Consistencya
8.68 6.37 = 1.236
...
...
Apparent viscosity calculated f r o m Equation 4.
116
11X
116
114 114 114 113
117
118 118 118 119 119 120 120
116 116 116
600 115 116 117 118 118 119 120 120 120 121
122 122
122 123 123 124 124
650
700
750
118
122 122 123 124 124
125 125 126 127
I25
128 128 129 129 129 130
119 120 121 121 122 122
123 123 123 124 124 125 125 126 126
127
125 126 126 126 127 127 128 128 129 129 130
800 128 129 130 130 130 131 131 132 132 132 132 133 133 133 134 134 134
127
130
130 131 131 131 132
850 180 131 132 132 132 133 134 134 134 133 135 135 135 136 136 136 136
900 132 133 134 134 134
1000 130 137
135
136 136 136 137 137 137 137 138 138 138 138
138
138 139 139 140 140 140 141 141 142 142
142 142 143 143
Influence of Container Size Although not so critical as temperature, the size of the container used for Stormer measurements exerts sufficient influence to n-arrant mention. Naturally, the larger the container, the less the resistance offered to the rotating paddle. A11 preceding measurements hare been made in a standard one-pint friction-top can, 35/16 inches in diameter, and the constants have been derived for this container only. The results of a direct comparison of an oil and m i enamel a t 2.5.0' C. in three different containers under an applied weight of 100 grams are listed in Table VI. A pint can shows considerably less resistance to the paddle than does a halfpint can, but little or no more resistance than does the quart size. Measurements in larger size containers therefore do not appear necessary or convenient. In fact, the difficulties in using quart cans on the Stormer instrument as now construct'ed are sufficient to eliminate it from consideration in most cases.
TABTA: VI.
INFLUEXCE O F CONTAIKER SIZE COSITY O F OIL AND P a I N T Obsvd. Time,
Container Capacity Diam., in.
cos. Weight
Sec.
ON S T O R M E R V I S -
Consistency6
Oil F,p = 0.878
pt. 1 pt.
281, 3'/16 41/a
pt.
2s/a 35/15
'/a
1 qt.
Light enamel paint, 1/2
1 pt.
1 qt. a
73.2 69.6 69.6
30.0 28.2 28.2 p
= 1.238
42.1 40.1 40.1
4'/8
3.60 3.21 3.21
80.8 79.2 78.9
5.58 6.26 5.19
Apparent viscosity calculated from Equation 4.
The apparent viscosities for oil F (Table VI) can obviously be adjusted to equality simply by charging tlie value of constant A in Equation 4. To check this point, an entire series of measurements was made on standard oils A, B, C, D, and E in half-pint cans, and the data were treated similarly t o those obtained with pint cans in the qection on "Kinetic Energy Correction". This independent calculation gave the equation,
6.71a 5.25
t
n / 9Pint
=
!? (F - - 700 27f:0
)
February, 1942
INDUSTRIAL AND ENGINEERING CHEMISTRY
Therefore, it appears that containers of different sizes may be used on the modified Stormer viscometer although not interchangeably; furthermore, the viscosity may be calculated from the weight-time determinations,, provided K’ and A in Equation 3 have been determined with the same size containers.
Nomenclature q
viscosity, poises driving weight, grams time required for 100 revolutions of paddle, seconds density of liquid, grams/cc. volume of flow, cc. length of capillary tube
=
F = t
=
p
=
V =
I
=
167
m = end correction coefficient for capillary tube C, K , K‘, A = constants
Literature Cited (1) A. S. T . M . Group 1, Sub-committee V I I I , Committee D-1, Unpub. obaervations. (2) A. 5 . T . M. Standards, D-562-40T (Tentative) 1940. (3) Bingham, E. C., “Fluidity and Plasticity”, p. 5, New York McGraw-Hill Book Co., 1922. (4) Ibid., pp. 17-21. (5) Perry, J. H., Chemical Engineer’s Handbook, pp. 1271-7, New York, McGraw-Hill Book Co., 1934. (6) Sawyer, R. H., A . S. 2’. iM.Bull., Jan., 1940, 19. before t h e Division of P a i n t , Varnish, and Plastics Chemistry at PRESENTED t h e 102nd Meeting of t h e AMERICAN CHEMCAL SOCIETY, Atlantic City, N. J.
Front-End Volatility of Gasoline Blends J
N. B. HASKELL AND D. I
