CORRELATING FLUID VISCOSITY ALLEN S. SMITH1AND GEORGE GRANGER BROWN University of Michigan, Ann Arbor, Mich.
HE theorem of corre-
has the same value for all subAn equation derived from the theorem of stances in corresponding states. sponding states has been corresponding states is applied to viscosityThis term was derived from widely used for estitemperature data of gases and liquids at mating various physical the kinetic theory of viscosity atmospheric pressure, under saturated conand van der Waal's equation properties such as compresditions and under pressure to determine its of state. If the reduced temsibility, vapor pressure, and perature and pressure are surface tension. The success value in extending fluid viscosities. When introduced, it follows that of the method has been of the limitations of the theorem are congreat practical value in engito sidered, the equation is found applicable neering computations involvhomologous series and diatomic gases; vising these properties. Two cosities of the members of these series may There is also considerable exattempts have been made perimental evidence indicating to extend viscosity data by be represented by curves specific for each that viscosity depends on correlations based on the series. A plot is presented for the normal molecular weight (11, 16, theorem. paraffin hydrocarbons (excluding methane) 19, 88, 51). Nelson (18) plotted the and their mixtures which serves to extend If Equation 1 is valid, the viscosity of methane, ethane, viscosity data in this series for reduced viscosity of all compounds propane, isobutane, pentane, under all conditions of temperapressures up to 10 and reduced temperatwo n a t u r a l gases, and ture, pressure, or state may be several liquid hydrocarbons tures from 0.65 to 1.5 within the accuracy graphically represented by a against reduced pressure for of the experimental data used in the corsingle plot having the coordiconstant reduced temperarelation. The viscosities of ethane and nates?l/d/;i?and TRor PR,and tures. He realized that the propane in the radge 100 to 5000 pounds one parameter. It is known, relationship could have been per square inch and 15O to 200' C. have been however, that this equation greatly improved if the ratio can be correct only as a first apof the viscosity a t the given determined by the rolling ball viscometer. proximation, since it is derived conditions t o the viscosity with the aid of van der Waal's a t the critical point had been used. However, lack of viscosity a t the critical equation of state; and that the theorem of corresponding point made this impossible. states does not have universal application (IO). The value Comings and Egly (5) plotted the ratio of the viscosity and limitations of this equation in correlating viscosity at various conditions were determined by applying it first to a t an indicated reduced pressure and temperature to the visdata a t atmospheric pressure and subsequently to include the cosity a t 1 atmosphere, against reduced pressure a t constant reduced temperature. The curves proposed for general use pressure variable. The concepts developed led to a correlawere based on data for carbon dioxide, ammonia, methane, ntion specific in application for the saturated paraffins and their mixtures, excluding methane, which has a mathematical butane, isobutane, nitrogen, and ethylene (6). The basis of this method is an analogy between viscosity and kinetic presand experimental basis. sure. Boyd ( 3 ) had shown previously that the analogy was valid for nitrogen within the accuracy of his data. His GASES AT ATMOSPHERIC PRESSURE equation relating viscosity and pressure represented the The value for viscosity at atmospheric pressure divided by form of the relationship for air for which viscosities up to 160 the square root of the molecular weight was plotted against atmospheres had been obtained by Moulton and Beuschlein reduced temperature for thirty-five compounds in the vapor (27) but only if the constants in the equation had different state. These compounds may be grouped in the following values than those predicted from compressibility data. manner, on the basis of the temperature coefficient or slope The fact that theRe methods of correlation gave results of the straight line on a log-log plot such as the right-hand varying as much as 20 per cent from experimental data indihalf of Figure 1 which represents the data for some paraffins: cated that the limitations of the theorem may not have been adequately considered, and that it might be possible to obd log ?/.\/z tain a more satisfactory correlation. Compounds d log T R In 1894 Onnes (90) postulated that the term,
T
1.113 1.015
where 71 = viscosity P, = critical pressure T , = critical temperature M = molecular weight 1
Present address, Blaw-Xnox Company, Pittsburgh, Penna.
0.945 0.932 0.910 0.895 0,882 0,863 0.851
Water Methyl and ethyl acetates; methyl, ethyl, and methyl ethyl ethers; CaHe COz SOz C q , NHa Ethane r o p a i e , n-butahe, isobutane, n-pentane, n-hexane Methyfc loride, chloroform, CCla E t h lene allylene, propylene CscYoheGane Acetylene Methyl, ethyl, n-pro yl, and isopropyl alcohols 01, ~ 2 HP, , CO, metgane
-
The same function, q / v ' M , was plotted against the reciprocal of the critical pressure, corresponding to atmospheric '105
INDUSTRIAL AND ENGINEERING CHEMISTRY
706
pressure, at constant reduced temperature for those of the thirty-five compounds for which critical pressures are available. The reduced pressure is l / P c , since the data for the compounds were obtained a t normal pressure. It was found that straight lines representing a given reduced temperature could be drawn through points plotted for some members of the previous groupings. This is illustrated in the left-
Figure 1. Viscosity Correlation of Hydrocarbon 7;apors at One Atmosphere (7 = Viscosity in Poises)
hand half of Figure 1 for the paraffins. Regrouping the compounds on the basis of equal values of d log v / d @ / d log l / P c as well as of equal temperature coefficients gives the following arrangement: Grouv 1 2
3
Compounds Methyl, ethyl, and methyl ethyl ethers Ethane, propane, n-butane, n-pentane, n-hexane 0 2 , Nz,HI, CO, methane
Since sufficient data are lacking, other compounds may be tentatkely arranged on the same basis in other groups: Group 4
6
6 7
Compounds Methyl chloride, chloroform, CClr Ethylene, propylene Ethyl and n-propyl alcohols Methyl and ethyl acetates
Vol. 35, No. 6
product of a constant, m, characteristic of the compound and its molecular weight; m is a constant in the equation, loglo (loglo ?I)
=
md
- 2.9
which Souders obtained by plotting the viscosity as a function of the density of each compound. Values of I and m as given by Souders are reproduced in Table I for the liquids investigated. The values of m for the normal paraffins in Table I are essentially the same. Therefore, association in this series can be neglected, and the viscosity of the members can be correlated by a plot of q/dLVagainst TRif the temperature coefficients of viscosity are the same a t the same temperature level. Figure 2 shows this to be true. The values of m in other homologous series are not constant. Therefore the molecular weight cannot be used, If, however, v / d J is plotted against reduced temperature, the data for all the members of homologous series may be represented by single curves. The curves are shown in Figure 3 and represent the following groups: Group 1 2
3 4 5
Compounds n-Pentane n-hexane n-heptane, n-octane, n-nonane, n-decane, n-undecke, n-dodlcane Ethyl and ethyl propyl ethers Propionic, n-butyric, isobutyric, and n-valeric acids Ethyl, n-propy!, and n-butyl alcohols Isopropyl and isobutyl alcohols
An implication derived from the study of the liquids is that viscosity-temperature data can be extended for compounds for which limited data are available which are members of series. From the consideration of both liquids and vapors, Equation 1 should make it possible to correlate viscosity data for the normal paraffins under any conditions of temperature, pressure, or state, and for other homologous series (except the first member) under any conditions in the vapor or gaseous state if the vapor is neither associated nor disassociated. If molecular weight is replaced by constant I , Equation 1 should be applicable to the alcohols and ethers and, in general, to any series in the liquid state under any conditions. SATURATED LIQUIDS AND VAPORS
The first member of the homologous series of paraffins and alcohols is anomalous as are the isomeric compounds. Of the remaining compounds (benzene, carbon dioxide, sulfur dioxide, carbon disulfide, and ammonia) , no one can be compared with another or included in any group given. The results of the investigation of the thirty-five compounds in the vapor state suggest that (a) the viscosity a t any temperature at one atmosphere can be obtained for any vapor, if the critical temperature is known, from measurements at two temperatures; (b) the vapor viscosity of any member of a homologous series a t one atmosphere can be obtained if data are available a t two temperatures for any other two members, and the critical temperature and pressure are known; and (c) the viscosity function might be useful in correlating data on each series a t pressures other than atmospheric. LIQUIDS AT ATMOSPHERIC PRESSURE
The application of the general viscosity function to twentysix compounds in the liquid state was investigated. Pressure has little or no significance in the liquid state a t normal conditions, and PRin Equation 1 can be neglected. Changes in molecular aggregation impose limitations on the use of the equation which must be considered. This has been done by the use of an association factor derived from viscosity-density data by Souders (29) for 117 compounds. The factor I , designated as the viscosity-constitutional constant, is the
Viscosity data obtained by Khalilov (16) for saturated vapors of n-hexane, n-heptane, methyl alcohol, ethyl alcohol, and n-propyl alcohol, and for saturated liquids of n-pentane,
' 2
3
4 6 8/0 @m~10~
L520
Figure 2. Viscosity Correlation for Normal Liquid Paraffins at One Atmosphere
n-hexane, n-heptane, ethyl alcohol, n-propyl alcohol, ethyl formate, sand n-propyl formate have been correlated by Equation l. Since all the viscosity data for the saturated vapors and liquids mere a t different pressures (the vapor pressure), it was necessary to include the pressure term in the viscosity function of Equation 1 and adjust it for a reference compound. Each measurement v a s referred to ethane and
June, 1943
INDUSTRIAL AND ENGINEERING CHEMISTRY
ethyl alcohol, respectively, for the vapors, and to pentane, ethyl alcohol, and ethyl formate, respectively, for the liquids, The ordinates plotted against reduced temperature were: HYDROCARBON VAPORS: critical pressure of ethane (critical pressure of compound)
(,/,/%)
pressure (reduced of compound )
HYDROCARBON LIQUIDS:
critical pressure of pentane (critical pressure of compound)
(
reduced pressure of compound
(
)
LIQUIDALCOHOLSAKD FORMATES, ALCOHOLVAPORS: critical pressure of ethyl compound critical pressure of compound The data are plotted in Figures 4 and 5. The excellent correlations obtained add confidence to the general use of Equation 1 for paraffis, and to the equation as modified by constant I for other liquids.
707
I
TABLE I. VISCOSITY CONSTANTS FOR ORGANIC LIQUIDS Vicosity-Density Constant m 0' C. 20' C. 40' C. 60° C.
Compound n-Pentane n-Hexane n-Heptane n-Octane n-Nonane n-Decane n-Undecane n-Dodecane
3.961 3.956 3.934 3.937 3.946 3.950 3.956 3,954
Acetic acid Propionic acid n-Butyric acid
~
$
~
~
a
$
... ... ... ... d ...
Methyl aloohol Ethyl alcohol n-Propyl alcohol Isopropyl alcohol n-Butyl aloohol Isobutyl alcohol
3.529 3.717 3.785 3.881 3.806
Acetone Benzene Toluene Ethyl bromide. n-Propyl chloride Ethyl ether Ethyl propyl ether
3.293 3.201 3.220 1.820
...
3:4?6 3.55
3,935 3.949 3.933 3.937 3.941 3.944 3.951
cz$?t;$ial Constant I
...
3 940 3.931 3.939 3.940 3.943 3.953
3:922 3.936 3.942 3.946 3.956
283-285 339-341 393-394 449 505 561 617 673
2.800
2.811
168-1130 218
3:iiz
3.23 3.11
... ...
3:i23
3.522 3.716 3.773 3.871 3.788 3.857
3.510 3.709 3.758 3.840 3.768 3.846
31746
3.299 3.197 3.218 1.831 2.96 3.462
3.301 3.203 3.219
3:i62 3.219
.....
2.798 2.94 3.104
..
:
.....
_.. ... ...
...
...
... ... ...
...
3 632
... ... ... ...
...
274 330 112-113 117 225-227 230-233 279-282 283-285 191-192 249.8 296.2 198-199 232 257 313
FLUIDS UNDER PRESSURE
use of Bridgman's values (4) for alcohols, only the data for by Gibson (12) a t pressures up to 965 atmospheres and a t the normal paraffis (excluding methane) can be correlated three temperatures, and of hydrogen a t 25" C. up to 295 ataccording to the study of the application of Equation 1 at atmospheric pressure. To obtain additional data, mospheres. These data enable a test of Equation 1 to be made with a fourth class of compounds. Isobars of the vismeasurements of the viscosity of ethane and propane were cosity function are plotted against reduced temperature in made. While this work was in progress, the results of Sage and Lacey (24) on propane over a smaller temperaFigure 6. Because of the small temperature range and the large spread in reduced temperature between nitrogen and ture and pressure range than that of the data reported hydrogen a t equal absolute temperature, this correlation here were published. might be considered only fortuitous. However, nitrogen differs from hvdronen in viscosity at'kqual conditions "by 750 per cent, yet this method of plotting allows the values to be represented by single curves. The isobar a t a reduced pressure of 5 is a straight line joining the points for nitrogen and hydrogen. OTHERCOMPOUNDS. High-pressure viscosity-temperature data are available for other compounds: carbon dioxide ($1, 26, 30); ammonia, methyl chloride, and sulfur dioxide (SO); ether (26); decane (8); water vapor (27); air (IS); propane (94); n- and isobutane (66); methane and natural gas (24); pentane (14); and thirty liquids a t two temperatures Figure 3. Viscosity Correlation of Liquids at One Atmosphere (4). As limitations of the data preclude DIATOhlIC
,
GASES.The viscosity of nitrogen was measured
TABLE 11. Pressure. Lb./Sq. In. Abs.
100
200
300 400 500 600 750 1000 1500 2000 3000 4000 5000
30' C. 94.6 95.1 96.4 98.2 104.7 120.2 339.6 400.0 470.0 524.8 603.9 674.5 737.9
40' C. 97.4 98.0 99,l 100.2 104.7 115.6 151.4 319.9 411.0 473.2 553.4 623.7 683.9
VISCOSITY O F ETH.4NE
50'C.
100.2 100.5 100.9 101.6 104.7 113.5 135.5 234.4 356.0 419.8 508.2 576.8 635.3
Viscosity, Poise X 100
60°C. 102.8 103.0 103.3 103.8 105.7 113.5 129.4 164.8 308.0 374.1 460.3 524.8 580.8
75O C. 107.6 107.6 108.2 108.6 110.6 113.5 119.1 141.2 227.5 291.7 376.7 443.6 502.4
1000 c. 114.3 114.3 114.3 114.6 114.8 115.1 119.4 134.9 181.0 231.2 316.2 378.4 433.5
125" C. 121.4 121.6 121.6 121.6 121.9 122.4 124.2 134.0 167.0 204.2 277.3 335.0 385.5
150' C. 128.2 128.2 128.2 128.2 128.3 128.7 130.6 140.0 162.5 191.0 258.2 315.5 363.9
175' C . 135.5 135.8 135.8 136.2 136.8 137.4 140.3 148.9 162.5 190.1 248.3 302.7 348.3
2000 c. 141.9 143.2 144.0 145.2 146.9 148.8 152.1 159.6 172.5 191.9 241.6 293.8 338.1
INDUSTRIAL AND ENGINEERING CHEMISTRY
708
VISCOSITYOF ETHAXE ASD PROPANE. The inclined tube and rolling ball method vias used. The apparatus was constructed by Hubbard who described it in detail (14). It was modified in two ways: (a) An electrical contact \\-as broken within the tube rather tlian outside as the ball started its travel; precautions vere taken to minimize arcing. ( b ) A system of valves was added so that a sample in the tube
1
.6
1
.7
I
I
.8
.9
Reduced Temperature
could be removed by evacuation, and the tube flushed and filled with another sample without dismantling the apparatus. Measured viscosities were therefore relative to those of the fluids used for calibration. The instrument was calibrated with benzene a t 1 atmosphere and 25', 40°, and 60" C.; pentane a t 1 atmosphere arid 25" C.; carbon dioxide at 20" C. and 100-952 pounds per square inch; propane at 1 atmosphere and 40-190O C.; and nitrogen a t 25", 50", and 75" C. and 15-142 atmospheres. The calibration data were represented by the following equations: Turbulent region: Y = 2 2 . 2 X-o.ao1 Viscousregion: Y = 6 . 3 1 X-0.495
density of the fluid, grams/cc. density of the ball, grams/cc. roll time, seconds viscosity, poises X lo4
The density of ethane was obtained from tlie work of Yee (53) and of Beattie, Hadlock, and Poffenberger ( 1 ) ; that for propane was taken from Deschner and Brown ( 7 ) , Beattie, Kay, and Kaminsky (b) , and Sage and Lacey (23). Snioothed viscosity data for ethane and propane are given in Tables I1 and 111. The values for propane differ from those reported 11y Sage and Lacey (@) by a maximum of 10 per cent.
LU
Figure 4. Viscosity Correlation of Saturated Liquids
p = po = 8 = 7 =
Vol. 35, No. 6
Figure 5.
Viscosity Correlation of Saturated Vapors
CORRELATION OF PARAFFINS. Viscosities of normal paraffins from the various sources were cross-plotted, and reduced isotherms of the viscosity function are shown in Figure 7 plotted against reduced pressure. All the data were obtained by the inclined tube and rolling ball method except those at atmospheric pressure and those of Bridgman (Q), who used a vertical cylinder and falling body. Bridgman's data were adjusted to agree with those of Evans (9) a t atmospheric pressure. The uncertainty of the data is probably not greater than *5 per cent. There is no regular dispersion of the plotted data shown in Figure 7 . At equal reduced pressures tlie points for the series do not shift with relation to the compound but differ in their relation to one another at different reduced temperatures. This indicates the presence of experimental errors. The greatest dispersion occurs in the region of the critical pressure; this is a characteristic of van der Kaal's equation of state from which the viscosity function was derived. I n estimating the viscosities of the normal paraffins a t reduced pressures of 0.02-10 and reduced tem-
*
INDUSTRIAL AND ENGINEERING CHEMISTRY
June, 1943
---
TABLE 111. VISCOSITY OF PROPANE
Pressure, Viscosity, Poise X log--7 Lb./Sq. In. Abs. 21.85' C. 40.3' C. 58.7' C. 77.2' C. 95' C. 115' C. 150' C. 190' C. 100 90.8 93.1 96.3 100.2 104.7 113.6 123.2 124.2 105.7 113.8 102.6 99.3 100.2 104.0 200 831.8 115.3 125.6 107.2 108.3 108.1 859.0 719.5 300 993.1 127.6 111.8 117.2 114.3 751.6 119.4 876.0 400 1002 121.8 130.5 128.5 118.9 770.9 535.8 891.2 500 1009 600 1022 903.7 787.1 568.9 328.1 131.8 129.1 133.8 750 1038 922.6 807.2 609.5 414.1 174.6 143.9 140.8 177.8 159.2 505.2 297.2 839.5 666.8 952.8 1000 1067 1500 1135 1014 895.4 753.3 608.4 430.5 285.1 213.3 269.8 516.4 364.8 679.2 948.4 818.5 1069 2000 1202 2500 1265 1119 988.5 869.0 736.2 591.6 426.6 319.9 364.3 645.7 478.6 779.8 1026 912.0 1162 3000 1318 4000 1419 1236 1092 986.3 858.0 721.1 579.4 454.5 5000 1493 1291 1140 1040 918.3 770.9 671.4 529.7
TABLE IV. Paraffin Ethane
CONPARISONOF OBSERVEDVISCOSITIESWITH VALUESCOMPUTED FROM FIGURE 7 TR
PR
0.95
0.82 2.05 4.10 0.922 2.05 4.10 1.024 2.05 4.10 1,537 2.05 4.10 1.024 2.05 4.10
1.00 1.05 1.10 1.25
Propane
0.80 0.90 0.95 1.00 1.05 1.10 1.25
Pentane
0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00
----n X Calcd. 414 553 700 137 452 598 132 346 505 176 263 433 118 157 291
0.953 2.34 4.17 0.953 2.34 4.17 0.953 2.34 4.17 0.953 2 ,'34 4.17 1.072 2.34 4.17 1.19 2.34 4.17 0,953 2.34 4.17
1012 1125 1248 770 885 985 531 718 850 179 581 727 166 458 618 153 364 526 140 219 352
0.825 2.02 0.825 2.02 0.825 2.02 0,825 2.02 0.825 2.02 0.825 2.02 0,825 2.02 1.03 2.02
2240 2370 1861 1972 1530 1635 1280 1410 1144 1268 965 1105 646 880 395 697
lo'---
Obsvd. % ' Differenoe 417 - 0.7 558 0.9 672 4.2 138 0.7 456 0.9 598 d= 0 . 0 135 0.2 371 6.7 5 16 2.1 179 1.7 287 8.3 434 - 0.2 120 1.7 170 7.6 298 2.3 Average 2.1 - 2.4 1000 1.2 1112 1.2 1242 0.5 +, . R R 744 - 0.2 883 0.1 986 540 1.7 734 2.2 1.4 862 160 +11.9 584 0.5 725 0.3 147 +12.9 421 8.9 596 3.7 150 2.0 +ll.O 328 498 5.6 133 4- 5 . 2 211. 3.8 327 7.6 Average 5.2 - 1.2 2215 4- 1.1 2330 1.7 1855 0.3 1965 0.4 1567 - 2.5 1675 2.4 1325 - 3.4 1440 - 0.7 1110 3.1 1240 2.3 .914 5.6 1050 5.2 714 9.5 893 - 1.6 460 -14.1 775 -10.0 Average 2.5 5.5
+--
--
---
+ + +
+ -+-
+ ++ + ++ +
709
dicates that the accuracy is as good as that of the experimental data and well below the variation from an average viscosity. For example, a t TR = 0.95 and PR = 2.0, the observed viscosities of ethane, propane, and pentane differ by *22.5 per cent from an average viscosity. The calculated viscosities obtained from the value of the viscosity function in Figure 7 at the same reduced temperature and pressure difl'er from the observed viscosities by a maximum of +2.6 per cent. A comparison of observed and calculated data is given in Table IV. Figure 7 is not recommended for use with methane or compounds other than the normal paraffins. FLUID MIXTURES
The application of the correlation to mixtures of hydrocarbons was investigated, starting with data at atmospheric pressure. It is applicable where the change of viscosity with concentration is linear. Few compounds exhibit this linearity; the majority have a curvature, and many show a maximum or minimum. I n using Equation 1the molecular weight is replaced by a molar average molecular weight, and the reduced temperature and pressure are replaced by the pseudocritical properties. For a gaseous mixture a t atmospheric pressure the difference in critical pressure of the components is taken into account by combining the pressure term with the viscosity function. The following coordinates are used: temperature
(pseudocritical temperature) critical pressure of component 1 pseudocritical pressure of mixture or critical pressure of component 2 Data obtained by Trautz and Sorg (32) for mixtures of methane-ethane, methane-propane, and ethane-propane are plotted in Figure 8 on these coordinates. A single curve represents all mixtures of ethane-propane. It is evident that methane cannot be a component of paraffin mixtures in correlation, as separate curves are necessary for each composition. The viscosity of mixtures of other paraffins should be
+ ++ + + + +-
+ -
Reduced Temperature
peratures of 0.65-1.5 by Figure 7, it is necessary only to compute the reduced conditions, read the viscosity function from the ordinate corresponding to the reduced values, and multiply that ordinate by the square root of the molecular weight of the compound. The unit of viscosity is the poise. The reliability of the correlation was estimated by comparison of observed data with values read from Figure 7. A weighted average made of fifty-two measurements in-
Figure 6 . Viscosity Correlation of Diatomic Gases
represented by the correlation shown in Figure 7 . The methane mixtures do not have a linear concentration-viscosity relation, and methane and the second component have; different temperature coefficients.
710
INDUSTRIAL AND ENGINEERING CHEMISTRY
0 GHs. A CaHs.
Authors Authors A C3Hs. Sage and Lacey ( 2 4 ) CIHIO.Sage, Yale, 8- Laoey (25)
+
Viscosity data (62)for four natural gases obtained under pressure were compared with values read from Figure 7. The gases contained from 69.74 to 98.4 per cent methane. The deviations between observed and calculated values varied from -5.3 t o -24.8 per cent at a reduced temperature of 1.5 and reduced pressures from 0.22 to 2.99. Good agreement, however, is obtained between DOW’Smeasurements (8) and those read from Figure 7 for hexane-decane mixtures a t reduced pressures up to 10. Table V shows a comparison a t
Figure 8.
Vol. 35, No. 6
CaHn. Hubbard ( 1 4 ) 0 CzHs-CnH2e. Evans (9) H CsH~z-CdIia. Bridgman, Dow (4, 8 )
some conditions recorded by DOW,and also a comparison between values of the viscosity function read from a plot of against TR a t constant P R for all mixtures of hexane-decane and those read from Figure 7. It has not been possible t o correlate viscosity-temperature data a t atmospheric pressure for carbon monoxide-oxygen or nitrogen-hydrogen mixtures although these mixtures have linear concentration relations and the compounds havezessentially equal temperature and pressure coefficients.
v/da
Viscosity Correlation of Hydrocarbon Mixtures at One Atmosphere
INDUSTRIAL AND ENGINEERING CHEMISTRY
June, 1943 -
TABLEV.
COMPAR_ISON OF OBSERVED AND CALCULATED VALUES OF 7 / 2 / M FOR HEXANE-DECANE MIXTURES
SPOTDATAWITH CALCULATED VALUED READFROM FIQURE 7
CI?&
C&a
0 19.7 40.1
100 80.3 59.9
100
0
TR 0.685 0.658 0.628. 0.558
PR Obsvd. 0.0328 214 0.0360 257 0.0386 275 0.0472 393
/ d Z x 10-
?Crtlod.
220 251 273 380
% difference
2;:: -0.7 -3.3
COMPOSITE DATAIATBRPOLATED AT TABULATED COWDITIOW~
dqB
10e
Obsvd. Calcd. % difference
-TR PR = 5 320 310 -3.1
-
0.65PR = 10 360 363 +0.8
(13) (14) (15) (16) (17)
-TR PR= 5 270 261 -3.3
- -
0.70PR 10 306 311 S1.6
CONCLUSIONS
The conclusions which have been reached in other applications of the theorem of corresponding states are true when the theorem is applied to viscosity in the manner described. I n general, the theorem is not valid because individual differences between compounds are too great. The dispersion of the curves from one another is not evidence of deviations from ideal lines. As with other properties, the theorem has been found of value in correlating the viscosity of closely related groups of compounds. The log of 7/2/zis a linear function of the reduced temperature for gases and vapors a t normal pressure. From two measurements the straight line can be used to obtain viscosities by interpolation, but it should not be extrapolated to the boiling point near which curvature begins. The viscosity a t normal pressure of members of homologous series of liquids is represented by curves specific for each series if the log of v/dT is plotted against the reduced temperature, These curves can be used to obtain viscosities of other members of a series for which limited data are available. The first member of a series may be anomalous. The viscosity of saturated liquids and vapors is represented by curves specific for each homologous series if the reduced temperature is plotted against q/.\/M or 7 / 4 7 multiplied by a pressure term. The curves can be used for interpolation and to obtain viscosities a t saturated conditions for members of a series for which data are incomplete. A plot of q/dZ against reduced pressure a t constant reduced temperature represents the viscosity of the normal paraffin hydrocarbons (excluding methane) within the limits of the accuracy of the data used. It can be used to estimate the viscosity of single compounds or mixtures in the reduced temperature range 0.65 to 1.5 and up to a reduced Dressure of
(18) (19) (20) (21) (22) (23)
711
Golubev, I. F., J. Tech. Phys. (U. 5. S . R.), 8, 1932 (1938). Hubbard, R. M., thesis, Univ. Mich., 1940. Khalilov, K., J . Exptl. Theoret. Phys. (U. S . S . R.), 9, 335 (1939). McLeod, D. B., Trans. Faraday SOC.,21, 151 (1925). Moulton, R. W., and Beuschlein, W. L., Trans. Am. Inst. Chem. Engrs., 36,113 (1940). Nelson, W. L., OiE f f a s J., 38, No. 9, 50 (1939). Nelson, W. L., “Petroleum Refinery Engineering”, p. 167, New York, McGraw-Hill Book Co., 1936. Onnes, H. K., Commun. Phys. Lab. Univ. Leiden, No. 12 (1894). Phillips, P., Proc. Roy. SOC.(London), A87, 48 (1912). Sage, B. H., and Lacey, W. N., Am. Inst. Mining Met. Engrs., Tech. Pub. 845 (1937). Sage, B. H., and Lacey, W. N., IND.ENQ. C H ~ M 26, . , 1218
(1934). (24) Ibid., 30, 829 (1938). (25) Sage, B. H., Yale, W. D., and Lacey, W. N., Ibid., 31, 223 (1939). (26) Schriier, E., and Becker, O., 2. physilc. Chem., A173, 178 (1935). (27) Shugaev, V., and Sorokin, S. J., J . Tech. Phys. (U. S . S . R.), 9, 930 (1939). (28) Smith, C. J., Proc. Roy. SOC.(London), 34, 155 (1923). (29) Souders, M., J . Am. Chem. SOC.,60, 154 (1938). (30) Stakelbeck, H., 2. ges. Kalte-Ind., 4 0 , 3 3 (1933). (31) Sutherland, W., Phil. Mag., 36, 507 (1893). (32) Trautn, M., and Sorg., K. G., Ann. Physik [5], 10, 81 (1931). (33) Yee, E. G., thesis, Univ. Mich., 1936.
LITERATURE CITED
Beattie, J. A., Hadlock, C., and Poffenberger, N., J . Chem. Phys., 3, 93 (1935): J . Am. Chem. SOC.,61, 926 (1939). Beattie, J. A., Kay, W C., and Kaminsky, J., J . Am. Chem. SOC.,59, 1589 (1937). Boyd, J. H., Phys. Rev., 35, 1284 (1930). Bridgman, P. W., Proc. Natl. Acad. Sci., 11, 603 (1925). Comings, E. W., and Egly, R. S., IND.ENO.CHEM.,32, 714 (1940).
Ibid., 33, 1224 (1941). Deschner, W. W., and Brown, G. G., Ibid., 32. 836 (1940). Dow, R. B., Physics, 6 , 71 (1935). Evans, E. B., J . Inst. Petroleum Tech., 24, 38 (1938). Fales, H. A., and Shapiro, C., J. Am. Chem. SOC.,60, 794 (1938). Gartenmeister, R., 2.physik. Chem., 6, 524 (1890). Gibson, R. C., “Viscosity of Gases a t High Pres8ures”, Amsterdam, 1933.
Westinghouse Photo
Proper Mixing Is Important for Efficient Production of Industrial Chemicals; Here Shown Is a Step in Making Phosphors, the Coatings Used on Fluorescent Lamps. Phosphor Powders Can Be Blended to Produce Any Color Desired. When Electric Current Passes through the Lamp Tube, Ultraviolet Rays Strike This Coating. The Phosphors Glow Brilliantly to Give Off Fluorescent Light
