I n d . Eng. Chem. Res. 1988,27, 2377-2384
I,, I , = UV irradiance defined in Figure 1, W.m-2 K G u = capacity coefficient for mass transfer between bubble a n d liquid phase, s-’ k , = reaction rate coefficient defined in eq 14, mo14~78.m2.34.s-’ k b = reaction r a t e coefficient defined in e q 15 mol-’-m3-s-’ k i = reaction r a t e coefficient for ith reaction in T a b l e I LT = height of water t r e a t m e n t unit, m 1 = thickness of rectangular reactor in Figure 1, m N A = Avogadro’s number, mol-l [0,] = concentration of ozone in liquid phase, m o l d [OH-] = concentration of OH- in liquid phase, m ~ l - m - ~ P = total pressure, Pa R = gas constant, J.mo1-l.K-l RG = fraction of ozone reacted in gas phase RL = fraction of ozone reacted i n liquid phase T = temperature, K t = time, s UG = superficial gas velocity, ms-’ x = axial coordinate from bottom of reactor, m
Greek Symbols = gas holdup in water t r e a t m e n t reactor Y = frequency of light 4G = overall q u a n t u m yield for ozone decomposition in gas CG
phase
&, = overall q u a n t u m yield for ozone decomposition in liquid phase Literature Cited Czapski, G.; Samuni, A.; Yelin, R. “The Disappearance of Ozone in Alkaline Solution”. Isr. J . Chem. 1986,6,969-971. Glaze, W. H.; Peyton, G. R.; Lin, S.; Huang, R. Y.; Burleson, J. L. “Destruction of Pollutants in Water with Ozone in Combination with Ultraviolet Radiation. 2. Natural Trihalomethane Precursors”. Environ. Sci. Technol. 1982,16,454-458. Glinski, R. J.; Birks, J. W. “Yields of Molecular Hydrogen in the Elementary Reactions HOz + H 0 2 and O(lD,) + HzO“. J. Phys. Chem. 1985,89,3449-3453. Griggs, M.; “Absorption Coefficients of Ozone in the Ultraviolet and Visible Regions”. J. Chem. Phys. 1968,49,857-859. Hewes, C. G.; Davison, R. R. “Kinetics of Ozone Decomposition and Reaction with Organics in Water”. AIChE J . 1971,17,141-147. Ikemizu, K.; Morooka, S.; Kato, Y. “Decomposition of Ozone in Water with Ultraviolet Radiation”. J . Chem. Eng. Jpn. 1987a,20, 77-81. Ikemizu, K.; Orita, M.; Sagiike, M.; Morooka, S.; Kato, Y. “Ozonation of Organic Refractory Compounds with UV Radiation”. J. Chem. Eng. Jpn. 1987b,20,369-374. Jones, I. T. N.; Wayne, R. D. “The Photolysis of Ozone by Ultraviolet
2377
Radiation IV. Effect of Photolysis Wavelength on Primary Step”. Proc. R. SOC.London, Ser. A 1970,A.319,273-287. Jones, I. T. N.; Kaczmar, U. B.; Wayne, R. P. “The Photolysis of Ozone by Ultraviolet Radiation 111. The Photolysis of Dry Ozone/Oxygen Mixtures at Low Pressures in a Flow System”. Proc. R. SOC.London, Ser. A 1970,A.316, 431-439. Morooka, S.; Ikemizu K.; Kato, Y. “The Decomposition of Ozone in Aqueous Solution”. Kagaku Kogaku Ronbunshu 1978,4,377-380; translated in Int. Chem. Eng. 1979,19,650-654. Norrish, R. G. W.; Wayne, R. P. “The Photolysis of Ozone by U1traviolet Radiation I. The photolysis of Pure, Dry Ozone”. Proc. R. SOC.London, Ser. A 1965a,A.288, 200-211. Norrish, R. G. W.; Wayne, R. P. “The Photolysis of Ozone by U1traviolet Radiation 11. The Photolysis of Ozone Mixed with Certain Hydrogen-containing Substances”. Proc. R. SOC.London, Ser. A 196513,A.288,361-370. Ogren, P. J.; Sworski, T. J.; Hachanadel, C. J.; Cassel, J. M. “Flash Photolysis of O3 in O2and 0, + Hz Mixtures. Kinetics of 02(’22) + O3 and O(’D) + H, Reactions”. J . Phys. Chem. 1982,86, 238-242. Peyton, G. P.; Glaze, W. H. “Mechanism of Photolytic Ozonation”. In Photochemistry of Environmental Aquatic Systems; Zika, R. G., Cooper, W. J. Eds.; ACS Symposium Series 327; American Chemical Society: Washington, DC, 1987; pp 76-88. Podolske, J. R.; Johnston, H. S. “Rate of Reaction Energy-Transfer Reaction between O p ( l A g )and HOO”. J. Phys. Chem. 1983,87, 628-634. Prengle, H. W., Jr.; Mauk, C. E.; Legan, R. W.; Hewes, C. G., 111. “Ozone/UV Process Effective Wastewater Treatment”. Hydrocarbon Process. 1975,Oct, 82-87. Rizzuti, L.; Augugliaro, V.; Marrucci, G. “Ozone Absorption in Alkaline Solutions”. Chem. Eng. Sci. 1976,31,877-880. Rothmund, V.; Burgstaller, A. “Uber die Geschwindigkeit der Zersetzung des Ozons in Wasserrger Losung”. Monatsh. Chem. 1913, 34,665-693. Sotelo, J. L.;Beltran, F. L.; Benites, F. J.; Beltran-Heredia, J. “Ozone Decomposition in Water: Kinetic Study”. Ind. Eng. Chem. Res. 1987,26,39-43. Staehelin, J.; Hoigne, J. “Decomposition of Ozone in Water: Rate of Initiation by Hydrogen Ions and Hydrogen Peroxide”. Enuiron. Sei. Technol. 1982,16,676-682. Stumm, W. “Der Zerfall von Ozon in Wassriger Losung”. Helu. Chem. Acta 1954,37,773-778. Teramoto, M.; Imamura, S.; Yatagai, N.; Hishikawa, Y.; Teranishi, H. “Kinetics of the Self-Decomposition of Ozone and the Ozonation of Cyanide Ion and Dyes in Aqueous Solutions”. J . Chem. Eng. J p n . 1981,14,383-388.
Received for review December 21, 1987 Revised manuscript received June 20, 1988 Accepted August 20, 1988
Generalized Viscosity Behavior of Fluids over the Complete Gaseous and Liquid States Huen Lee* Department of Chemical Engineering, Korea Institute of Technology, 400, Kusong-dong, Seo-gu, Taejon-shi, Chung-chong nam-do, Korea
George Thodos Department of Chemical Engineering, Northwestern University, Euanston, Illinois 60201
A generalized correlation of viscosity of both nonpolar and polar fluids over the entire temperature and pressure ranges has been developed. In addition to the triple-point properties, a volume expansion factor, defined as the ratio of liquid molar volume to solid molar volume at the triple point, was employed. Comparison between experimental and predicted values for 101 substances shows an average absolute deviation of 4.03% (2515 p o i n t s ) . The present state of our knowledge dealing w i t h the generalized prediction of the transport properties continues to be limited to t h e dilute and m o d e r a t e l y dense gaseous states. A t t e m p t s to extend this generalized a -p p- r o a c h to -
* Author t o whom
correspondence should be addressed.
0888-5885/88/2627-2377$01.50/0
gases at high pressures and the liquid state associated with t e m p e r a t u r e s below the normal boiling p o i n t and app r o a c h i n g the triple-point region of substances h a v e not y e t been p r o p e r l y resolved to p e r m i t the formulation of a unified approach for viscosity; thermal conductivity, ar d self-diffusivity. Because of the complexity associated with 0 1988 American Chemical Society
2378 Ind. Eng. Chem. Res., Vol. 27, No. 12, 1988
the aggregation of the liquid state, the development of the transport property behavior for this dense-phase region has not advanced sufficiently, and consequently any attempt to predict these properties in this region is presently inadequate. The difficulty encountered with the liquid region is not unexpected because of the complex nature associated with this state of aggregation. The kinetic theory offers the theoretical basis for estimating properties of substances in the gaseous state, while the lattice theory provides the theoretical background needed for treating the solid state. The liquid state bridges these two extremes, and so far it has proven to be rather formidable to permit the estimation of properties in this state of aggregation from theoretical arguments. In view of the elusive nature of this state, liquids are considered to be disordered solids, and for their description solidlike theories have been advanced, while other theories consider liquids as dense gases. Since van der Waals proposed the existence of continuity between the gaseous and liquid states, no significant development on the theory of the liquid state was advanced until the 1930s when the similarity of liquids and crystalline solids was proposed. This concept led to the development of the solidlike theory. On the viscosity of liquids, Hildebrand (1971) pointed out that "Viscosity of liquids has been treated copiously in engineering and scientific literature, but nearly all that I have read seems unrealistic in one respect or another, such as the assumption of quasi-lattice structure that ignores clear evidence to the contrary, or that temperature dependence is exponential, or that there is an energy of activation, a notion that disregards the basic distinction between liquid and plastic flow." Lee (1971) also pointed out reasons underlying the phenomenological existence of the liquid state, not from the point of view of similarity between the liquid and solid states but rather from the dissimilarity existing between them. A comprehensive study correlating viscosity was undertaken with special emphasis placed in the highly dense gaseous and liquid states. Under these conditions, the state of aggregation of substances becomes highly sensitive to the structural aspects of their molecular configuration. Crawford et al. (1975) pointed out that such nonuniformities become accentuated for liquids as they are made to approach their triple-point temperature. To obtain an overall assessment of the pattern existing with transport properties, it becomes necessary to examine the behavior of viscosity for a variety of substances including both the polar and the nonpolar over wide temperature and pressure conditions and coordinate their behavior into a unified pattern capable of predicting this transport property in a generalized manner consistent with the theorem of corresponding states. In this connection, a comprehensive study was conducted for a generalized prediction of self-diffusivity of nonpolar and polar fluids over all fluid-state conditions ranging from the dilute and dense gaseous state to the saturated and compressed liquid regions in our previous paper (Lee and Thodos, 1988). The purpose of the present study is therefore to extend this approach for the development of the generalized viscosity correlation of pure fluids over the entire pressure and temperature range.
Viscosity for the Dilute Gaseous State For the dilute gaseous state, Stiel and Thodos (1961) investigated the viscosity of both polar and nonpolar gases and presented for their behavior the expressions P*
1.50 (2) where 5 = T,'I6/ M 1/2P:/3, The predictive reliability of eq 1 and 2 has been verified with the exception of helium and hydrogen, using monatomic gases, diatomic gases, carbon dioxide, carbon tetrachloride, and paraffinic, olefinic, naphthenic, acetylenic, and aromatic hydrocarbons to produce for them a mean deviation of 1.8% (785 points). In their study, Stiel and Thodos (1961) utilized 52 gases for which the 2, values range from 0.308 for neon to 0.260 for n-nonane and concluded that the relationship of p*[ versus T R is independent of 2,.In this context, Stiel and Thodos (1962) applied this approach to the comprehensive correlation for the viscosity of polar substances and presented the following relationships, for hydrogen-bonding types, ( P * E ) Z , ~=/ ~ ( 7 . 5 5 T ~- 0.55) x T R < 2.0 (3) and for non-hydrogen-bonding types, (P*[)Z:I~ = (1.9OTR - 0.29)4/5X lo4 TR < 2.5 (4) Viscosities calculated with eq 3 for 11 polar substances exhibiting hydrogen bonding were compared with the corresponding experimental values to produce an average absolute deviation of 1.47% (129 points). For the 41 polar gases which do not exhibit hydrogen bonding, viscosities calculated with eq 4 produced an average absolute deviation of 2.59% (197 points).
F*< =
17.78 X 1OW5(4.58TR - 1.67)5/s
Viscosity Models for the Dense Gaseous and Liquid States A number of viscosity correlations for the dense gases and liquids have been proposed in the literature (Reid et al., 1987). The free volume method and corresponding states method have been most popularly used. Continued interest in the application of the free volume model was expressed in the study of Dymond and Brawn (1977), who presented for liquid viscosity the expression In
pu213 ~
(MT)'12
=A
+ B-u -UOu g
(5)
where uo is the close packing molar volume of the molecules. Equation 5 has been generally accepted as capable of predicting reliable viscosities for the compressed liquid state by allowing uo to depend on temperature; however, this relationship proves inadequate for predicting viscosities at high densities in the proximity of the freezing curve (Trappeniers et al., 1980) and furthermore contains two adjustable parameters that must be determined from experimental viscosity data. In the recent study, Przezdziecki and Sridhar (1985) also used Hildebrand's (1971) modification of the Batschinski equation for modeling liquid viscosity and correlated the parameters with the pure component properties as follows:
where 0.33~~ B=-1.12
(7)
fl
fl = 4.27
+ 0.032M - 0.O77Pc + 0.014Tt - 3.82T,/Tc (8)
~g
= 0.0085Tp
-
2.02
+
Ult
Tt 0.342Tc
+ 0.894
(9)
Ind. Eng. Chem. Res., Vol. 27, No. 12, 1988 2379 This purely empirical equation is only applicable in the saturated liquid region and, compared with corresponding experimental measurements, produced an average deviation of 8.7% (146 points) for the 27 fluids. Ely and Hanley (1981) developed a corresponding states model for the perdiction of the viscosity of nonpolar fluids over a wide range of thermodynamic states from the dilute gas and dense fluids. This model was tested for 36 substances including alkanes, aromatics, and a few other simple compounds and produced an overall average absolute deviation of 8.42% (1869 points). On the critical evaluation of the results, they concluded that “The overall deviations become somewhat worse, and negative, as the freezing point is approached. It is not clear why this should be the case but one can say that there is a good chance that the fluids become non-Newtonian in this region and that pre-freezing nucleation effects are important.” Ely and Hanley’s model failed to predict the viscosity of highly branched alkanes and polar fluids. A comprehensive review of other empirical viscosity correlations is given by Reid et al. (1987). They also concluded that there is the problem of joining both high- and low-temperature liquid viscosity correlations. The inability of the current status to predict in a generalized manner liquid viscosities in the highly compressed fluid region and particularly in the proximity of the liquid-solid transition state requires scrutiny on the behavior of this transport property with particular emphasis placed at this extreme state of liquid aggregation.
Comprehensive Treatment of Viscosity Data for Dense Gases and Liquids The critical constants of substances have so far proven to be satisfactory normalizing parameters for the generalized treatment of thermodynamic and transport properties, consistent with the theorem of corresponding states. In this regard, temperature, pressure, and volume are ordinarily normalized with corresponding critical temperatures, critical pressures, and critical volumes to produce reduced quantities which are then applied to the correlation of thermodynamic and transport properties. These normalized quantities have proven satisfactory for the correlation and prediction of transport properties associated with the dilute and dense gaseous states of fluids; however, its application to the liquid region has so far proven to be of limited utility. Thus, for liquids existing at temperatures above their normal boiling point, these generalized methods of correlation have been found to conform reasonably well to the prediction of transport properties; however, for temperatures below their corresponding normal boiling points, and particularly for conditions approaching the triple-point region, these methods fail to account properly for the generalized behavior of thermodynamic and transport properties. This pattern of behavior is not unexpected since the involvement of the critical point stipulates a frame of reference near its vicinity and properly accommodates the dilute and dense gaseous states, but may not necessarily conform to the behavior of liquid at low temperatures and particularly for temperatures approaching the triple-point region. Because of this duality in behavior, it could be well argued that the triple point as well constitutes a frame of reference related to its immediate region in the same manner that the critical point has been found to apply for state conditions in close proximity to it. In a previous paper (Lee and Thodos, 1988), this concept has been successfully applied to predict self-diffusivity of pure fluids over the entire range of PVT states. Introducing triple-point values for
a basis of reference, the excess viscosity can be expressed as follows: ( P - p*)y = F(T, w )
(10)
where the viscosity parameter y = V , ~ ~ ~ / M ’ the /~T,~~~, normalized temperature T = TIT,, and the normalized density w = p / p l t . The extensive experimental measurements for viscosity available for the subcritical and supercritical states of neon and argon present adequate information to describe the ( p - p*)y versus w = PIPlt behavior of these substances for densities ranging from moderately compressed gaseous state to liquids approaching their freezing line. The viscosity data of Haynes (1973) cover the supercritical, saturated liquid, and compressed state regions. In particular, it was noted that the separate isothermal relationships between ( p - p * ) y and w for the three normalized temperatures of T = 1.285,1.493, and 1.667 exist, for which compressed liquid viscosities are reported by Haynes. Similar relationships were noted for the supercritical data of Trappeniers et al. (1980) for argon at T = 2.663, 3.594, and 3.857 and of Vermesse and Vidal (1973) at T = 3.678. The similar behavior exhibited by argon was also noted with neon, for which the compressed liquid data of Herreman and Grevendonk (1974) exhibit separate isothermal relationships for the six subcritical temperatures of T = 1.100, 1.215, 1.340, 1.467, 1.597, and 1.707 and the supercritical data of Vermesse and Vidal (1975) at T = 12.150. Similar patterns of behavior were noted for a number of polar and nonpolar substances extensively treated in this study. The dependence of ( p - ~ * ) on y reduced temperature and reduced density, r and w, has been combined into a generalized single variable. By use of viscosity data for 101 substances including nonpolar, polar, quantum, and even associating liquids, a nonlinear regression analysis produced the following expression:
This density-temperature variable has been shown to possess the capability of eliminating the presence of bifurcations by producing the single relationships for each of these substances. The dependence of ( p - p * ) y on x is best represented by the expression ( p - p*)y
x
io5 = exp(axm+ pxn) - 1
(12)
Equation 12 properly accounts for the boundary condition ( p - p*)y = 0 at x = 0. The basic physical constants and viscosity parameters are presented in Table I. A nonlinear regression analysis generated for each substance the coefficients a and p and the exponents m and n presented in Table 11. Although the viscosity behavior of each substance is a unique function of the density-temperature variable x , these relationships do not, as such, conform to a generalized pattern. Therefore, an additional parameter associated with the molecular orientation at the liquidsolid phase transition could prove of value in unifying this pattern of behavior aimed toward a generalized prediction of viscosity.
Generalized Viscosity Behavior for Dense Gaseous and Liquid States In the vicinity of the critical point, a highly disorganized order of molecular orientation prevails for both saturated liquids and saturated vapors and extends into the dense fluid state provided the temperature and pressure conditions are not significantly removed from the critical point. However, with decreasing temperature and par-
2380 Ind. Eng. Chem. Res., Vol. 27, No. 12, 1988 Table I. Basic Physical Constants and Viscosity Parameters for 101 ComDounds monatomic neon argon krypton xenon diatomic n-hydrogen nitrogen oxygen fluorine chlorine alkanes methane ethane propane n-butane 2-methylpropane n-pentane 2-methylbutane 2,2-dimethylpropane n-hexane n-heptane n-octane 2,2,4-trimethylpentane n-nonane n-decane n-undecane n-dodecane n-tridecane n-tetradecane n-pentadecane n-hexadecane n-heptadecane n-octadecane n-eicosane alkenes ethylene 1-pentene 1-hexene 1-heptene 1-octene naphthenes cyclopentane methylcyclopentane ethylcyclopentane cyclohexane methylcyclohexane ethylcyclohexane aromatic hydrocarbons benzene toluene o-xylene m-xylene p-xylene ethylbenzene isopropylbenzene n-butylbenzene styrene biphenyl o-terphenyl m-terphenyl p-terphenyl halides fluoroform methyl chloride dichloromethane chloroform carbon tetrachloride chlorodifluoromethane dichlorofluoromethane dichlorodifluoromethane trichlorofluoromethane chlorodifluoroethane trichlorotrifluoroethane ethyl bromide fluorobenzene chlorobenzene
30.948 83.800 131.300
150.65 209.41 289.73
48.02 54.18 57.64
75.50 92.29 18.29
0.293 0.291 0.287
83.79 115.94 161.36
28.21 34.31 42.66
0.031 39 0.01859 0.015 04
0.181 98 0.107 12 0.083 87
2.016 28.013 32.000 37.997 70.906
33.30 126.20 154.58 144.30 417.00
12.81 33.54 49.77 51.47 76.00
65.00 89.20 73.39 66.19 124.00
0.305 0.289 0.288 0.288 0.275
13.95 63.14 54.36 53.48 172.20
26.06 32.29 24.81 22.29 41.30
0.230 74 0.040 69 0.030 27 0.026 85 0.018 09
1.657 67 0.241 10 0.203 97 0.175 72 0.108 14
16.043 30.070 44.097 58.124 58.124 72.151 72.151 72.151 86.178 100.198 114.232 114.232 128.259 142.286 156.313 170.340 184.367 198.394 212.421 226.448 240.475 254.484 282.556
190.56 305.50 369.99 425.18 408.10 469.60 460.40 433.80 507.40 540.30 568.80 566.30 594.60 617.60 638.80 658.30 675.80 694.00 707.00 717.00 733.00 745.00 767.00
45.39 48.50 42.10 37.47 36.00 33.30 33.40 31.60 29.30 27.00 24.50 26.90 22.80 20.80 19.40 18.00 17.00 16.00 15.00 14.00 13.00 11.90 11.00
100.00 141.72 195.70 254.91 263.00 304.00 306.00 303.00 370.00 431.94 492.00 461.00 548.00 608.00 660.00 713.00 780.00 830.00 880.00 944.00 1000.00 1178.20 1177.00
0.288 0.274 0.271 0.274 0.283 0.263 0.271 0.269 0.260 0.263 0.259 0.267 0.260 0.248 0.240 0.238 0.240 0.233 0.230 0.225 0.220 0.229 0.206
90.66 89.88 85.44 134.86 113.60 143.40 113.30 256.60 177.84 182.57 216.38 163.90 219.66 243.51 247.60 263.60 267.80 279.00 283.00 291.00 295.00 301.35 310.00
35.37 45.58 60.28 78.44 79.32 95.10 92.48 114.50 113.45 129.67 150.38 143.06 165.58 184.25 202.37 221.28 239.94 255.01 273.99 292.27 310.17 327.73 364.17
0.047 07 0.035 59 0.033 34 0.032 12 0.032 77 0.031 71 0.031 54 0.032 41 0.032 01 0.031 68 0.031 93 0.029 98 0.031 84 0.032 35 0.032 51 0.032 90 0.033 00 0.033 27 0.033 67 0.034 23 0.035 02 0.036 21 0.036 39
0.282 57 0.245 47 0.250 50 0.207 00 0.227 19 0.204 86 0.226 18 0.173 30 0.189 33 0.188 99 0.179 90 0.19991 0.17968 0.173 98 0.17521 0.172 65 0.173 78 0.17092 0.172 05 0.171 56 0.17204 0.171 68 0.172 31
28.054 70.135 84.162 98.189 112.216
282.40 464.70 504.00 537.20 566.60
49.70 40.00 31.30 28.00 25.90
129.00 300.00 350.00 440.00 464.00
0.276 0.310 0.260 0.280 0.260
104.00 107.90 133.30 154.30 171.40
42.62 87.52 104.35 121.59 138.87
0.035 77 0.028 41 0.030 96 0.031 20 0.031 02
0.225 92 0.207 39 0.209 26 0.199 40 0.193 36
70.135 84.162 98.189 84.162 98.189 112.216
511.60 532.70 569.50 554.15 572.10 609.00
44.50 37.40 33.50 40.40 34.30 29.90
260.00 319.00 375.00 311.70 368.00 450.00
0.276 0.273 0.269 0.277 0.269 0.270
179.30 130.70 134.70 279.80 146.60 161.80
79.24 95.18 110.46 106.15 110.85 126.75
0.026 89 0.027 75 0.027 96 0.026 53 0.027 54 0.028 53
0.164 51 0.19876 0.187 26 0.141 62 0.192 34 0.187 26
78.115 92.141 106.168 106.168 106.168 106.168 120.195 134.222 104.152 154.21 2 230.310 230.310 230.310
562.09 591.70 630.20 617.00 616.20 617.10 631.00 660.50 647.00 789.00 891.00 924.80 926.00
48.34 40.60 36.80 35.00 34.70 35.60 31.70 28.50 39.40 38.00 38.50 34.60 32.80
258.66 316.00 369.00 376.00 379.00 374.00 428.00 497.00 354.00 502.00 769.00 784.00 779.00
0.271 0.264 0.263 0.260 0.260 0.263 0.260 0.261 0.263 0.295 0.405 0.358 0.336
278.69 178.00 248.00 225.30 286.40 178.20 177.10 185.02 242.50 342.40 330.00 360.00 485.00
87.31 95.32 116.07 115.83 121.94 110.45 126.13 154.19 110.04 155.68 221.56 221.22 240.43
0.024 49 0.025 55 0.025 69 0.026 47 0.026 61 0.026 17 0.026 67 0.027 30 0.024 89 0.021 66 0.017 93 0.019 37 0.020 08
0.13341 0.162 94 0.146 64 0.153 64 0.141 02 0.167 36 0.17238 0.182 38 0.144 49 0.12594 0.132 82 0.127 03 0.11569
70.010 50.488 84.933 119.378 153.823 86.469 102.923 120.914 137.368 100.496 187.380 108.966 96.104 112.559
298.89 416.30 510.00 536.40 556.40 369.20 451.60 385.00 471.20 410.20 487.20 503.80 560.09 632.40
47.73 65.90 60.00 54.00 45.00 49.10 51.00 40.70 43.50 40.70 33.70 61.50 44.90 44.60
133.40 139.00 193.00 239.00 276.00 165.00 197.00 217.00 248.00 231.00 304.00 215.00 269.00 308.00
0.258 0.268 0.277 0.293 0.272 0.267 0.272 0.280 0.279 0.279 0.256 0.320 0.265 0.265
117.95 175.40 178.10 209.60 250.00 113.00 138.00 115.40 162.00 142.00 238.20 154.60 234.00 227.60
41.45 44.77 55.83 73.09 91.96 50.50 60.61 66.85 78.14 69.51 110.34 63.81 88.12 96.21
0.02349 0.023 57 0.020 01 0.018 26 0.018 28 0.021 48 0.019 85 0.020 73 0.019 24 0.022 98 0.01964 0.017 34 0.023 18 0.021 96
0.131 80 0.13398 0.11877 0.11051 0.103 91 0.13822 0.12947 0.13944 0.122 52 0.141 52 0.108 89 0.12303 0.13205 0.131 18
Ind. Eng. Chem. Res., Vol. 27,No. 12, 1988 2381 Table I (Continued) bromobenzene iodobenzene perfluorocyclobutane alcohols methanol ethanol phenol amines methylamine n-propylamine isopropylamine n-butylamine isobutylamine di-n-ethylamine di-n-propylamine tri-methylamine aniline miscellaneous carbon dioxide sulfur hexafluoride boron trichloride tetramethylsilane diethyl ether acetone methyl isobutyl ketone methyl acetate ethyl acetate n-propyl acetate ammonia acetic acid propionic acid n-butyric acid pyridine picoline
M
TC
UC
2,
Tt
Ult
l
Y
157.010 204.010 200.032
670.00 721.00 388.50
44.60 44.60 26.70
324.00 351.00 326.80
0.263 0.265 0.274
242.30 241.80 231.80
100.79 107.52 117.77
0.01877 0.016 67 0.021 38
0.11104 0.101 81 0.111 58
32.042 46.069 93.113
512.60 516.20 694.20
79.90 63.00 60.50
118.00 167.00 229.00
0.224 0.248 0.240
175.50 159.10 314.00
33.50 48.42 88.32
0.026 94 0.026 36 0.019 97
0.138 58 0.155 17 0.11537
31.058 59.112 59.112 73.139 73.139 73.139 101.193 101.193 93.129
430.00 497.00 476.00 524.00 516.00 496.60 550.00 535.00 699.00
73.60 46.80 50.00 41.00 42.00 36.60 31.00 30.00 52.40
140.00 233.00 229.00 288.00 284.00 301.00 407.00 390.00 270.00
0.292 0.267 0.290 0.270 0.280 0.270 0.280 0.270 0.247
179.70 190.00 177.90 224.10 188.00 223.40 210.00 158.40 267.00
39.17 72.31 66.39 90.10 88.25 90.87 124.77 120.32 89.03
0.028 07 0.028 19 0.026 78 0.027 92 0.027 41 0.029 85 0.028 83 0.029 34 0.022 05
0.15439 0.163 78 0.159 89 0.15698 0.16904 0.158 12 0.171 29 0.192 50 0.126 44
44.010 146.050 117.169 88.230 74.123 58.080 86.134 74.080 88.107 102.134 17.031 60.052 74.080 88.107 78.102 93.129
304.19 318.70 452.00 448.61 466.70 508.10 553.40 506.80 523.20 549.40 405.50 594.40 612.00 628.00 620.00 646.00
72.85 37.10 38.20 27.84 35.90 46.40 38.00 46.30 37.80 32.90 1113.30 57.10 53.00 52.00 55.60 44.02
94.04 198.00 245.65 362.00 280.00 209.00 310.00 228.00 286.00 345.00 72.50 171.00 230.00 292.00 254.00 311.00
0.274 0.281 0.253 0.273 0.262 0.232 0.259 0.254 0.252 0.252 0.242 0.200 0.242 0.295 0.277 0.260
216.55 222.50 165.90 182.00 156.50 178.20 181.00 175.00 189.60 178.00 195.41 289.80 252.50 267.90 231.50 276.90
37.37 79.70 73.48 114.14 86.41 64.48 95.71 68.38 86.38 101.17 23.11 54.83 71.51 90.14 75.79 96.14
0.022 41 0.019 44 0.022 56 0.032 07 0.029 73 0.02871 0.027 31 0.025 44 0.026 85 0.027 58 0.028 16 0.025 23 0.023 99 0.022 38 0.022 54 0.024 44
0.11451 0.102 74 0.125 83 0.185 72 0.181 24 0.15806 0.167 58 0.14686 0.151 19 0.161 03 0.140 64 0.109 54 0.125 97 0.13085 0.132 84 0.13069
PC
ticularly for conditions existing below the normal boiling point, this prevalent randomness gradually begins to disappear with the onset of a new realignment dictated by the specific crystalline configuration of the substance which must be realized as its freezing state is approached. Thus, in general, the critical point can be associated with vapor-liquid phase transition, while the triple point becomes of significance near liquid-solid phase transition. It is also likely that transport properties, such as viscosity, selfdiffusivity, and thermal conductivity, will be particularly sensitive to the molecular orientation of the solid and fluid states in equilibrium with each other. In this regard, the fractional volume expansion at the triple point defines a key parameter that should exert considerable influence in the near solid region of liquid. Therefore, its equivalent form, expressed as e
=
Vlt/USt
,r"
"rL
5
300
-
c12
O
C8
(13)
has been adopted and applied to many substances for which experimental information is available to permit the calculation of t, the volume expansion factor a t the triple point. Information of this type is rather limited, particularly for ust, the solid molar volume a t the triple point. For the solid-liquid phase transition, the Clausius-Clapeyron equation
provides a means for calculating the solid molar volume at the triple point. Unfortunately, information of this type is available only for a limited number of simple substances, and therefore eq 14 does not offer a convenient means for the calculation of ust The solid molar volume at the triple point has been found to relate directly with the modified van der Waals covolume parameter, b (Lee and Thodos,
I
10
20
I
I
1
I
,
I
'
I00
50
200
I
I
,
500
b
Figure 1. Dependence of vet upon b.
1988). The modified van der Waals equation of state is defined by the following form:
( P + u/u")(u - b) = R T Applying the critical conditions to eq 15,we find that n and b are related to the critical compressibility factor, Z,, by the following relationships: (16)
and
n = 22, + (42:
+ l)0.5
2382 Ind. Eng. Chem. Res., Vol. 27, No. 12, 1988 Table 11. Constants in Equation 12, t Values, and AAD 7% Resulting from Equation 21 for 101 Compounds constants in eq 12 CY P m n e data pts AAD lit. sources monatomic 3.153 a i 0.68364 1.696 58 -0.035 77 1.147 04 ai 4.32 Trappeniers et al. (1964); Vermesse and neon Vidal (1975); Herreman and Grevendonk (1974); Slyusar et al. (1973) 134 0.485 51 3.423 57 7.904 29 1.027 50 1.14396 3.36 Haynes (1973); Trappeniers et al. (1964); argon Vermesse and Vidal (1975) 1.12762 1.15251 19 0.85 Ulybin et al. (1978) 0.25406 3.56094 12.04691 krypton 3.34 Ulybin and Makarushkin (1977) 56 1.45769 2.55279 4.07248 0.59049 1.13843 xenon diatomic 12 0.98626 1.17640 4.01 Vargaftik (1975) 0.56137 3.17843 12.39454 n-hydrogen 1.054 17 1.121 60 111 4.74 Hellemans et al. (1970); Vermesse (1969) 0.708 25 3.538 77 7.004 69 nitrogen 0.89349 1.08855 79 1.61 Haynes (1977) 1.11968 3.57348 5.00948 oxygen 71 2.23 Haynes (1977) 1.048 83 1.085 31 1.08057 4.015 93 9.599 31 fluorine 0.19265 1.087 11 6 7.49 Weast (1979) 1.25442 3.43056 6.39434 chlorine alkanes 0.967 93 1.136 54 92 6.27 Diller (1981) methane 0.767 41 3.331 50 7.542 51 0.88972 1.054 13 125 1.29 Diller (1981) 1.84003 4.039 39 6.939 93 ethane 1.283 34 1.022 04 68 6.38 Diller (1981) 2.378 51 5.386 75 12.976 11 propane 7 0.65 Vargaftik (1975) 4.398 87 1.602 24 3.668 27 -0.724 47 1.044 68 n-butane 1.31 Vargaftik (1975) 3.579 93 1.025 90 3.442 14 3.579 93 6.055 47 8 2-methylpropane 1.42 Lee and Ellington (1965) 0.679 71 1.040 17 243 2.168 46 3.901 98 6.058 66 n-pentane 2 0.43 Stephan and Lukas (1979) 1.030 73 1.022 87 2.501 39 3.548 14 2.738 55 2-methylbutane 1.11932 1.11708 19 6.55 Gonzalez and Lee (1968) 0.292 22 3.903 00 9.881 93 2,2-dimethylpropane 1.078 17 1.052 31 32 1.76 Vargaftik (1975) 1.522 88 4.53043 10.605 85 n-hexane 5.71 Vargaftik (1975) 0.944 02 1.041 32 36 2.256 19 4.234 47 7.947 73 n-heptane 4.47 Brazier and Freeman (1969) 0.966 18 1.055 60 27 1.70809 3.91625 5.35946 n-octane 0.892 19 1.020 78 21 1.57 Vargaftik (1975) 2,2,4-trimethylpentane 3.859 04 4.553 49 9.290 59 17 2.58 Vargaftik (1975) 0.95803 1.045 57 1.82314 4.51129 9.78271 n-nonane 136 3.29 Vargaftik (1975) 1.24569 4.78140 1.09696 1.15394 1.05095 n-decane 17 1.02902 1.04632 2.63 Vargaftik (1975) 1.64721 4.681 37 11.41781 n-undecane 12 1.380 25 1.048 78 1.64 Vargaftik (1975) 1.094 65 5.112 94 14.552 39 n-dodecane 1.14052 1.04468 16 3.13 Vargaftik (1975) 1.481 17 4.89683 12.243 10 n-tridecane 1.79204 1.046 13 10 1.66 Vargaftik (1975) 0.702 42 5.634 29 21.523 07 n-tetradecane 1.772 1 2 1.04342 9 1.55 Vargaftik (1975) 0.761 43 5.685 26 19.474 31 n-pentadecane 1.29941 1.042 15 16 5.47 Vargaftik (1975) 1.231 37 5.20594 13.21695 n- hexadecane 1.001 16 1.039 39 ia 8.73 Vargaftik (1975) 1.666 27 4.859.a~ 10.804 72 n-heptadecane a 2.99 Vargaftik (1975) 5.086 20 1.453 83 5.12622 -3.153 34 1.04046 n-octadecane 1.35877 1.03742 12 8.63 Vargaftik (1975) 1.119 10 5.51096 14.57967 n-eicosane alkenes 14 1.26 Vargaftik (1975) 1.541 73 3.51689 8.10601 0.50363 1.082 40 ethylene 2.81 Vargaftik (1975) 19 0.735 84 1.027 29 3.656 35 4.219 75 9.010 33 1-pentene 20 2.46 Vargaftik (1975) 4.350 60 2.562 93 5.292 40 -0.074 37 1.034 54 1-hexene 20 2.11 Vargaftik (1975) 0.010 62 1.036 41 3.727 22 3.092 58 6.569 88 1-heptene 24 2.06 Vargaftik (1975) 3.101 62 4.695 83 13.356 52 0.939 45 1.03583 1-octene naphthenes 5 0.48 Vargaftik (1975) 0.56345 1.04511 2.590 10 3.51475 5.777 63 cyciopentane 16 0.36 Vargaftik (1975) 0.76012 1.01206 3.96094 4.371 33 7.59445 methylcyclopentane 15 0.72 Vargaftik (1975) 6.35293 1.01384 3.27469 4.91873 0.11695 ethylcyclopentane 3.10 Jonas et al. (1980) 25 5.12360 0.079 39 2.949 03 -12.32844 1.076 35 cyclohexane 6.01 Vargaftik (1975) 22 0.882 38 1.007 67 4.465 61 4.325 09 7.398 88 methylcyclohexane 0.673 07 1.01669 5 0.97 Vargaftik (1975) 4.462 47 4.556 68 10.686 47 ethylcyclohexane aromatic hydrocarbons 35 3.35 Parkhurst and Jonas (1975) 3.58505 1.038 12 3.545 78 -2.015 44 1.100 a3 benzene 14 1.29207 1.042 19 3.52 Vargaftik (1975) toluene 2.390 43 4.936 43 13.32368 1.32865 1.069 14 31 3.62 Vargaftik (1975) o-xylene 1.03648 4.551 80 13.74880 1.175 55 1.068 30 14 2.91 Vargaftik (1975) 1.30963 4.407 92 12.70808 m-xylene 1.35832 1.102 15 13 1.28 Vargaftik (1975) 0.404 35 4.196 20 14.226 74 p-xylene 11 2.18 Vargaftik (1975) 0.35004 1.036 55 3.503 40 3.45843 7.13892 ethylbenzene 9.146 56 1.029 29 5 2.63 Vargaftik (1975) 3.490 03 4.592 84 0.034 02 isopropylbenzene 8 2.12 Vargaftik (1975) 1.679 50 1.026 35 n-butylbenzene 2.942 39 5.87256 19.13032 1.534 46 1.072 78 15 7.06 Vargaftik (1975) 1.106 12 4.662 31 18.207 87 styrene 2 5.89 Hedley et al. (1970) 1.58545 3.572 04 5.902 05 1.179 13 1.079 78 biphenyl 9 15.75 Hedley et al. (1970) 2.363 43 1.035 32 o-terphenyl 1.10897 6.03893 12.77105 6.75 Hedley et al. (1970) m-terphenyl 4.310 56 2.078 20 4.760 04 -0.17563 1.045 16 10 0.555 16 1.10204 6 0.71 Hedley et al. (1970) 1.44492 3.108 16 5.411 63 p-terphenyl halides 7 fluoroform 1.814 48 3.594 61 7.298 38 0.593 8; 1.065 60 3.93 Phillips and Murphy (1970) 9.52 Vargaftik (1975) 6 methyl chloride 0.532 09 3.527 23 0.694 85 0.583 28 1.073 75 dichloromethane 1.58 Phillips and Murphy (1970) 1.685 65 4.068 50 9.287 07 0.821 27 1.061 09 12 chloroform 1.64 Phillips and Murphy (1970) 0.813 50 1.072 35 11 1.35567 3.93398 8.174 51 carbon tetrachloride 1.99 McCool and Woolf (1972) 0.188 75 5.075 01 24.516 53 1.834 25 1.07389 27 4.10 Phillips and Murphy (1970) 8 0.889 a8 1.04143 4.821 52 4.506 27 15.995 73 chlorodifluoromethane 2.44 Phillips and Murphy (1970) 11 2.95265 3.371 44 6.476 54 0.32893 1.043 70 dichlorofluoromethane 14.19 Vargaftik (1975) dichlorodifluoromethane 2.619 10 3.461 53 6.549 95 0.142 00 1.029 31 30
Ind. Eng. Chem. Res., Vol. 27, No. 12, 1988 2383 Table I1 (Continued)
2.733 89 2.938 59 2.002 64 2.264 69 0.132 30 1.00969 2.21478 0.442 29 3.062 88
constants in eq 12 n B m 4.341 68 13.26881 0.732 07 3.032 25 5.229 66 -0.069 12 3.270 74 5.872 08 0.498 09 3.38968 2.211 20 2.029 52 4.999 26 65.607 32 2.088 44 4.723 26 13.799 31 1.400 47 3.534 10 10.224 98 -0.066 45 5.863 22 38.489 62 2.847 62 1.567 68 3.727 77 -1.188 13
1.046 56 1.030 54 1.072 36 1.057 50 1.074 90 1.060 53 1.061 13 1.048 54 1.09706
data pts 10 24 23 5 8 10 6 7 27
1.591 91 5.818 56 2.19949
4.072 10 3.242 99 4.137 13
1.29468 0.606 19 2.335 81
1.030 82 1.007 96 1.047 98
33 16 7
19.39 Vargaftik (1975) 3.10 Phillips and Murphy (1970) 9.10 Byers and Williams (1987)
1.121 02 2.912 75 3.100 39 1.924 39 7.20802 1.55192 3.59808 3.101 78 1.932 44
4.531 47 19.080 67 1.502 86 3.476 61 7.047 78 0.621 44 3.61806 2.249 19 1.63094 3.670 90 2.087 28 2.082 08 0.211 13 4.276 81 -8.11822 3.442 21 4.761 93 1.12509 2.550 17 5.509 65 -0.059 46 3.772 02 7.464 03 0.600 83 5.581 72 23.28830 2.12048
1.07981 1.052 76 1.014 98 1.05602 1.035 47 1.084 43 1.05205 1.039 19 1.035 98
41 4 3 5 7 5 6 5 9
7.80 2.32 1.65 0.97 3.53 1.93 1.73 0.75 10.05
Stairs (1980) Shah et al. (1969) Shah et al. (1969) Shah et al. (1969) Shah et al. (1969) Shah et al. (1969) Shah et al. (1969) Shah et al. (1969) Vertesi (1980)
1.206 27 1.127 29 1.072 29 1.06379 1.04947 1.05841 1.037 02 1.05338 1.056 92 1.037 37 1.13195 1.084 04 1.062 24 1.058 43 1.05875 1.084 71
57 12 10 43 20 13 4 3 14 5 14 8 4 7 42 8
1.39 12.71 2.50 8.74 9.25 3.24 0.96 0.80 8.54 2.38 2.09 3.45 0.78 3.10 7.10 1.69
Ulybin and Makarushkin (1976) Zerda et al. (1981) Ward (1969) Parkhurst and Jonas (1975) Vargaftik (1975) Weast (1979) Riggio et al. (1984) Weast (1979) Vargaftik (1975) Stephan and Lukas (1979) Vargaftik (1975) Vargaftik (1975) Weast (1979) Weast (1979) Munie and Jonas (1979) Byers and Williams (1987)
ff
trichlorofluoromethane chlorodifluoroethane trichlorotrifluoroethane ethyl bromide fluorobenzene chlorobenzene bromobenzene iodobenzene perfluorocyclobutane alcohols methanol ethanol phenol amines methylamine n-propylamine isopropylamine n-butylamine isobutylamine di-methylamine di-n-propylamine tri-n-ethylamine aniline miscellaneous carbon dioxide sulfur hexafluoride boron trichloride tetramethylsilane diethyl ether acetone methyl isobutyl ketone methyl acetate ethyl acetate n-propyl acetate ammonia acetic acid propionic acid n-butyric acid pyridine picoline
0.737 43 2.568 21 0.47551 3.525 20 1.679 99 3.393 90 1.810 48 3.832 46 1.478 63 4.957 80 1.467 15 4.438 84 7.210 56 3.21663 4.185 31 3.367 30 2.62306 4.819 27 2.34682 3.67366 0.567 80 3.673 52 0.596 93 4.74559 1.95700 3.765 00 2.634 77 3.198 93 0.538 63 5.22692 1.508 71 3.528 90
1.302 25 4.922 47 6.498 28
2.971 94 21.985 57 6.626 36 6.667 40 17.757 06 12.316 14 14.83076 11.37928 15.862 41 1.937 75 6.755 82 27.81845 10.537 53 7.468 50 17.417 28 7.835 36
1.00053 0.514 22 0.294 36 0.72681 0.363 61 0.996 84 -0.945 78 -0.053 61 1.274 29 1.94356 1.140 36 1.743 69 -0.024 40 -0.031 73 1.733 54 0.674 76
The linear dependence of ust upon b given in Figure 1can be expressed as follows: ust = 1.2b (18) In the absence of measurements for solid molar volume at the triple point, eq 18 can be used for a first-order approximation. However, it is more desirable to obtain the actual experimental uSt values measured with high accuracy. The values oft can be also derived directly from the generalized viscosity correlation developed in this study. In order to treat viscosity in a generalized manner, the density-temperature variable, x , has been related to 6, through a dependence similar to x , to define the preliminary comprehensive variable, g = X/(P€)flX' (19) where p , 0,and c are the universal constants that can be applied to all types of fluids irrespective of molecular structure details. Therefore, excess viscosity can be represented by two thermodynamic variables, temperature and density, normalized with the triple-point constants and a characteristic parameter, 6, specific to each substance through a general expression of ( M - P*)Y = F[glx(w,d; 41 (20) Using the functional relationship depicted by eq 12, but instead involving the global variable, g, the dimensionless excess viscosity becomes ( p - p * ) y X lo5 = exp(Ag' + Bg")- 1 (21)
t
~
AAD 2.76 10.73 1.08 1.79 3.50 5.28 5.07 9.58 4.82
lit. sources Vargaftik (1975) Vargaftik (1975) Vargaftik (1975) Weast (1979) Ertl and Dullien (1973) Ertl and Dullien (1973) Ertl and Dullien (1973) Ertl and Dullien (1973) Finney et al. (1977)
A nonlinear regression analysis for the establishment of the seven constants, p , 0,and c of eq 19 and A , B, r , and s of eq 21, with the experimental viscosity measurements for 101 substances produced the following values: A = 2.9328, B = 4.5424, r = 8.3264, s = 0.9228, p = 0.976, p = 2.3566, and c = -0.6673. The t value was determined by minimizing the average absolute percent deviation (AAD%) defined by N
AAD% = ( l O O / N ) ~ l ( v ~ d-c dp , e x p t l ) / ~ y p t l l (22) i=l
The results for 101 substances are presented in Table 11. Viscosity values calculated with eq 21 have been compared with corresponding experimental measurements for each of the 101 substances included in this study to yield an overall average absolute deviation of 4.03% (2515 points).
General Remarks The generalized viscosity model developed in this work can be applied over the entire fluid region from the dilute gas to the highly compressed liquid. The volume expansion factor, defined as the ratio of liquid molar volume to solid molar volume a t the triple point, was found to be a kay parameter for predicting the generalized viscosity behavior. It should be noted that the global variable, g, used in the present model only requires the triple-point constants of the pure components. Extensive comparisons with experimental viscosity data for 101 substances, including highly branched alkanes, alkenes, naphthenes,
2384 Ind. Eng. Chem. Res., Vol. 27, No. 12, 1988
aromatics, and polar and hydrogen-bonding compounds show an overall absolute average deviation of 4.03% (2515 points). Nomenclature M = molecular weight P = pressure, atm P, = critical pressure, atm T = temperature, K T, = critical temperature, K TR = reduced temperature, TIT, Tt = triple-point temperature, K u = molar volume, cm3/mol u, = critical volume, cm3/mol ult = liquid molar volume at triple point, cm3/mol uo = close packing molar volume of molecules, cm3/mol uSt = solid molar volume at triple point, cm3/mol x = density-temperature variable, o/7°~070*"9, eq 11 2, = critical compressibility factor Greek Letters y =
viscosity parameter, u1,2I3/Mll2T,lI2
= volume expansion factor at triple point, ult/uSt p = viscosity, P F* = viscosity of dilute gas, P E = viscosity parameter, T,'Ie/M 1/2P:/3 p = density, g/cm3 p c = critical density, g/cm3 p~ = reduced density, p / p c plt = liquid density at the triple point, g/cm3 7 = normalized temperature, TIT, w = normalized density, p / p a o = acentric factor, eq 9 t
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Hedley, W. M.; Mines, M. V.; Yanko, W. H. J . Chem. Eng. Data 1970, 15, 122-127. Hellemans, J.; Zink, H.; Van Paemel, 0. Physica 1970,47A, 45-57. Herreman, W.; Grevendonk, W. Cryogenics 1974, 14, 395-398. Hildebrand, J. H. Science (Washington,D.C.) 1971, 174,490-493. Jonas, J.; Hasha, D.; Huang, S. G. J . Chem. Phys. 1980, 84, 109. Lee, L. L. S. Ph.D. Dissertation, Northwestern University, Evanston, IL, 1971. Lee, A. L.; Ellington, R. T. J. Chem. Eng. Data 1965,10, 101-104. Lee, H.; Thodos, G. Znd. Eng. Chem. Res. 1988,27, 992-997. McCool, M. A.; Woolf, L. A. J . Chem. SOC.,Faraday Trans. 1 1972, 68, 1971-1981. Munie, M. F. G.; Jonas, J. J . Chem. Phys. 1979, 70, 1260-1265. Parkhurst, H. J., Jr.; Jonas, J. J. Chem. Phys. 1975,63,2705-2709. Phillips, T. W.; Murphy, K. P. J. Chem. Eng. Data 1970, 12, 304-307. Przezdziecki, J. W.; Sridhar, T. AZChE J . 1985,31, 333-335. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed. McGraw-Hill: New York, 1987. Riggio, R.; Martinez, H. E.; Espindola, J. A.; Ramas, J. F. J. Chem. Eng. Data 1984, 29, 11-13. Shah, J. K.; DeWitt, K. J.; Stoops, C. E. J. Chem. Eng. Data 1969, 14, 333-335. Slyusar, V. P.; Rudenko, N. S.; Tretyakov, V. M. Ukr. Fiz. Zh. 1973, 18, 190-194. Stairs, R. A. J . Chem. Eng. Data 1980,25, 379-381. Stephan, K.; Lukas, K. Viscosity of Dense Fluids; Plenum: New York, 1979. Stiel, L. I.; Thodos, G. AZChE J . 1961, 7, 611-615. Stiel, L. I.; Thodos, G. AZChE J. 1962,8, 229-232. Trappenieru, N. J.; Botzen, A.; van den Berg, H. R.; van Oosten, J. Physica 1964, 30, 985-996. Trappeniers, N. J.; van der Gulik, P. S.; van den Hooff, H. Chem. Phys. Lett. 1980, 70, 438-443. Ulybin, S. A.; Makarushkin, V. I. Teploenergetika 1976, 6 , 65-69. Ulybin, S. A.; Makarushkin, V. I. High Temp. (Eng. Transl.) 1977, 15, 430-434. Ulybin, S. A.; Makarushkin, V. I.; Skorodumov, S. V. High Temp. (Eng. Transl.) 1978,16, 233-238. Vargaftik, N. B. Tables on the Thermophysical Properties of Liquids and Gases, 2nd ed.; Wiley: New York, 1975. Vermesse, J. Ann. Phys. 1969, 4, 245-252. Vermesse, J.; Vidal, D. C. R. Hebd. Seances Acad. Sci., Ser. B 1973, 277, 273-276. Vermesse, J.; Vidal, D. C. R. Hebd. Seances Acad. Sci., Ser. B 1975, 280, 749-751. Vertesi, E. J . Chem. Eng. Data 1980, 25, 387-388. Ward, T. J. J . Chem. Eng. Data 1969, 14, 167-168. Weast, R. C. CRC Handbook of Chemistry and Physics; CRC: Boca Raton, FL, 1979. Zerda, T. W.; Schroeder, J.; Jonas, J. J. Chem. Phys. 1981, 75, 1612-1622.
Receiued for review March 1, 1988 Revised manuscript received J u n e 13, 1988 Accepted August 4, 1988
