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Chemical Engineering Fundamentals Review
MoIecuIar Transport Properties of Fluids by Ernest F. Johnson, Princeton University, Princeton, N. J.
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Both experimental and theoretical studies have extended the ranges
of temperature and pressure over which fluid properties are known
THIS
review is concerned with the important publications on the viscosity and thermal conductivity of homogeneous, Newtonian fluids which have appeared from October 1958 through most of 1959. Of particular interest are experimental methods and theoretical or empirical methods of estimating properties. I n contrast with past years a considerable effort has been expended in studies of the effects of pressure on viscosity.
ing-disk viscometers, Coremans was able to get reliable results for gaseous helium, neon, hydrogen, and deuterium in the temperature range 20° to 80' K. (72) and also for hydrogen deuteride (73). H e compared his results with theoretical predictions based on a quantum mechanical modification of the law of corresponding states and with results based on different models for intermolecular potentials. New data on the gas phase viscosity
of nitrogen, nitric oxide, boron trifluoride, silicon tetrafluoride, and sulfur hexafluoride a t temperatures as high as 1000° C. were presented (76). Kestin and Wang (34) showed that their empirical correlation for lowdensity viscosity with temperature is satisfactory for carbon dioxide at temperatures u p to the critical but breaks down for nitrogen a t high density and low temperature. A new calculation for the relation of viscosity to various
Viscosity
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An improved capillary type viscometer having an absolute accuracy of ~ t 0 . 3 7was ~ applied by Eakin and Ellington (75) to the study of ethane a n d propane at room temperature and pressures u p to 9000 p.s.i.a. Their results, which were somewhat higher than those reported in the literature, confirmed the linearity of viscosity with pressure a t high pressures for these compounds. Lazarre and Vodar (39) used a borosilicate glass capillary in a bomb to measure the viscosity of nitrogen il% at 25O, 50°, and 75O C. a t pressures u p to 3000 atm. The level of the driving fluid was positioned by an electromagnetically operated plunger. I n the viscometer of Pavlovich and Timrot (52) the driving fluid lies in a semicircular tube mounted on a knife edge. A turning moment is applied to the tube and the turning rate becomes the basic measure. This method was used to determine the viscosity of methane a t - 1 6 1 . 4 O to 50' C. and 20 to 200 kg. per sq. cm. A steady-flow coiled capillary viscometer was constructed (61)and used for nitrogen and carbon dioxide a t 25' C. and pressures up to 270 and 48 atm., respectively. By making corrections usually omitted with oscillat-
116 C O I L S )
PIEZOMETER RING PRESSURE T A P 9
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TRANSFORMERS BUBBLE BOTTLE
CONDENSATE COLLECTOR
1 Viscometer for npnreacting gases, vapors, and mixtures consisted of capillary electric furnace, gas flowmeter, pressure-stabilizingsystem, and manometer (6 7 ) VOL. 52,
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special intermolecular potentials was described by Le Fevre (40) who gave equations for the case at very high temperatures, where most internal collisions occur with a large relative kinetic energy, and for the converse case a t very low temperatures. For inert gases the effect of pressure on viscosity is not significant between about 1 mm. of mercury and 1 atm., but below 0.01 mm. of mercury viscosity decreases rapidly. The reducedstate correlation of Shimotake and Thodos (63) accommodates this behavior and also applies satisfactorily to diatomic gases, but not to polyatomic gases. An equation for the viscous drag on a thick disk in an oscillation-type of viscometer: derived by Azpeitia and Newell (5), shows that this kind of device can be used for precise absolute measurement of viscosity. A new equation for the temperature and pressure dependence of the viscosity of gases and liquids w a s given by Brablc (7). This equation includes the relations of Maxwell, .4ndrade, and Sutherland and is as accurate over wide ranges of temperature and pressure as an equation of state. Another viscometer was described (8) for organic liquids a t high temperatures (up to 400' C.). The glass capillary is sealed against oxygen. In a study of undercooled liquid alkyl halides over temperature ranges such that the viscosity changes by six orders of magnitude, Denney (74) found that the temperature dependence was similar to that of the dielectric relaxation time. The viscosity of highly purified aluminum was measured (23) at 690' to 950" C. using two vibrating cylinders. The data fit Arrhenius' equation. A rotational viscometer which uses a reference liquid was described by Hills (28). I t covers a thousandfold range in viscosity accurate to =t0.5yowith results in a form which lends itself to digital readout. Khalilov (35)described a closed system of capillaries for measuring liquid viscosities near the freezing point down to temperatures as low as -150" C. 4 cylindrical falling body viscometer was used by Swift, Christy, and Kurata (69) to measure the viscosity of liquid methane and propane at temperatures from -150" C. to the critical and -185' to 90" C., respectively, with maximum errors of =t8 and
another study of the effect of pressure Griest, Webb, and Schiessler (25), using a rolling ball viscometer, measured the viscosity of seven hydrocarbons having 25 to 26 carbon atoms and three binary mixtures of them at pressures to 3450 bars and 37.8' to 135' C. They showed that viscosity is an additive function of the constituent groups whether these groups are combined in the same or different molecules as long as the molecular symmetry is unchanged. Zolotykh (76) found from measurements on a variety of oils and viscous liquids with a dropping ball viscometer at pressures up to 5000 kg. per sq. cm. that the expression q = ~0 exp. P was representative It 6 to 15y0. A concentric-cylinder viscometer capable of accommodating pressures up to 25,000 p.s.i. and 500' F. was shown by Reamer, Cokelet, and Sage (57) to be precise *0.3yc for gaseous helium at room conditions. They obtained new data for n-pentane up to 5000 atm. and 100' to 280" F. I n a study of the viscosity and surface tension of some liquid halogen fluorides Rogers and Garver (60) found that Arrhenius' equation gives a good fit. Their data revealed association in some of the compounds. Rao and Subra-
1 , / /;
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2
&5%. The effect of pressures up to 2000 atm. on the viscosity of high molecular weight liquids was studied by Kuss (37). H e found that the frequency factor in the Arrhenius equation was independent of pressure, whereas the activation energy was dependent on both temperature and pressure. I n
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New viscosity data for n-pentane were obtained with this special viscometer
(57) 7 . Inner cylinder. 2. Cylindrical sleeve. 3,4. Platinum-tungsten wire supports for inner cylinder. 5,6. Fixed ruppo ris fcr 3,4
INDUSTRIAL AND ENGINEERING CHEMISTRY
manian (56) calculated from dimensional analysis the effect of surface tension on the measurement of viscosity for water and benzene at 32" and 38' C. Papougek (50) presentcd an approximate relation between fluidity and the potential energy of the intermolecular interaction related to the free fluidity volume in nonassociated liquids. H e related empirically this potential energy, as well as the compressibility and surface tension, to the available volume of the liquid. A three-constant empirical equation for the viscosity of solutions of nonelectrolytes was presented by Fried, Hala, and Pick (79). A theoretical treatment for strong electrolytes was given by Falkenhagen (77). O n the basis of extensive data in the literature, Winning (75) derived a simple, reliable expression for the temperature dependency of the viscosity of various families of hydrocarbons. For the pressure depcndency of the viscosity of hydrocarbons and also of alcohols and halogenated hydrocarbons hlamedov (44) recommended a second degree polynonial for temperatures u p to 0.85 T , and pressures up to 4000 arm. A modified Ubbelohde viscometer which is especially suited for solutions 'at high temperatures was described by Akhmedov and Pogorel'ski? ( 7 ) . Golik and Klassen (24) found that the activation energy for viscous flow for zinc and cadmium amalgams in the range 20' to 300" C. is linear in concentration. The interpolation formula of Gromakov was shown by him and Cherkasov (26) to be applicable to ternary and quaternary nonreciprocal systems involving water and alcohols despite differences in pure component viscosities by a factor of 2600. A new- ideal mixture law for viscosity was presented by Ishikawa (37) who used it to determine the degrees of association for a wide variety of organic compounds. Precise data for sodium perchlorate solutions at 25" C. were interpreted by ATightingale (48) on the basis of the local disruption of water structure by the small hydrated perchlorate ion. A simple, one-constant empirical equation for the temperature dependency of lubricating oils was suggested by Qurashi (55). C n the basis of studies of 10 binary systems of various halogenated organic compounds Reed and Taylor (58) divided all mixtures into three classes according to the temperature dependence of the temperature coefficient of viscosity. For all the solutions they studied the enthalpy of activation was independent of temperature. Slovinskaya and Mukimov (64)presented extensive tables and graphs for the viscosity and also the solubility and density of saturated aqueous solutions
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of potassium and sodium iodide and chloride and their ternary and reciprocal quaternary mixtures, 0' to 75' C. Maxima in viscosity occurred a t the eutonic point. Suryanarayana and Venkatesan (67) found that Andrade's equation for nonassociated liquids is applicable to the description of the temperature dependency of highly concentrated aqueous solutions of strong electrolytes. For gaseous mixtures of low molecular weight hydrocarbons at high pressures (450 to 600 atm.) Meshcheryakov and Golubev (46) found that the single two-constant equation of Golubev and Petrov fits the data. They used a capillary-type viscometer which gave results differing by as much as 20% from results obtained with rolling ball viscometers. An oscillating disk was used by Rietveld, van Itterbeck, and Velds (59) to measure the viscosity of binary mixtures of hydrogen isotopes, helium, and neon, 14' to 293' K. Viscosities were also calculated from the LennardJones potential. Equations for the viscosity of gas mixtures in terms of the pure component viscosities were given by Francis (78). The fit to experimental data was i 2 7 0 for nonpolar systems, and for systems of not more than one polar component the accuracy was reasonable. Critical reviews of the current best methods for estimating the viscosity of gases (20) and liquids (27) were given in a series of articles by Gambill. The effects of temperature and pressure were considered for both pure components and mixtures. A new mechanism for the bulk viscosity of liquids derived from the hole theory of liquids and rate process theory was shown by Hirai and Eyring (29) to explain the temperature and pressure dependencies of acoustic absorption for associated liquids and viscous nonassociated liquids.
Thermal Conductivity 1p
A simple, horizontal, cylindrical cell for measuring the thermal conductivity of gases to 3000 atm. and 400' F. was described by Comings, Lee, and Kramer ( 7 7). Another coaxial, cylindrical cell, in which internal heating and insulation between bomb and cell permitted maintaining the bomb exterior at room temperature, was used by Johannin (32) to measure nitrogen to 1600 atm. and 700" C. With a specially designed cell to control convection Guildner (27) found that the thermal conductivity of czrbon dioxide at the critical temperature and critical density is very high if not infinite. In a study of binary mixtures of water with nitrogen and carbon dioxide using
Chemical Engineering Fundamentals Review
a hot wire apparatus, Kulakov (36) found that the thermal conductivity was much higher than additive because of the dipoles in the water molecules. Srivastava and Srivastava (65) determined the thermal conductivity and Eucken 'correction factor for a variety of diatomic gases and gas mixtures by means of a thick wire cell a t 38' C. These values were compared with values calculated from the Lennard-Jones 12:6 model and also with Hirschfelder's expression for polyatomic gas mixtures, which was found to be substantially correct. New equipment which uses a thin filament of mercury as both heater and resistance thermometer was described by Vargaftik (70). From data obtained on fused salts and aqueous solutions of acids, alkalies, and salts he developed a temperature relation for thermal conductivity valid within 3% for nonassociated liquids and within 570 for associated liquids. A concentric cylinder technique was used by Lawson, Lowell, and Jain (38) to measure the thermal conductivity of water to 800 kg. per sq. cm. and 30' to 140' C. Their results are discussed in terms of Hall's two-fluid model of water. Sutherland, Davis, and Seyer (68) found from studies of the thermal conductivity of solid and liquid octadecane between copper plates that molecular orientation effects extend out as much as 0.35 cm. into the liquid. New data on the thermal conductivity of liquid ozone from -128' to -196" C. were presented by Waterman, Kirsh, and Brabets (73). Powell and Tye (53) used a longitudinal heat flow set-up to determine the thermal conductivity of electrically conductive molten metals, specifically lead, bismuth, and their eutectic mixture, from the respective melting points up to 500' to GOO' C. The theoretical Lorenz function predicts their findings within about 8%. A chart of reduced thermal conductivity for methane with average deviations of 2.2% from 117 experimental points was prepared by Owens and Thodos (49) based on the unique relation between density and residual conductivity. Equations relating thermal conductivity and specific gravity for methane and natural gas were presented by Pavlovich (57). Schaefer and Thodos (62) derived a correlation for the reduced thermal conductivity of both liquid and gaseous states for diatomic gases which is valid to better than 3.2%. Their empirical relation for the critical thermal conductivity for use in the correlation was estimated to be valid within 3.4%. Losenick9 (43) used known experimental data to derive
equations for isotherms giving the dependence of thermal conductivity for both gases and liquids on pressure and temperature. I n a review of the advances made in methods of calculating directly the thermal conductivity of gases, Vines (77) showed that Keyes' correlation equation is satisfactory for mono- and diatomic gases u p to possibly 2000' C., but not for complex gases. Waelbroeck (72) gave a theoretical discussion of the thermal conductivity of imperfect gases from a consideration of the limiting cases where intermolecular forces are negligible and where they predominate, namely, at high and low temperatures, respectively. An approximate formula for the thermal conductivity of gas mixtures was derived by Mason and Saxena (45) from kinetic theory via reasonable approximations. The resulting expression requires only pure component conductivity, molecular weight, and either the viscosity or the specific heat of the pure components at the temperature of interest; it is applicable to ternary mixtures of polyatomic nonpolar compounds as well as to simpler systems. Muckenfuss and Curtiss (47) derived a complete second approximation to the thermaI conductivity of multicomponent gas mixtures which is identical with the approximation formula derived on the assumption of negligible thermal diffusion coefficients. From statistical mechanics and the thermodynamics of irreversible processes Bearman (6) derived an expression relating the thermal conductivity of binary liquid solutions to the pure component conductivities and self-diffusion coefficients, the composition, and the component molecular volumes. The agreement with experiment was semiquantitative. Methods for estimating the thermal conductivities of fused salts were summarized by Gambill (22). The notion of an equivalent thermal conductance analogous to the equivalent electrical conductance was introduced by Kapustinskii and Ruzavin (33) for treating ionic solutions. X o inherent relation was found between the two quantities. A generalization of the Eucken approximation for the thermal conductivity of polyatomic or chemically reacting gas mixtures was presented by Hirschfelder (30), along with details of the derivation and results calculated for mixtures of hydrogen and carbon dioxide at 0' C. and atmospheric pressure. Prigogine and Waelbroeck (54, in a discussion of thermal conductivity and chemical reactions in gases, presented plots of the conductivity of helium and argon as functions of pressure. VOL. 52, NO. 5
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General
A comprehensive review up through most of 1958 appeared in a survey of recent work on the viscosity, thermal conductivity, and self diffusion coefficients of gases and gas mixtures by Liley (47). A detailed calculation and compilation of the thermodynamic and transport properties of heavy water by Whalley (74)includes data on viscosity and thermal conductivity. Arajs and Legvold (4) discussed the limitations of the Senftleben method of estimating the thermal conductivity, viscosity, and specific heat capacity of gases. A report by Amdur and Ross ( 3 ) showed that intermolecular force potentials extrapolated from low temperatures cannot be used to calculate transport coefficients and second virial coefficients for gases at high temperatures. A better practice is to use potentials based on the elastic scattering of high energy molecular beams. This latter practice was used by Amdur and Mason ( 2 ) to calculate the coefficients for rare gases and nitrogen at 1000° to 15,000° K. Cheung ( 9 ) devised an improved empirical correlation derived from the kinetic theory of gases relating thermal conductivity and viscosity to the selfdiffusion coefficient. This correlation applies to polar and polar-nonpolar mixtures. A simplified kinetic theory for spherical molecules interacting according to a square wave potential was derived by Longuet-Higgins and Valleau (42). Their theory predicts that thermal conductivity, (shear) viscosity v, and bulk viscosity K should be in the ratio k / 2 : m / 5 : m / 3 , where k is the Boltzmann constant and m is the molecular mass. Viscosity, calculated for liquid argon from experimental values for self-diffusion coefficient, was in good agreement with experiment, but the observed ratio of K/q was much smaller than predicted. Collins and Raffel (70) treated the statistical mechanica1 theory of transport processes in liquids in terms of the instantaneous time derivatives of the stresses in a molecular scale nonequilibrium region of a system otherwise at equilibrium. Standart and Chihla (66) undertook a theoretical appraisal and application of Schrage’s theories of the transport properties of a onecomponent heterogeneous gas-liquid (or solid) system on the basis of the kinetic theory of ideal gases.
literature Cited
(1) Akhmedov, K. S., Pogorel’skiY, K. V., Doklady Akad. Nauk Uzbek. S.S.R. 1958, NO. 2. 35-7. (2) Am&, I., Mason, E. A., Phys. Fluids 1, 370-83 (1958).
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(3) Amdur, I., Ross, Jr., Combustion and Flame 2, 412-20 (1958). (4) Arajs, S., Legvold, S., J.Appl. Phys. 29, 1001 (1958). (5) Azpeitia, A. G., Newell, G. F., 2. angew. Math. u. Phys. 10, 15-34 (1959)
(in Enrlish). “
I
( 6 j Bearman, R. J., J. Chem. Phys. 29, 1278-86 (1958). (7) Brablc,’J., C;echoslou. J . Phys. 8, 450-6 (1958) (in German). (8) Burns, W. J., Morris, B., Wilkinson, R. W., J . Sci. Instr. 35, 291-3 (1958). (9) Cheung, H., U. S. Atomic Energy Comm. Rept. UCRL-8230 (1958). (10) Collins, F. C., Raffel, H., J. Chem. Phys. 29, 699-710 (1958). (11) Comings, E. W., Lee, W. B., Kramer,
F. R., Proc. Conf. Thermodynamic and Transport Properties Fluids, London, 1957, pp. 188-92 (1958). (12) Coremans, J. M. J., van Itterbeck, A., others, Physica 24, 557-76 (1958) (in English). (13) Ibzd., 1102-4 (1958). (14) Denney, D. J., J . Chem. Phys. 30,
159-62 (1959). (15) Eakin, B. E., Ellington, R T., J. Petrol Technol. 11, No. 4, 71 (1959). (16) Ellis. C. P.. Raw. C. J. G.. J. Chem. ‘ Phys. 30, 574-6 (1959). (17) Falkenhagen, H., Proc. Intern. Sym-
posium Transport Processes Statist. Mech. Brussels, 1956, pp. 251-60 (1958). (18) Francis, W. E., Trans. Faraday SOC. 54, 1492-7 (1958). (19) Fried, V., Hala, E., Pick, J., Chem. lis9 52, 1007-10 (1958). (20) Gambill, W. R., Chem. Eng. 65, No. 19, 169-72; NO. 21, 157-62; NO. 23, 157-60 (1958). (21) Ibid., 66, No. 1, 127-30; No. 3, 123-6; NO. 5, 151-2 (1959). (22) Ibid., 66, NO. 16, 129-30 (1959). (23) Glazov, V. M., Ghistyakov, Yu. D., Izuest. Akad. Nauk S.S.S.R., Otdel. Tekh. Nauk 1958, No. 7, 141-3. (24) Golik, A. Z., Klassen, I. F., Ukrain. Fiz. Zhur. 3. 683-7 (1958). (25) Griest, E. M., Webb,’W., Schiessler, R. W., J . Chem. Phys. 29, 711-20 (1958). (26) Gromakov, S. D., Cherkasov, A. P., Zhur. Fit. Khim.32, 2473-8 (1958). (27) Guildner, L. A,, Proc. Natl. Acad. Sci. U.S. 44, 1149-53 (1958). (28) Hills, J. F., J . Sci. Znstr. 35, 415-18 (1958). (29) Hirai, N., Eyring, H., J . Appl. Phys. 29, 810-16 (1958). (30) Hirschfelder, J. O., Proc. Conf.
Thermodynamic and Transport Properties Fluids, London, 1957, pp. 133-41 (1958). (31) Ishikawa, T., Bull. Chem. SOC.Japan 31, 524-9 (1958). (32) Johannin, P., Proc. Conf. Thermo-
dynamic and Transport Properties Fluids, London 1957, pp. 193-4 (1958). (33) Kapustinski:, A. F., Ruzavin, I. I., Izvest. Vjmhykh Ucheb. ZavedeniY, Khim. i Khim. Tekhnol. 1958, No. 3, 21-6. (34) Kestin, J., Wang, H . E., Physica 24, 604-8 (1958) (in English). (35) Khalilov, Kh. M., Pribory i Tekh. Ekspt. 1958, NO. 4, 104-5. (36) Kulakov, I. A., Referat. Zhur. Khim. 1957, Abstr. No. 7477. (37) Kuss, E., Z. angew. Phys. 10, 566-75
(1958). (38) Lawson, A. W., Lowell, R., Jain, A. L., J . Chem. Phys. 30, 643-7 (1959). (39) Lazarre, F., Vodar, B , Proc. Conf.
Thermodynamic and Transport Properties Fluids, London, 1957, pp. 159-62 (1958). (40) Le Fevre, E. J., Zbid., pp. 124-7.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
(41) Liley, P. E., “Thermodynamic and Transport Properties of Gases, Liquids, and Solids,” pp. 40-69, Am. SOC. Mech. Engrs., New York, 1959. (42) Longuet-Higgins, H. C., Valleau, J. P., Mol. Phys. 1, 284-94(1958). (43) Losenick?, Z., Czechoslov. J . Phys. 9, 258-9 (1959) (in German). (44) Mamedov, A. M., Zzvest. Vysshikh Ucheb. ZavendeniY, N e f t i Gaz 1958, No. 2, 89-94. (45) Mason, E. A., Saxena, S. C., Phys. Fluids, 1, 361-9 (1958). (46) Meshcheryakov,N. V., Golubev, I. F., Referat. Zhur. Khim. 1958, Abstr. No. 3831. (47) Muckenfuss, C., Curtiss, C. F., J . Chem. Phys. 29, 1273-7 (1958). (48) Nightingale, E. R., J. Phys. Chem. 63, 742-3 (1959). (49) Owens, E. J., Thodos, G., Proc. Conf.
Thermodynamic and Transport Properties Fluids, London, 1957, pp. 163-8 (1958). (50) PapouSek, D., Chem. lis9 52, 901-8 (1958). (51) Pavlovich, N. V., Gazouaya Prom. 1959, NO. 5, 45-9. (52) Pavlovich, N. V., Timrot, D. I.., Teploenergetika 5 , No. 8, 61-5 (1958). (53) Powell, R. W., Tye, R. P., Proc. Conf. Thermodynamic and Transport Properties Fluids, London, 1957, pp. 182-7 (1958). (54) Prigogine, I., Waelbroeck, F., Zbid., pp. 128-32. (55) Qurashi, M. M., Pakistan J. Sci. Ind. Research 1, 116-28 (1958). (56) Rao, P. R., Subramanian, N., J . Sci. Ind. Research (India) 18B, 170-1 (1959). (57) Reamer, H. H , Cokelet, G., Sage, B. H., Anal. Chem. 31, 1422-8 (1959). (58) Reed, T. M., Ta lor, T. E., J. Phys. Chem. 63, 58-67 (19J9). (59) Rietveld. A. O., van Itterbeck, A., Velds, C. A,, Physica 25, 205-16 (1959) (in Enelishi. (60) Rogers, M. T., Garver, E. E., J. Phys. Chem. 62, 952-4 (1958). (61) Savino, J. M.. Sibbitt. W. L.. IND. . ENG.CHEM.51, 551-4 (1959). (62) Schaefer, C. A., Thodos, G., A.Z.Ch.E. Journal 5, 367-72 (1959). (63) Shimotake, H., Thodos, G., Ibid., 4, 257-62 (1 958). (64) S1ovinskaya;V. M., Mukimov, S. M., Uzbek. Khim. Zhur. 1959. No. 2. 12-19. (65) Srivastava, B. N., Srivastava, R. C., J.Chem. Phys. 30, 1200-5 (1959). (66) Standart, G., Chihla. Z., Chem. listy 52, 787-829 (1958). (67) Suryanarayana, C. V., Venkatasan, V. K., Trans. Faraday Soc. 54, 1709-11 (1958). (68) Sutherland, R. D., Davis, R. S., Seyer, W. F., IND.ENG.CHEM. 51, 585-8 (1959). (69) Swift, G. W., Christy, J. A,, Kurata, F.. A.I.Ch.E. Journal 5. 98-102 (1959). (70)‘Vargaftik, N. B., Prbc. Conf. Thermodynamic and Transport Properties Fluids, London, 1957, pp. 142-9 (1958). (71) Vines. R. G.. Ibid., pp. 120-3. (72) Waelbroeck,’ F. .G.; Proc. Intern. SvmDosium TransDort Processes Statist. Me&., Brussels, 1556, pp. 382-6 (1958). (73) Waterman, T. E., Kirsh, D. P., Brabets, R. I., J. Chem. Phys. 29, 905-8 (1958). (74) Whallev, E., Proc. Conf. Thermo. dynamic ‘ and ’ Transport Properties Fluids. London. 1957. DD. 15-26 (1958). (75) Winning, W: c., J..inst. Petroleum 45, NO. 421, 9-15 (1959). (76) Zolotykh, E. V., Referat. Zhur. Khim 1956, Abstr. No. 53849. U
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