Viscosities available in the literature for the gaseous and liquid states of eleven substances have been correlated with reduced density by the use of dimensional analysis and the Abas-rade expression for the residual viscosity to produce a single generalized relationship which is presented both graphically and analytically. The substances are argon, nitrogen, oxygen, carbon dioxide, sulfur dioxide, methane, ethane, propane, i-butane, n-butane, and n-pentane. The properties required for the calculation of viscosity with this relationship are the molecular weight, the critical constants, and the density of the substance a t the temperature and pressure considered.Separate relationships were developed for hydrogen, ammonia, and water which do not follow the consistent behavior of the other substances. Viscosity values for ethylene calculated with the generalized relationship compared favorably with the corresponding experimental values.In 1944 Uyehara and Watson developed a generalized correlation for the prediction of the viscosity of a pure substance at any temperature and pressure ( 7 9 ) . Although this correlation has proved to be of extreme utility for industrial calculations, current demands for highly accurate viscosity values in such areas as heat transfer and reactor design necessitate the development of a more exacting method for obtaining viscosities of both gases and liquids.Recent studies on the prediction of the transport properties of pure substances have been primarily concerned with the viscosity and thermal conductivity of gases at normal pressures (47, 74, 7 5 ) . Using a dimensional analysis approach and viscosity data reported in the literature for fifty-two nonpolar and fifty-three polar gases, Stiel and Thodos (74, 7 5 ) have developed relationships which can easily be applied for the prediction of the viscosity of any pure gas at moderate pressures (0.1 to 5 atm.). For nonpolar gases the following relationships resulted: (2), (3), and (4) for all the substances investigated were found to compare favorably with the corresponding experimental values. Therefore it would be desirable to utilize a similar approach to develop relationships for the prediction of the viscosity of pure substances at high pressures in both the gaseous and liquid states.In 1952 Abas-zade (1) proposed that the following relationship exists between the residual thermal conductivity of a liquid and its corresponding density:Thodos and co-workers (23, 33, 50, 66, 68) have studied the transport properties of several individual substances over a complete range of temperatures and pressures and have found that Equation (5) and a similar expression for the residual viscosity

In 1949 Gamson (13) produced a reduced state correlation from available thermal conductivity data in which the reduced thermal conductivity, k/kc, is plotted against reduced temperature and pressure. Experimental data, which were subsequently obtained, were found to deviate considerably from values resulting from Gamson's correlation ( 4 5 ) . Comings and Nathan (9) combined the Enskog relationships for viscosity and thermal conductivity to obtain an expression for the ratio, k/k", in terms of the viscosity ratio, p /~" , and the quantity, y. In the resulting relationship, the effects of the internal degrees of freedom of the molecules are neglected. Values of y were obtained from experimental P-V-T data as suggested by Enskog (lo), and experimental and calculated viscosities were used to develop a correlation between k/k* and reduced temperature and pressure. Lenoir and Comings (29) found that their experimental thermal conductivities for argon, nitrogen, methane, ethylene, and carbon dioxide were in good agreement with those resulting from the correlation of Comings and Nathan. Lenoir, Junk, and Comings (30) used their experimental values for nitrogen, methane, and argon, and the values obtained previously by Lenoir and Comings to develop a new correlation for k/k* which is very similar to that of Comings and Nathan, except that it predicts higher values for conditions in the vicinity of the critical point. Thermal-conductivity values determined by Lenoir, Junk, and Comings for ethane were found to be inconsistent with corresponding values resulting from their correlation, as were the subsequent values obtained by Leng and Comings (28) for propane and those of Kramer and Comings (27) for n-butane. Therefore, it would be desirable to develop an improved correlation for thermal conductivity which is also applicabIe to a wider range of substances.Jossi, Stiel, and Thodos (20) have obtained reliable expressions for the viscosity of pure substances in the dense gaseous and liquid phases by the use of a relationship between the residual viscosity, p -EL*, and density, along with a dimensional analysis approach. Thodos and coworkers (22, 38, 47, 48) have found that the residual thermal conductivity, k -k*, is a unique function of density for all the substances investigated. A theoretica1 basis for such a dependence has been provided by Predvoditelev (41). Therefore, in the present study an approach similar to that of Jossi, Stiel, and Thodos for viscosity has been utilized to develop a generalized correlation for the thermal conductivity of nonpolar substances by the use of the residual relationship for this property and dimensional analysis.Leonard I . Stiel is with Syracuse University, Syracuse, New York. DIMENSIONAL ANALYSISSeveral investigators have suggested that the thermal conductivity in the dense gaseous and liquid regions is dependent on Cp, the heat capacity (10, 12). If th' is variable is included in a dimensional analysis treatment of the residual relationship, the resulting expression would indicate th...

Experimental viscosity data available i n the literature for fifty-two nonpolar gases have been utilized i n conjunction with a dimensional analysis approach to relate the viscosity at atmospheric pressure to temperature. The substances investigated are both simple and complex and include the inert and diatomic gases, carbon dioxide, carbon disulfide, carbon tetrachloride, and the hydrocarbons up to n-nonane, including normal and isoparaffins, olefins, acetylenes, naphthenes, and aromatics. The dependence of the product p*( on reduced temperature was found to be the same for a l l of these substances, except helium and hydrogen.Both theoretical considerations and dimensional analysis indicate that the viscosity product of a gas might depend on the compressibility factor a t the critical point. However the results of this study show that for these nonpolar substances this viscosity product a t normal pressure is independent of zo and depends only on temperature.The only information required for the calculation of viscosity with the relationships developed in this study is the molecular weight, critical temperature, and critical pressure of the substance.Values calculated with these relationships have been compared with 785 experimental points from a l l reliable sources of experimental data and produced an average deviation of 1.77%. Comparisons have also been made with the Bromley-Wilke equations. * Use [ = 0.0396 for fluorine, E = 0.0115 for bromine, and E = 0.00905 for iodine. a Average deviation greater than 5%; critical constants and reliability of viscosity data uncertain.With these exponents Equation (6) becomes where z , = P, v , / R To. For convenience the group T,1/'/kP P,'/" will be referred to in this study as 6. This each substance and is the same group suggested by Kamerlingh Onnes (30) and later utilized by Licht and Stechert (37). However, contrary to their con-= pzam T," ( 7 ) group is a characteristic constant for clusions, dimensional analysis indicates that ,L* is a function not only of T,

A method has been developed for the calculation of the viscosity of nonpolar gas mixtures a t moderate and elevated pressures from the molecular weights and critical constants of the components. By the use of available experimental data and appropriate pseudocritical constant rules, results obtained previously for the viscosity of pure gases have been extended to mixtures.Viscosity values calculated by the method developed in this study for a number of nonpolar gas mixtures were found to reproduce reported values with a high degree of accuracy.Reliable methods have recently been developed for the prediction of the viscosity of pure substances in the dilute and dense gaseous regions. Similar generalized relationships are not available at present for the calculation of the viscosity of gas mixtures at elevated pressures. Accurate values of this property for gaseous mixtures are required in many important applications. It is apparent that reliance on experimental data for the viscosity values of gaseous mixtures is hopelessly inadequate, because of the wide ranges of composition, temperature, and pressure encountered.Rigorous theoretical expressions are available only for the transport properties of gaseous mixtures at approximately atmospheric pressure. Lee, Starling, Dolan, and Ellington (51 ) have recently presented a semiempirical relationship for the calculation of the viscosity of binary mixtures of methane, ethane, propane, and n-butane. The only generalized methods that have been suggested for the calculation of the viscosity of dense gaseous mixtures are modifications of correlations for pure components in which the group p/p* (or p / p , -) is empirically related to TR and P, through ,the available experimental data (18, 8 7 ) . The critical temperatures and pressures of the mixtures are calculated from the critical constants of the pure components by the use of the linear combination rules proposed by Kay (43). However, it is well established that reduced state correlations of this type are specific only to individual substances or substances having a similar nature, and that a generalized correlation must contain an additional parameter (such as the critical compressibility factor of the substance) to account for the size and shape of the molecules ( 7 ) .For pure substances, Jossi, Stiel, and Thodos ( 4 2 ) have developed analytical relationships between the residual viscosity group, ( p -p*)(, and the reduced density of the substance from experimental data for twelve substances (including monatomic and diatomic gases, hydrocarbons, and carbon dioxide). This method for the prediction of the viscosity of pure substances does not possess the limitations of the previous correlations for the reduced viscosity which contain an insufficient number of parameters to be applicable to a wide range of substances. In addition, analytical expressions are much more suitable for computer calculations than graphical correlations. which require the storage of a large number of values and tedious interpolation calculatio...

SynopsisThe solubility of gases and volatile liquids in lowdensity polyethylene (LDPE) and polyisobutylene (PIB) at elevated temperatures has been correlated, using the experimental data available in the literature. In the present study, a Henry's constant K, at a total pressure of approximately 1 atm defined as P, = KpV, where P I is the partial pressure of the solute in the vapor phase and is the solubility (cm3 solutelg polymer at 273.2 K and 1 atm), is correlated for nonpolar solutes with the following expressions: (1) For LDPE, ln(l/K,) = -1.561 + (2.057 + 1.4380) (TJn2; (2) For PIB, ln(l/KJ = -1.347 + (1.790 + 1.5680) (TJ W , in which o is the acentric factor and T, the critical temperature of the solute. In obtaining the above correlations we have used 27 solutes covering 115 data points for LDPE, and 18 solutes covering 148 data points for PIB. We have calculated values of l/Kp from the literature data reported in terms of the retention volume (c), weight-fraction Henry's constant (HI), activity coefficient at infinite dilution (at), Flory-Huggins interaction parameter (x), or V / P obtained from high pressure sorption experiments. The correlations obtained in this study permit one to estimate with reasonable accuracy the solubility of gases and volatile liquids in either LDPE or PIB, with information on the acentric factor (01 and critical temperature (T,) only. The relationship for LDPE is also applicable for solubilities in highdensity polyethylene. Relationships for the heat of vaporization of solutes from infinitely dilute LDPE or PIB solutions are also derived from the temperature variation of l/Kp,