Viscosity Virial Coefficient Research Articles

The Viscosity of Gaseous Isobutane and Its Initial Density Dependence1

Results of new relative high-precision measurements on gaseous isobutane are reported. Six series, each differing in density, were performed in a quartz oscillating-disk viscometer from 297 to 627 K and for densities between 0.010 to 0.048 mol·L−1. Isothermal values recalculated from the original experimental data were evaluated with a first-order expansion, in terms of density, for the viscosity. Reduced values of the second viscosity virial coefficient derived from the zero-density and initial-density viscosity coefficients agree with the representation of the Rainwater–Friend theory when using energy and length scaling factors specific for the interactions of the isobutane molecules. With the same scaling factors an individual correlation in the limit of zero density was developed including only a few values from the literature. The uncertainty of the zero-density viscosity correlation is estimated to be ±0.4%.

The Viscosity of Electrostatically Stabilized Dispersions of Spherical Colloid Particles

The viscosity virial coefficient characteristic of a moderately concentrated dispersion [and proportional to the Huggins coefficient] is calculated for electrostatically stabilized monodisperse suspensions of spherical colloid particles. The energy of interaction between two colloid particles is modeled as the sum of dispersion (van der Waals) and electric double-layer contributions. Comparisons of theoretical predictions and experimental data permit conclusions to be drawn about the adequacy of this model.

The Viscosity of Polymerically Stabilized Dispersions of Spherical Colloid Particles

A recently developed theory and computational procedure are used to generate theoretical estimates of the viscosity virial coefficient for polymerically stabilized monodisperse suspensions of spherical colloid particles. Numerical results are presented for representative values of the five parameters that characterize the interactions among the colloid particles.

Improved initial density dependence of the viscosity and a corresponding states function for high pressures

The initial density correction to gaseous viscosity using accurate realistic potentials of the noble gases is evaluated using the Rainwater–Friend theory. It is shown that this theory works satisfactorily for densities up to about 2 mol dm −3 . Due to the superimposability of the noble gas potential functions, a universal function of the reduced second viscosity virial coefficient is obtained over the entire reduced temperature range. At densities beyond the range of the theory, a variant of the excess viscosity is developed, by which the viscosity of the different gases can be easily calculated above the critical temperature for pressures up to 900 MPa. The accuracy of this method is within the experimental uncertainties.

The interaction of sodium alginate with univalent cations

The M/G ratio, dyad and triad frequencies in the sodium alginate chain, were determined from 13C-nmr spectra. The interactions of sodium alginate in solution with the univalent cations K+ ion and Na+ ion have been investigated by viscometry and membrane osmometry. The dependencies of intrinsic viscosity, Huggins constant, and second virial coefficient on ionic strength were observed, and the maximums in reduced viscosity were obtained in low KCl and NaCl concentrations, respectively. These show that the electroviscous effects play an important role in polyelectrolyte solution, and the effect of the Na+ ion on aqueous solution of sodium alginate is greater than the K+ ion. The experimental observations are interpreted in terms of ion-pair formation with carboxyl groups of mannuronate and isolated guluronate residues and cooperation “egg-box” binding between polyguluronate chain sequence. The difference of interaction between univalent cations and alginate chains in solution is attributed to the ability of their binding with the polyion, which depends on the properties of ions itself. © 1998 John Wiley & Sons, Inc. Biopoly 46: 395–402, 1998

The viscosity of a moderately dense, polydisperse suspension of spherical particles

A recently developed formalism for computing the low-frequency, Newtonian viscosity of moderately dense monodisperse suspensions is extended to include polydisperse suspensions. In the form presented here this general theory is applicable to spherical solute particles suspended in a Newtonian solvent. Explicit formulas are obtained for the viscosity virial coefficients associated with first and second order terms in powers of the solute volume fraction. It is proved that the second order term in the viscosity virial series for a polydisperse suspension of solute particles is fully characterized by a single, dimensionless function b 2( λ), with 0⩽ λ⩽1. Numerical values are presented for the second order (Huggins) coefficient specific to hard-sphere particles with general stick-slip solute–solvent boundary conditions and for “spherical surfactant particles” as well. Calculations are included also for suspensions with log-normal particle-size distributions.

Thermophysical properties of diluted F-containing heavy globular gases predicted by means of temperature dependent effective isotropic potential

The temperature dependencies ( T = 200 ÷ 850 K, P ≤ 0.1 MPa) of viscosity (η) and second virial coefficient ( B) of five heavy globular gases (CF 4, SF 6, MoF 6, UF 6 and WF 6) and the five mixtures (CH 4CF 4, CH 4SF 6, CF 4SF 6, MoF 6UF 6 and WF 6UF 6) are reported. They are calculated by means of an effective potential with temperature dependent parameters. The temperature dependencies of the potential parameters are obtained by an optimization of the squared deviations between the experimental and calculated values of B and η, normalized to the experimental errors. The similarity between the heavy hexafluorides is used to reproduce the temperature dependencies B( T) and η( T) for MoF 6 and WF 6 and their mixtures with UF 6. In these cases, the enlargement of the equilibrium distance is presented as a linear function of the temperature when the normal vibrational frequencies are not available. The obtained information can be used for fast approximate calculations.

Gas-phase viscosity of the alternative refrigerant R134a at low densities

New measurements of the gas-phase viscosity of 1,1,1,2-tetrafluoroethane (R134a) were carried out within an international round-robin project of IUPAC, which was initiated because of the large discrepancies between the results reported by various authors for the transport properties of R134a. Six isochoric series of high-precision measurements were performed by means of a quartz oscillating-disk viscometer between 297 and 438 K and at densities from 12 to 90 mol m −3. Isothermal values recalculated from the experimental data were evaluated with a first-order expansion for the viscosity, in terms of density, to deduce zero-density and initial-density viscosity coefficients. The accuracy of the zero-density values is estimated to be ±0.2%. A representation based on the new results and on reliable data sets from literature is proposed for the viscosity in the limit of zero density to replace a correlation recommended by Krauss et al. Reduced second viscosity virial coefficients deduced from the experiments are in close agreement with predictions of the Rainwater-Friend theory.

The viscosity of gaseous propane and its initial density dependence

Results of five series of high-precision viscosity measurements on gaseous propane, each differing in density, are reported. The measurements were performed in a quartz oscillating-disk viscometer with small gaps from room temperature up to about 625 K and for densities between 0.01 and 0.05 mol · L−1. The experimental data were evaluated with a first-order expansion, in terms of density, for the viscosity. Reduced values of the second viscosity virial coefficients deduced from the zero-density and initial-density viscosity coefficients for propane and for furthern-alkanes are in close agreement with the theoretical representation of the Rainwater-Friend theory for the potential parameter ratios by Bich and Vogel. A new representation of the viscosity of propane in the limit of zero density is provided using the new experimental data and some data sets from literature. The universal correlation based on the extended principle of corresponding states extends over the temperature range 293 to 625 K with an uncertainty of ±0.5 % and deviates from earlier representations by about 1 % at the upper temperature limit.

An isotropic intermolecular potential for sulfur hexafluoride based on the collision-induced light scattering spectrum, viscosity, and virial coefficient data

Recent effective intermolecular potentials of sulphur hexafluoride from the literature have been evaluated using the interaction-induced light scattering spectrum, viscosity, and pressure virial coefficient data. It was found that none of the potentials reproduce all three sets of experimental data. A Hartree–Fock-dispersion-type isotropic potential is proposed that reproduces all the experimental data reasonably well.

Vapor-phase viscosity of phenol

New measurements of the vapor-phase viscosity of phenol were performed from 437 up to 624 K and for densities between 0.006 and 0.023 mol · L−1 in an all-quartz oscillating-disk viscometer with small gaps. Thus, including our own measurements reported earlier, experimental data are available in the temperature range between 376 and 639 K and in the density range from 0.001 up to 0.023 mol · L−1. The data were evaluated with a density series for the viscosity in which only a linear density contribution is included. The values of the second viscosity virial coefficient obtained for phenol as well as for benzene, toluene, and p-xylene were compared with results of the Rainwater-Friend theory and of the modified Enskog theory on the basis of the Lennard-Jones 12-6 potential. The agreement is reasonable, when the potential parameter ratios determined by Bich and Vogel are used. The influence of bound dimers seems to be already taken into account in the three-monomer contribution according to Hoffman and Curtiss.

Vapor phase viscosity of toluene and p-xylene

Abstract New measurements of the vapor phase viscosity of toluene and p-xylene have been performed in an all-quartz oscillating-disk viscometer with small gaps. Thus, including own measurements reported earlier experimental data are available in the temperature range between 305 and 630 K (toluene) and between 340 and 635 K (p-xylene) and for densities from 0.002 up to 0.045 mol·L −1 (toluene) and from 0.003 up to 0.038 mol·L −1 (p-xylene). The data have been evaluated with a density series for the viscosity in which only a linear density contribution has been included. The values of the second viscosity virial coefficient obtained for toluene, p-xylene as well as for benzene have been compared with results of the Rainwater-Friend theory on the basis of the Lennard-Jones 12-6 potential. The agreement is excellent when using the potential parameter ratios determined by Bich and Vogel.

The viscosity of gaseous ethane and its initial density dependence

New high-precision measurements of the viscosity η of gaseous ethane from near room temperature up to 630 K and at densities between 0.3 and 1.6 kg-m −3 and between 0.01 and 0.05 mol · L −1 respectively, carried out in an all-quartz oscillating-disk viscometer with small gaps are reported. The data for the viscosity of ethane at 0.1013 MPa are in good agreement with other high-precision experimental data from literature near room temperature. Additionally, the new experimental data were used to create an individual correlation of the zero-density viscosity coefficient. Only positive values with a maximum in the middle of the temperature range were found for the second viscosity virial coefficient B η. These results corroborate the Rainwater-Friend (1984) theory and the recent investigation by Bich and Vogel (1991).

Temperature dependence and initial density dependence of the viscosity of sulphur hexafluoride

Results of a new investigation of the viscosity of sulphur hexafluoride are reported. The measurements have been performed in an oscillating-disk viscometer, with small gaps, completely made of quartz, from room temperature up to 690 K and for densities between 1.0 and 8.5 kgm −3, i.e., between 0.007 and 0.058 mol 1 −1. The values of the second viscosity virial coefficient B η obtained from the initial density dependence of viscosity increase with increasing temperature from zero at room temperature up to about 75 cm 3 mol −1 at 690 K. They are compared with results of the complete modified Enskog theory as well as of the Rainwater-Friend theory for the Lennard-Jones 12-6 potential. Furthermore, our experimental results at 0.1 MPa are compared with data from existing literature and additionally used in order to deduce an improved individual data correlation similar to one by Wakeham and co-workers.

Prediction of second virial coefficients from intrinsic viscosities in ternary polymer systems

AbstractDeviations in the determination of the unperturbed dimensions of polymers arising in ternary polymer systems (solvent (1)/solvent (2)/polymer) can be explained by the inaccurate use of an interaction parameter independent of polymer molecular weight. On this basis, a new formalism for the calculation of the second virial coefficient from intrinsic viscosity is proposed. This formalism was tested (and compared with well established formalisms) for all ternary polymer systems with simultaneous intrinsic viscosity and second virial coefficient data in the literature.

The initial density dependence of the viscosity of organic vapours: Cyclohexane and neopentane

This paper presents new measurements on the viscosity of the vapours of cyclohexane and of neopentane from near room temperature to 630 K and for densities to 4.8 kg m −3 and 0.057 mol 1 −1 (cyclohexane) and to 5.0 kg m −3 and 0.069 mol 1 −1 (neopentane). Two all-quartz oscillating-disk viscometers with small gaps were used in the investigation. The data for cyclohexane and neopentane as well as earlier results for benzene show that the negative and positive values of the second viscosity virial coefficient B η, dependent on temperature represent the normal behaviour for all substances. The experimental data on the three hydrocarbons are suitable for the further development of the Rainwater-Friend theory concerning the transport properties of moderately dense gases in respect to their temperature range and their limitation to the Lennard-Jones 12-6 potential.

Second viscosity and thermal-conductivity virial coefficients of gases: Extension to low reduced temperature.

A recent theory of the initial density dependences of both viscosity and thermal conductivity has been extended to include lower reduced temperatures. New data on the second viscosity virial coefficients of some organic vapors are found to be in substantial agreement with the theory even at the lowest temperatures. We present in tabular form the numerical values for both transport virial coefficients in the reduced temperature range 0.5\ensuremath{\le}${T}^{\mathrm{*}}$\ensuremath{\le}100 and include values for the constituent two-monomer, three-monomer, and monomer-dimer contributions. A brief discussion of the theoretical approach and calculational methods is also given.

The initial density dependence of the viscosity of organic vapours: Benzene and methanol

The paper reports the results of a new investigation of the viscosity of the vapours of benzene and methanol measured in an oscillating-disk viscometer, with small gaps, completely made of quartz. The measurements have been carried out from near room temperature to about 600 K and for densities to 4.3 kg m −3 and 0.055 mol l −1 (benzene) as well as to 1.2 kg m −3 and 0.038 mol l −1 (methanol). The results for benzene have revealed that negative values of the second viscosity virial coefficient B η are not confined to dipolar compounds or helium. Negative values of B η at reduced temperatures (less than 1) seem to represent normal behaviour for all substances. Both the fully modified Enskog theory and as far as possible the theory for the transport properties of moderately dense gases due to Rainwater and Friend have been used for the Lennard-Jones 12-6 potential in order to explain the experimental data.

Methane–methane isotropic interaction potential from total differential cross sections

Total differential cross sections (DCS) for methane–methane scattering at three collision energies were determined using the crossed molecular beams technique. These DCS’s were used along with literature viscosity and second virial coefficient data to determine a spherical methane–methane interaction potential energy function. The potential has a zero crossing point σ of 3.62 Å, a well depth ε of 200 K, and an intermolecular separation at the minimum rm of 4.02 Å.

Neon–methane and argon–methane isotropic interaction potentials from total differential cross sections

Total differential cross sections have been measured at three collision energies each for Ne–CH4 and Ar–CH4 using the crossed molecular beams technique. The differential cross sections were used along with literature viscosity and second virial coefficient data to determine reliable isotropic interaction potentials. The Ne–CH4 potential has a well depth of 66±4 K and an intermolecular separation of 3.68±0.02 Å at the minimum while the Ar–CH4 potential has a well depth of 170±8 K and an intermolecular separation of 3.85±0.04 Å at the minimum.