Viscosity Virial Coefficient Research Articles

Coupling between long ranged repulsions and short ranged attractions in a colloidal model of zero shear rate viscosity

In this work, we analyzed an isotropic colloidal model incorporating both short-range sticky attractions and long-range electrostatic repulsions. We computed the zero-shear viscosity and second virial coefficient for a dilute colloidal suspension (i.e., pair interactions only) as a function of the strength of attractions and repulsions. We also developed an analytical approximation that allows us to better understand the coupling of the two types of interactions. The attractions and repulsions contribute to the zero-shear viscosity and second virial coefficient in different ways, leading to cases with the same second virial coefficient but different zero-shear viscosity. The analytical approximation shows that the mechanism of the coupling of interactions is that long-range repulsions can weaken the influence of short-range attractions. This effect alters how repulsions change the zero-shear viscosity. Acting independently, both attractions and repulsions increase the viscosity coefficient of the system. However, when both types of interactions are considered together, repulsions can screen the effect of attractive interactions, thereby reducing the viscosity.

Measurement and modeling of the viscosity of (nitrogen + carbon dioxide) mixtures at temperatures from (253.15 to 473.15) K with pressures up to 2 MPa

Abstract The viscosity of pure nitrogen and of three (nitrogen + carbon dioxide) mixtures was measured over the temperature range from (253.15 to 473.15) K with pressures up to 2 MPa utilizing a rotating-body viscometer. The relative combined expanded uncertainty (k = 2) in viscosity was estimated to be between (0.14 and 0.19)% for nitrogen. For the binary gas mixtures, the uncertainty ranged between (0.19 and 0.39)%. The new data for nitrogen show very good agreement with experimental data from the literature and with recent ab initio calculations. The experimental data for the binary mixtures were compared with an Extended Corresponding States (ECS) model as implemented in the NIST REFPROP 9.1 database. The relative deviations of the data from the model were generally found to increase in magnitude with increasing density and ranged between (−2.1 and 0.4)% near the greatest density studied. The experimental data were correlated using the modified Enskog theory for hard sphere mixtures correct to the second viscosity virial coefficient. In this analysis, the effective hard-sphere diameters determining (a) the zero-density viscosity and (b) the leading term in the radial distribution function at contact were correlated as functions of temperature. The resulting model was found to represent all measured data with absolute relative deviations

The Viscosities of Dilute Kr, Xe, and CO $$_2$$ 2 Revisited: New Experimental Reference Data at Temperatures from 295 K to 690 K

Previously reported, but also unpublished experimental data of our group for the viscosities of dilute krypton, xenon, and carbon dioxide, obtained in the range from 295 K to a maximum of 690 K using oscillating-disk viscometers, were re-evaluated and corrected or extrapolated to the limit of zero density (\(\eta _0\)). The combined standard uncertainty of the data is 0.1 % at room temperature and 0.2 % at higher temperatures. For krypton and carbon dioxide, our \(\eta _0\) data were compared with \(\eta _0\) values theoretically calculated using the kinetic theory and highly accurate ab initio potentials for the krypton atom pair and the CO\(_2\) molecule pair, but also with recent experimental \(\eta _0\) data from the literature. Our data for krypton differ up to 690 K from the theoretical values by \(-0.10\,\%\) to \(+0.28\,\%\), whereas that of Lin et al. (Fluid Phase Equilib. 418:198, 2016) show deviations of +(0.04 to 0.20) % at temperatures from 243 K to 393 K, in each case proving that experiment and theory are in consistent agreement. The re-evaluated \(\eta _0\) data for xenon were compared with recent data from the literature and with calculated values resulting from the HFD-B potential for xenon via the corresponding-states principle to verify that they are reference values. For carbon dioxide, \(\eta _0\) values obtained from 26 re-evaluated isotherms and from eight isotherms of Schafer et al. (J Chem Thermodyn 89:7, 2015) between 253 K and 473 K are mutually consistent with ab initio calculated and subsequently scaled viscosity values of Hellmann (Chem Phys Lett 613:633, 2014). The isotherms of Schafer et al. are especially suitable for determining the initial density dependence of the viscosity. Concomitantly inferred reduced second viscosity virial coefficients were checked against two theoretical approaches of the Rainwater–Friend theory.

Prediction of transport properties of CO2-N2 binary mixtures via the inversion of reduced-viscosity collision integrals

In the present study, the main purpose is to extract information about the effective intermolecular potential energy function for binary mixture of nitrogen and carbon dioxide by the usage of a direct inversion of the experimentally reduced viscosity and second virial coefficient data and then to reproduce the dilute gas transport properties from the inverted potential energy. The Lennard-Jones (12, 6) potential energy function has been employed as the initial potential model required by the inversion method. The MSV potential obtained in this way is in reasonable agreement with the independently known Co2-N2 potential energy function. Using the inverted pair potential energies, the Chapman-Enskog scheme is employed to calculate transport properties of CO2-N2 in a wide composition and temperature range. The close agreement between the predicted values and the literature results of transport properties demonstrate the predictive power of the inversion scheme.

Temperature Dependence of the Hydrodynamic and Conformational Properties of Hyperbranched Polycarbosilanes

Three types of carbosilane hyperbranched polymers were studied in dilute solution in toluene. The samples had different lengths of chains between branch points and the structure of terminal groups (butyl, undecenyl, or fluorine containing). The temperature dependences of intrinsic viscosity and second virial coefficient values were determined by viscometry and static light scattering methods. It is shown that conformational characteristics of hyperbranched polycarbosilanes do not depend on the thermodynamic quality of a solution in the wide range of temperatures.

Calculation of the second self-diffusion and viscosity virial coefficients of Lennard-Jones fluid by equilibrium molecular dynamics simulations

The second self-diffusion and viscosity virial coefficients of the Lennard-Jones (LJ) fluid were calculated by a detailed evaluation of the velocity and shear-stress autocorrelation functions using equilibrium molecular dynamics simulations at low and moderate densities. Accurate calculation of these coefficients requires corresponding transport coefficient values with low degrees of uncertainty. These were obtained via very long simulations by increasing the number of particles and by using the knowledge of correlation functions in the Green-Kubo method in conjunction with their corresponding generalized Einstein relations. The values of the self-diffusion and shear viscosity coefficients have been evaluated for systems with reduced densities between 0.0005 and 0.05 and reduced temperatures from 0.7 to 30.0. This provides a new insight into the transport coefficients beyond what can be offered by the Rainwater-Friend theory, which has not been developed for the self-diffusion coefficient.

MODELING THERMOPHYSICAL PROPERTIES OF NOBLE GAS INVOLVED MIXTURES

The present work involves in determining isotropic and effective pair potential energy of binary gas mixtures of Kr–Xe , Kr–C2H6 , Xe–C2H6 , Kr–C3H8 , and Xe–C3H8 from thermophysical properties consisting of viscosity and second virial coefficients through inversion method. Typically, the calculated intermolecular potential energy of Kr–Xe system has compared with HFD model potential reported in literature. A desirable harmony between our model potential and HFD model has been obtained. In order to assess the potential energies obtained, transport properties including viscosity, diffusion, thermal diffusion factor, and thermal conductivity of aforementioned mixtures were predicted using the calculated models potential. The deviation percentage of the calculated viscosity and thermal conductivity of above-mentioned mixtures from the literature values are, respectively, within ±2%, ±3%.

The viscosity of triethylamine vapor at low densities and in the saturated vapor phase

For the first time, results of high-precision measurements of the viscosity coefficient of triethylamine vapor at low densities are reported. The relative measurements with an all-quartz oscillating-disk viscometer were carried out along seven isochores at densities from 0.002 to 0.009 mol m −3 in the temperature range between 298 and 498 K. The uncertainty is estimated to be ± 0.2% at ambient temperature, increasing up to ± 0.3% at higher temperatures. First isothermal values were recalculated from the original experimental data and then evaluated with a first-order expansion for the viscosity, in terms of density. In addition, viscosity values of the saturated vapor were determined at low temperatures. The results are utilized to model the viscosity coefficient of triethylamine vapor at moderately low densities. A so-called individual correlation on the basis of the extended theorem of corresponding states was employed to describe the zero-density viscosity coefficient, whereas the Rainwater–Friend theory was used to represent the initial density dependence expressed as second viscosity virial coefficient.

Reference Viscosities of H2, CH4, Ar, and Xe at Low Densities

The zero-density viscosity $${\eta_{0,T}^{\rm gas}}$$ of hydrogen, methane, and argon was determined in the temperature range from 200 to 400 K, with standard uncertainties of 0.084% for hydrogen and argon and 0.096% for methane. These uncertainties are dominated by the uncertainty of helium’s viscosity $${\eta_{0,T}^{\rm He}}$$ , which we estimate to be 0.080% from the difference between ab initio and measured values at 298.15 K. For xenon, measurements ranged between 200 and 300 K and the zero-density viscosity $$\eta _{0,T}^{\rm Xe} $$ was determined with an uncertainty of 0.11%. The data imply that xenon’s viscosity virial coefficient is positive over this temperature range, in contrast with the predictions of corresponding-states models. Furthermore, the xenon data are inconsistent with Curtiss’ prediction that bound pairs cause an anomalous viscosity decrease at low reduced temperatures. At 298.15 K. the ratios $$\eta _{0,298}^{\rm Ar}\!/\eta_{0,298}^{\rm He} ,{\eta _{0,298}^{{\rm CH}_{4}} }\!/\eta_{0,298}^{\rm He },{\eta _{0,298}^{{\rm H}_2} }\!/{\eta_{0,298}^{\rm He}},{\eta_{0,298}^{\rm Xe} }\!/{\eta _{0,298}^{\rm He} }, {\eta _{0,298}^{{\rm N}_2} }\!/{\eta _{0,298}^{\rm He}}$$ , and $${\eta _{0,298}^{{\rm C}_2{\rm H}_6} }/{\eta _{0,298}^{\rm He} }$$ were determined with a relative uncertainty of less than 0.024% by measuring the flow rate of these gases through a quartz capillary while simultaneously measuring the pressures at the ends of the capillary. Between 200 and 400 K, a two-capillary viscometer was used to determine $${\eta_{0,T}^{\rm gas} }/{\eta_{0,T}^{\rm He} }$$ with an uncertainty of 0.024% for H2 and Ar, 0.053% for CH4, and 0.077% for Xe. From $${\eta_{0,T}^{\rm gas} }/{\eta_{0,T}^{\rm He} }, \eta_{0,T}^{\rm gas} $$ was computed using the values of $$\eta_{0,T}^{\rm He}$$ calculated ab initio. Finally, the thermal conductivity of Xe and Ar was computed from $$\eta_{0,T}^{\rm gas} $$ and values of the Prandtl number that were computed from interatomic potentials. These results may help to improve correlations for the transport properties of these gases and assist efforts to develop ab initio two- and three-body intermolecular potentials for these gases. Reference viscosities for seven gases at 100 kPa are provided for gas metering applications.

A New Reference Correlation for the Viscosity of Methanol

A new reference-quality correlation for the viscosity of methanol is presented that is valid over the entire fluid region, including vapor, liquid, and metastable phases. To describe the zero-density viscosity with kinetic theory for polar gases, a new expression for the collision integral of the Stockmayer potential is introduced. The initial density dependence is based on the Rainwater–Friend theory. A new correlation for the third viscosity virial coefficient is developed from experimental data and applied to methanol. The high-density contribution to the viscosity is based on the Chapman–Enskog theory and includes a new expression for the hard-sphere diameter that is a function of both temperature and density. The resulting correlation is applicable for temperatures from the triple point to 630K at pressures up to 8GPa. The estimated uncertainty of the resulting correlation (with a coverage factor of 2) varies from 0.6% in the dilute-gas phase between room temperature and 630K, to less than 2% for the liquid phase at pressures up to 30MPa at temperatures between 273 and 343K, 3% for pressures from 30to100MPa, 5% for the liquid from 100to500MPa, and 10% between 500MPa and 4GPa. At very high pressures, from 4to8GPa, the correlation has an estimated uncertainty of 30% and can be used to indicate qualitative behavior.

Determination of potential energy functions of CO–CO, CO 2–CO 2, and N 2O–N 2O and calculation of their transport properties

The potential energy functions of CO–CO, CO 2–CO 2, and N 2O–N 2O systems have been determined via the inversion of reduced viscosity collision integrals at zero pressure and fitted to obtain analytical potential forms. The potentials produce viscosity, thermal conductivity, self-diffusion coefficient, and second virial coefficients of carbon monoxide, carbon dioxide, and nitrous oxide over wide temperature ranges within experimental errors. The potentials of carbon monoxide and carbon dioxide have been compared with the recently obtained ab initio potentials and the potential of nitrous oxide has been compared with the Stockmayer potential. We have also derived very accurate equations for viscosity, self-diffusion coefficient, and second virial coefficient of CO, CO 2, and N 2O in a wide temperature range.

A Reference Multiparameter Viscosity Equation for R134a with an Optimized Functional Form

An optimization technique was applied to develop a functional form for a multiparameter viscosity equation η=η(ρ,T) for R134a. The results obtained are very promising, with an average absolute deviation of 0.55% for the currently available 549 primary data points. Compared to viscosity equations available in the literature, this is a significant improvement. Advantages become evident especially at gaseous states. As usual, both the development and the use of the viscosity equation require a highly accurate equation of state in order to convert the independent variables used for the experimental data and in most applications, (P,T), into the independent variables of the viscosity equation, (ρ,T). Though the equation was developed directly using the available data, the zero-density viscosity and the reduced second viscosity virial coefficient are correctly reproduced in the data range. The technique used to develop the equation, which is heuristic and not theoretically founded, is capable of selecting consistent data sets and thus is a powerful tool for screening the available experimental data. For the viscosity surface representation of a pure fluid this study shows that the limit in the achievement of a better accuracy is much more due to the present experimental uncertainty level for this property rather than to the effectiveness of the proposed modeling method.

Determination of potential energy functions and calculation transport properties of oxygen and nitric oxide via the inversion of reduced viscosity collision integrals at zero pressure

The potential energy functions of oxygen and nitric oxide have been determined via the inversion of reduced viscosity collision integrals at zero pressure and fitted to obtain the analytical potential forms. The potentials reproduce viscosity, self-diffusion coefficient, and second virial coefficient of oxygen and nitric oxide in excellent accordance with the experimental data over a wide range of temperature. We have also derived very accurate equations for viscosity, self-diffusion coefficient, and second virial coefficient of O 2 and NO at different temperatures. Comparisons of O 2 O 2 potential with experimental potentials of Perugia group and ESMSV-type potential and ab initio potentials (MCRI-1/B3 and CCSD (T)/MCRI mixed model) and NO NO potential with the recently determined potential by means of ab initio electronic structure calculations, CASSCF/CASPT2 (18/14)/6-311G(2d) have been also included.

Viscosity Measurements on Methanol Vapor and Their Evaluation

The viscosity coefficient of methanol vapor was measured at low densities by means of an all-quartz oscillating-disk viscometer of high precision. The relative measurements were performed along 10 isochores at densities from (0.004 to 0.050) mol·dm-3 in the temperature range between (298 and 603) K. The uncertainty is estimated to be ± 0.2 % at room temperature, increasing up to ± 0.3 % at higher temperatures. Isothermal values recalculated from the original experimental data were evaluated with a first-order expansion for the viscosity in terms of density. A reasonable agreement with experimental values from the literature was found for those of Golubev and Likhachev (up to 1 % higher) measured with a capillary viscometer in an extended temperature range up to high pressures. The new results, some older ones obtained in our laboratory, and those of Golubev and Likhachev are used to model the viscosity of methanol vapor at moderately low densities. Whereas an individual correlation according to the extended theorem of corresponding states was necessary to represent the zero-density viscosity coefficient within its uncertainty, the Rainwater−Friend theory proved to be suitable for the description of the second viscosity virial coefficient. In addition, viscosity values of the saturated vapor were determined at low temperatures (299 to 339 K). They are in reasonable good consistency with values of Golubev determined at higher temperatures (373 to 513 K).

Viscosity Measurements on Water Vapor and Their Evaluation

Results of new high-precision measurements of the viscosity of water vapor at low densities are reported. The measurements were performed using an all-quartz oscillating-disk viscometer with small gaps. Ten isochoric series were carried out at temperatures between (298 and 438) K and at densities from (0.001 to 0.013) mol·L- 1. The uncertainty is estimated to be ± 0.2 % at ambient temperature increasing up to ± 0.3 % at higher temperatures. Isothermal values were analyzed with a density series for the viscosity in which only a linear contribution is considered. Values for the viscosity of the saturated vapor were also obtained at low temperatures. The new results and reliable data sets from literature are used to represent the viscosity of water vapor at moderately low densities. The second viscosity virial coefficient was modeled by means of the Rainwater−Friend theory. An individual correlation according to the extended theorem of corresponding states was necessary to describe the zero-density viscosity...

Viscosity and pVT–Second Virial Coefficient of Binary Noble–Globular Gas and Globular–Globular Gas Mixtures Calculated by Means of an Isotropic Temperature-Dependent Potential

This work presents results of an extension of our earlier studies of the transport and equilibrium properties of pure heavy globular gases. It demonstrates a simple and reliable procedure for estimating the equilibrium and transport properties of their mixtures using the pure gas potentials of interaction when there are no available experimental data. Here we consider binary gas mixtures of globular gases between themselves and with the noble gases as well. The gases involved are: BF3, CH4, CF4, SiF4, SiCl4, CCl4, SF6, MoF6, WF6, UF6, C(CH3)4, Si(CH3)4, Ar, Kr, and Xe. The calculations were performed by means of the so called isotropic temperature–dependent potential (ITDP) introduced by us earlier and applied to some binary mixtures (CH4–CF4, CH4–SF6, CF4–SF6). The CH4–CH4 and noble gases potentials of interactions have been determined in a (n−6) Lennard-Jones shape in the temperature range 200–1000 K by fitting a large number of viscosity and pVT–second virial coefficient data measured by different authors with different experimental techniques. The ITDP parameters of molecular gases were taken from the tables we have determined and published earlier [L. Zarkova and U. Hohm, J. Phys. Chem. Ref. Data 31, 183 (2002)]. Simple combination rules allow us to take into account the influence of the temperature on the thermophysical properties of the binary gas mixtures containing heavy globular molecules. Tables with potential parameters of equal and unequal particles and properties of the equimolar mixtures are given for all mixtures in the temperature range 200–900 (1000) K. The deviations between experimental and calculated viscosity and second virial coefficient data of some more examined mixtures permit to evaluate the quality of the proposed approach.

Determination of the Potential Energy Function of CF4−CF4 via the Inversion of Reduced Viscosity Collision Integrals at Zero Pressure

The potential energy function of carbon tetrafluoride has been determined via the inversion of reduced viscosity collision integrals at corresponding states and zero pressure and fitted to obtain an analytical potential form. A comparison of the potential with the recently determined potential by means of ab initio molecular orbital calculations at the MP2/6-31+G(3d) level of theory has been included. The interaction potential energy from the inversion procedure reproduces, within experimental error, the viscosity, self-diffusion coefficient, and second virial coefficient of carbon tetrafluoride over a wide temperature range. We have also derived very accurate equations for the viscosity, self-diffusion coefficient, and second virial coefficient of carbon tetrafluoride in a more extended temperature range than those of previous ones.

The viscosity surfaces of R152a in the form of multilayer feed forward neural networks

A multilayer feedforward neural network (MLFN) technique is adopted for developing a viscosity equation η=ηρ,T for R152a. The results obtained are very promising, with an average absolute deviation (AAD) of 0.36% for the currently available 300 primary data points, and they are a significant improvement over those of a corresponding conventional equation in the literature. The method requires a high accuracy equation of state for the fluid in order to convert the experimental P,T into the independent variables ρ,T, but such equation may not be available for the target fluid. Aiming at overcoming this difficulty, two viscosity explicit equations in the form η=ηP,T, avoiding the density variable, are also developed, one for the liquid surface and the other for the vapor one. The reached accuracy levels are equivalent to that of the former η=ηρ,T equation. The trend of the reduced second viscosity virial coefficient is correctly reproduced in the data range. The proposed technique, being heuristic and non theoretically founded, is also a powerful tool for experimental data screening.

Dilute-solution properties of arborescent polystyrenes: further evidence for perturbed-hard-sphere behavior

Toward improved understanding of the dilute-solution properties of arborescent polystyrenes, new measurements are reported for osmotic second virial coefficients and for intrinsic viscosities in three common organic solvents. As observed for other branched polymers, branching decreases the second virial coefficient in good solvents and lowers the theta temperature for a polymer–solvent system. For generation-zero arborescent polystyrene in methylcyclohexane, the theta temperature is 36±2°C.A correspondence between intrinsic viscosity and second virial coefficient, valid for hard-spheres solutions, holds in good solvents; this correspondence improves with decreasing branch molecular weight.The osmotic-pressure data are interpreted with a colloid-like thermodynamic framework using a van der Waals-type equation of state. The reference state is the hard sphere and the perturbation is given by an attraction decaying with the sixth power of the center-to-center distance between polymers. The hard-sphere diameter is obtained from intrinsic-viscosity data. Predicted and observed osmotic pressures are in good agreement.

A Fugacity Model for Gas Hydrate Phase Equilibria

A classical thermodynamic model for the equilibrium pressures of different guests of structure I and II gas hydrates is proposed that removes the need for reference energy parameters used in the van der Waals and Platteeuw (vdWP) type models. The assumption of a constant crystal lattice for different guests within a structure, which is not in agreement with quantum chemistry calculations, is removed. This model uses published Kihara cell potential parameters determined from viscosity and second virial coefficient data, unlike previous models that fit these parameters to hydrate data. Quantum mechanical calculations were used to reduce the number of fitted parameters in the new model. This model greatly improves upon the accuracy of previous models and is applicable over a wide temperature range. Percent absolute average deviations in the predicted equilibrium pressures is 3.27% with two or three guest-hydrate specific parameters compared to more than 11% with three adjustable parameters in the vdWP type models and 8.55% using a recent thermodynamic model that uses five guest-hydrate parameters.