Initial Density Dependence Research Articles

Recommended Values of the Viscosity in the Limit of Zero Density for R134a and Six Vapors of Aromatic Hydrocarbons as Well as of the Initial Density Dependence of Viscosity for R134a. Revisited from Experiment Between 297\xa0K and 631\xa0K

Previously published experimental viscosity data at low density, originally obtained using all-quartz oscillating-disk viscometers for R134a and six vapors of aromatic hydrocarbons in the temperature range between 297 K and 631 K at most, were re-evaluated after an improved re-calibration. The relative combined expanded (k=2) uncertainty of the re-evaluated data are 0.2 % near room temperature and increases to 0.3 % at higher temperatures. The re-evaluated data for R134a as well as for the vapors of mesitylene, durene, diphenyl, fluorobenzene, chlorobenzene, and p-dichlorobenzene were arranged in approximately isothermal groups and converted into quasi-isothermal viscosity data using a first-order Taylor series in temperature. Then, the data for R134a were evaluated by means of a series expansion truncated at first order to obtain the zero density and initial density viscosity coefficients, eta ^{(0)} and eta ^{(1)}. For the six aromatic vapors, the Rainwater–Friend theory for the initial density dependence of the viscosity was used to derive eta ^{(0)} values. Finally, reliable eta ^{(0)} and also eta ^{(1)} values for R134a were selected as reference values in the measured temperature range to be applied when generating a new viscosity formulation.

Recommended Values for the Viscosity in the Limit of Zero Density and its Initial Density Dependence for Twelve Gases and Vapors: Revisited from Experiment between 297 K and 691 K

Previously published experimental viscosity data at low density, originally obtained using all-quartz oscillating-disk viscometers for 12 gases and vapors in the temperature range between 297 K and 691 K, were re-evaluated after an improved re-calibration. The relative combined expanded (k = 2) uncertainty of the re-evaluated data is 0.2% near room temperature and increases to 0.3% at higher temperatures. The re-evaluated data for sulfur hexafluoride, methanol, n-pentane, n-hexane, n-heptane, neopentane, cyclohexane, benzene, toluene, p-xylene, phenol, and triethylamine were arranged in approximately isothermal groups and converted into quasi-isothermal viscosity data using a first-order Taylor series in temperature. Then, they were evaluated by means of a series expansion truncated at first order to obtain the zero-density and initial density viscosity coefficients, η(0) and η(1). When the number of isothermal data or their quality was not adequate, the Rainwater–Friend theory for the initial density dependence of the viscosity was additionally used to derive η(0) and η(1) values. Finally, reliable η(0) and η(1) values, preferably obtained from the isotherms, were recommended as reference values for the 12 gases and vapors in the measured temperature range to be applied when generating any new viscosity formulation.

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.

Discreteness inducing coexistence

Consider two species that diffuse through space. Consider further that they differ only in initial densities and, possibly, in diffusion constants. Otherwise they are identical. What happens if they compete with each other in the same environment? What is the influence of the discrete nature of the interactions on the final destination? And what are the influence of diffusion and additive fluctuations corresponding to random migration and immigration of individuals? This paper aims to answer these questions for a particular competition model that incorporates intra and interspecific competition between the species. Based on mean field theory, the model has a stationary state dependent on the initial density conditions. We investigate how this initial density dependence is affected by the presence of demographic multiplicative noise and additive noise in space and time. There are three main conclusions: (1) Additive noise favors denser populations at the expense of the less dense, ratifying the competitive exclusion principle. (2) Demographic noise, on the other hand, favors less dense populations at the expense of the denser ones, inducing equal densities at the quasi-stationary state, violating the aforementioned principle. (3) The slower species always suffers the more deleterious effects of statistical fluctuations in a homogeneous medium.

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.

Viscosity Prediction for Oxygen, Nitrogen and Their Mixtures at Zero and Moderately Dense Regimes via Semi‐Empirically Based Assessment

AbstractThe viscosity coefficients for the gaseous states of N2 and O2 and their mixtures are determined at zero and moderately density regimes. The Lennard‐Jones 12–6 (LJ 12–6) potential energy function is used as the initial model potential required y the technique. The interaction potential energies from the inversion procedure reproduce the viscosity commensurate to the best measurements. The initial density dependence of gaseous viscosity coefficient according to the Rainwater‐Friend theory, which was given by Najafi et al., has been considered for pure N2 and pure O2.

Mating preference in the invasion of growth enhanced fish

Fish with a transgene for growth hormone grow faster than the wild type and may have an advantage in sexual selection due to their larger size and earlier maturation. The cost in these genetically modified organisms (GMOs) is a lower viability of their offspring. The Trojan gene effect is a hypothesis that predicts that the release of such fish in nature can lead to an invasion by GMOs but ultimately decrease population size to extinction. We modelled GMO invasion with Mendelian inheritance of two alleles in one locus and the resulting mating and population dynamics of wild, GMO and hybrid genotypes. Invasion was attempted over a range of initial densities, representing scenarios from accidental escape to large‐scale deliberate introduction of the transgenic genotype. Our results show that invasion strongly depends on hybrid fitness, requiring only a low initial density when GMOs and hybrids are preferred in mating. Preference against hybrids results in an invasion threshold, above which mating between GMOs are sufficiently frequent for invasion to take place. GMO invasion may decrease population size, but contrary to earlier studies on the Trojan gene effect, extinctions do not occur. This is due to the lower viability of GMOs being balanced by the decreased number of competitors reducing the effects of density dependence. The results emphasize the importance of initial density, hybrid fitness and density dependence when considering invasion through hybridization.

Viscosity and thermal conductivity of some refrigerants at moderate and high densities on the basis of Rainwater–Friend theory and the corresponding states principle

The initial density dependence of viscosity and thermal conductivity was formulated on the basis of Rainwater–Friend (RF) theory. In this work, we have first focused on the calculation of viscosity and thermal conductivity of moderately dense argon by using RF theory and an accurate ab initio potential function. This theory which was originally presented for spherical potentials have been adapted for calculation of viscosity and translational contribution of thermal conductivity of some refrigerants by introducing the corresponding states correlations for the second transport virial coefficients. Then the internal states contribution for the thermal conductivity has been determined based on the Mason–Monchick and modified Enskog theories. So, we have calculated the viscosity and thermal conductivity of some refrigerants, R32, R14, R12, R13, R22, R134a, R143a, R125, R123, R142b, at moderate densities up to about 2 mol dm −3. At high densities, beyond the validity range of RF theory, we have applied correlation expressions for the viscosity and thermal conductivity residual functions to calculate the viscosity and thermal conductivity of supercritical refrigerants and then compared with the available experimental data. In conclusion, we have shown that the RF theory in conjunction with the corresponding states residual functions present the reliable model for calculation of viscosity and thermal conductivity of refrigerants over a comparatively wide temperature and pressure range up to 65 MPa within the experimental errors.

Calculation of the Viscosity of Simple Fluids Based on the Rainwater-Friend Theory

Viscosities of noble gases have been calculated over a wide temperature-pressure range. Simple and accurate Tang-Toennies potential of the noble gases are used in the Chapman-Enskog calculation of the zero density viscosity and in the Rainwater-Friend theory to determine the initial density dependence of the viscosity. At densities beyond the range of the theory (up to 46 mol.dm -3 ), a variant of the residual viscosity is developed. A correlation function for the calculation of viscosity over the whole range of density is presented. A comparison of the calculated and experimental values of the viscosity yields an average absolute deviation of 1.5%.

Prediction of thermal conductivities of oxygen, nitrogen and carbon dioxide at the moderate density regime via semi-empirical assessment

Thermal conductivities coefficients for gaseous state of N2, O2 and CO2 at zero density are determined by the inversion technique. The Lennard-Jones 12-6 (LJ 12-6) potential energy function is used as the initial model potential required by the technique. The Wang Chang-Uhlenbeck-de Boer (WCUB) approach of the kinetic theory of gases has been used for calculating the contribution of molecular degree of freedom to the thermal conductivity of N2, O2 and CO2. Also, the initial density dependence of gaseous thermal conductivity according to the Rainwater-Friend theory, which was given by Najafi et al., has been considered for N2, O2 and CO2.

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.

Correlation for the Viscosity of Pentafluoroethane (R125) from the Triple Point to 500 K at Pressures up to 60 MPa

We present a correlation for the viscosity of pentafluoroethane (R125) based on a compilation and critical assessment of the available experimental data. The correlation covers a wide range of fluid states, including the supercritical region. It is applicable from the triple point at 172.52 to 500 K, with pressures varying up to 60 MPa. The formulation includes a zero-density contribution, initial density dependence based on the Rainwater−Friend theory, and a residual contribution for higher densities that combines virial terms with a free-volume term, both being temperature-dependent. The estimated uncertainty of the viscosity correlation (coverage factor of 2) is 3% along the liquid-phase saturation boundary, 3% in the compressed liquid phase at pressures to 60 MPa, and 0.8% in the vapor.

Calculation of hydrogen’s thermal conductivity at moderate and high densities

Based upon Rainwater–Friend (RF) theory, initial density dependence of the thermal conductivity of some gases was given using the realistic potentials. In this work hydrogen’s thermal conductivity is predicted by using an accurate realistic Morse–Spline–Van der Waals (MSV) potential on the basis of RF theory. The internal state contribution is calculated using the Mason–Monchick and hard-sphere Enskog theories. The results show that validity range of hydrogen’s thermal conductivity using this model extends to 5 mol dm −3. By the use of this model, for moderate densities in the temperature range 180–1500 K and pressure up to 15 MPa the hydrogen’s thermal conductivity can be calculated with mean (maximum) deviation of 0.30% (1.04%). At high densities, beyond the range of the RF theory, a residual function for hydrogen’s thermal conductivity has been extracted according to the corresponding states function which where used to calculate the thermal conductivity of supercritical gases which is valid over a wide temperature and pressure ranges. The measured values are in good agreement with data given in the literature. It is worth nothing that the available thermal conductivity data of high accuracy cover the restricted temperature range up to 1500 K and pressure up to 100 MPa and our calculation of this property is limited to that range.

Using a Generational Time-Step Model to Simulate Dynamics of Adaptation to Transgenic Corn and Crop Rotation by Western Corn Rootworm (Coleoptera: Chrysomelidae)

We expanded a simulation model of the population dynamics and genetics of the western corn rootworm for a landscape of corn, soybean, and other crops to study the simultaneous development of resistance to both crop rotation and transgenic corn. Transgenic corn effective against corn rootworm was recently approved in 2003 and may be a very effective new technology for control of western corn rootworm in areas with or without the rotation-resistant variant. In simulations of areas with rotation-resistant populations, planting transgenic corn to only rotated cornfields was a robust strategy to prevent resistance to both traits. In these areas, planting transgenic corn to only continuous fields was not an effective strategy for preventing adaptation to crop rotation or transgenic corn. In areas without rotation-resistant phenotypes, gene expression of the allele for resistance to transgenic corn was the most important factor affecting the development of resistance to transgenic corn. If the allele for resistance to transgenic corn is recessive, resistance can be delayed longer than 15 yr, but if the resistant allele is dominant then resistance usually developed within 15 yr. In a sensitivity analysis, among the parameters investigated, initial allele frequency and density dependence were the two most important factors affecting the evolution of resistance. We compared the results of this simulation model with a more complicated model and results between the two were similar. This indicates that results from a simpler model with a generational time-step can compare favorably with a more complex model with a daily time-step.

Using a Generational Time-Step Model to Simulate Dynamics of Adaptation to Transgenic Corn and Crop Rotation by Western Corn Rootworm (Coleoptera: Chrysomelidae)

We expanded a simulation model of the population dynamics and genetics of the western corn rootworm for a landscape of corn, soybean, and other crops to study the simultaneous development of resistance to both crop rotation and transgenic corn. Transgenic corn effective against corn rootworm was recently approved in 2003 and may be a very effective new technology for control of western corn rootworm in areas with or without the rotation-resistant variant. In simulations of areas with rotation-resistant populations, planting transgenic corn to only rotated cornfields was a robust strategy to prevent resistance to both traits. In these areas, planting transgenic corn to only continuous fields was not an effective strategy for preventing adaptation to crop rotation or transgenic corn. In areas without rotation-resistant phenotypes, gene expression of the allele for resistance to transgenic corn was the most important factor affecting the development of resistance to transgenic corn. If the allele for resistance to transgenic corn is recessive, resistance can be delayed longer than 15 yr, but if the resistant allele is dominant then resistance usually developed within 15 yr. In a sensitivity analysis, among the parameters investigated, initial allele frequency and density dependence were the two most important factors affecting the evolution of resistance. We compared the results of this simulation model with a more complicated model and results between the two were similar. This indicates that results from a simpler model with a generational time-step can compare favorably with a more complex model with a daily time-step.

Initial density dependence of the viscosity of hydrogen and a corresponding states expression for high pressures

Recently, the initial density dependence of gaseous viscosity and thermal conductivity, which was given by Rainwater–Friend, has been used to correct both viscosity and thermal conductivity by using accurate realistic potentials for gases. In this work, an accurate realistic Morse–Spline–Van der Waals (MSV) potential function for the hydrogen dimer is used to calculate the viscosity of hydrogen at low-densities on the basis of this theory. It is shown that in the case of hydrogen their theory works well up to densities of approximately 5 mol/l. We apply the theory to evaluate the viscosity of gaseous hydrogen over a wide temperature and pressure range. At high densities beyond the range of Rainwater–Friend theory, the excess viscosity was represented by a six-term correlation function similar to the noble gases. This correlation equation for the deviation viscosity of supercritical hydrogen is valid over the entire temperature range and pressures up to 200 MPa. The correlation represents experimental data within their uncertainty. By use of this deviation function, the viscosity of hydrogen can be calculated with mean (maximum) uncertainty of 0.76% (2.6%).

The isotope effect of gaseous hydrogen under shock compression

The shock compression method has been used to measure the Hugoniot data and shock temperature for gaseous hydrogen samples, covering the pressure range of 55-140 MPa and the temperature range of 3400-4500 K and with the initial conditions of P 0 = 0.6 MPa, 1.2 MPa and T 0 at room temperature. Spectral radiance histories emitted from shocked D 2 and H 2 + D 2 (equimolar mixture) are monitored by a pyrometer system with seven wavelength channels. Theoretical calculations based on the Saha model with Debye-Huckel correction for the shock compression behavior of shocked gaseous samples are in good agreement with the measured Hugoniot data, but show slightly higher values for the shock temperature when comparing with experiments. An isotope effect relevant to these shocked hydrogen species has been found in the linear shock velocity vs particle velocity relation, in which the correlation factor between these hydrogen isotopes or hydrogen mixtures is simply of initial density dependence.

New Correlation Functions for Viscosity Calculation of Gases Over Wide Temperature and Pressure Ranges

The viscosity of 14 supercritical gases over a wide temperature–pressure range is calculated with a new correlation scheme. Highly accurate realistic interatomic potentials of the noble gases are used in the Chapman–Enskog calculation of the zero-density viscosity and in the Rainwater–Friend theory to determine the initial density dependence of the viscosity. At densities beyond the range of the theory, a variant of the residual viscosity is developed. It is shown that the temperature dependence of the residual viscosity function increases with the number of atoms in the molecule. By including this temperature dependence, the accuracy of the predicted results improves significantly. The accuracy of this method is within the experimental uncertainties.

Prediction of the thermal conductivity of gases based on the Rainwater–Friend theory and a new corresponding states function

The Rainwater–Friend theory is used for the evaluation of the initial density dependence of the thermal conductivity of the noble gases using accurate realistic potentials. This theory, which was originally developed for spherically symmetric potentials, is adapted for the calculation of the initial density dependence of the translational contribution of the thermal conductivity of polyatomic gases. The internal state contribution is evaluated using a combination of Mason–Monchick theory and hard-sphere Enskog theory. At high density, beyond the range of the Rainwater–Friend theory, a deviation thermal conductivity function has been presented. With the help of this function, an easily usable corresponding-states function for the calculation of the thermal conductivity of supercritical gases has been developed, which is valid over a wide temperature range and for pressures up to 400 MPa.

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.