Binary Diffusion Coefficients Research Articles

Lattice Boltzmann Model for Rarefied Gaseous Mixture Flows in Three-Dimensional Porous Media Including Knudsen Diffusion

Numerical modeling of gas flows in rarefied regimes is crucial in understanding fluid behavior in microscale applications. Rarefied regimes are characterized by a decrease in molecular collisions, and they lead to unusual phenomena such as gas phase separation, which is not acknowledged in hydrodynamic equations. In this work, numerical investigation of miscible gaseous mixtures in the rarefied regime is performed using a modified lattice Boltzmann model. Slip boundary conditions are adapted to arbitrary geometries. A ray-tracing algorithm-based wall function is implemented to model the non-equilibrium effects in the transition flow regime. The molecular free flow defined by the Knudsen diffusion coefficient is integrated through an effective and asymmetrical binary diffusion coefficient. The numerical model is validated with mass flow measurements through microchannels of different cross-section shapes from the near-continuum to the transition regimes, and gas phase separation is studied within a staggered arrangement of spheres. The influence of porosity and mixture composition on the gas separation effect are analyzed. Numerical results highlight the increase in the degree of gas phase separation with the rarefaction rate and the molecular mass ratio. The various simulations also indicate that geometrical features in porous media have a greater impact on gaseous mixtures’ effective permeability at highly rarefied regimes. Finally, a permeability enhancement factor based on the lightest species of the gaseous mixture is derived.

Transport and Kinetic Property of the Butyric Acid in Water: A Simulation Study

Microbiota is defined as a class of all microorganisms which includes fungi, protozoa, bacteria and viruses. About 90 % of all microbiota in our body are found in our gut that regulates host immunity. The gut-brain axis is a bidirectional communication system that allows gut microbiota to communicate with the brain and vice versa. Studies suggest that the gut dysbiosis may enhance neurotoxic substance such as short-chain fatty-acids (SCFAs which are acetate, propionate, butyrate) to the blood circulation and even to the brain through damaged blood brain barrier (BBB) and may cause protein aggregation which are implicated in the pathogenesis of several neurodegenerative diseases like Alzheimer’s disease (AD), Parkinson’s disease (PD), prion disease, motor neuron disease, Huntington’s disease (HD), Amyotrophic lateral sclerosis (ALS). Specifically, butyric acid are the main SCFA product that may impact on gut health. Therefore, this article aims to investigate the transport and kinetic properties such as diffusion coefficient, activation energy and redial distribution function of butyric acid in water at different temperature through molecular dynamics simulations. The self and binary diffusion coefficient of butyric acid in water obtained from our MD simulation are found to be 0.8699×10−9m2s−1 and 0.8714×10−9m2s−1, respectively at 300 K and the activation energy for self-diffusion coefficient of water estimated from the slope of ln(D)versus1/T is equal to 16.07 kJ/mol. Our results are in accordance with those obtained from the experimental values. This study offers an alternate approach to researching the diffusion of butyric acid in living organisms. This knowledge contributes to advancements in various fields, including nutrition, gastroenterology, microbiology, and pharmacology.

Simulation and optimization of fatty acid extraction parameters from Nannochloropsis sp. using supercritical carbon dioxide

Microalgae, which are rich in fatty acids, have potential applications in various sectors such as bioenergy, health, food, and biomaterials. The Supercritical Fluid Extraction (SFE) method is commonly used to extract microalgae. This research estimated the process parameters of desorption rate constant (kd) and binary diffusion coefficient (DAB) for SFE fatty acid from Nannochloropsis sp. using a mathematical model called as hot sphere diffusion. Desorption models were used to model the release of fatty acids into the solvent (supercritical carbon dioxide). The parameter estimation process was conducted at temperatures of 313 and 333 K and pressures of 12.5, 20, and 30 MPa. The value of kd increased with increasing pressure and temperature and DAB values were obtained at varying pressures and temperatures.

Theoretical Study of Maxwell-Stefan Binary Diffusion Coefficients of n-alkanes-N2 at High Densities

ABSTRACT In this study, the Maxwell-Stefan binary diffusion coefficients ( D ij ) of C1-C6 n-alkanes-N2 are calculated using the Green-Kubo formula. The ratio of pD ij at different pressures (from 1 to 1000 bar) to that at 1 atm (reference condition) is studied. It is found that the ratio pD ij /(pD ij ) ref first decreases and then increases with increasing density, finally reaching 1.3 for n-C6H14-N2 at 1000 bar, 600 K. The gradual increase in molecular attraction at the beginning of the density increase results in a slower pressure increase compared to that of an ideal gas, contributing to the decreasing trend of pD ij /(pD ij ) ref . As the density continues to increase, the enhanced molecular repulsion and the molecular volume exclusion effect accelerate the pressure increase beyond that of an ideal gas, leading to an increasing trend in pD ij /(pD ij ) ref . Finally, the results obtained by the Green-Kubo method are compared with those obtained from empirical methods, and an equation for the refinement of D ij is formulated.

Predicting the artificial dynamical acceleration of binary hydrocarbon mixtures upon coarse-graining with roughness volumes and simple averaging rules.

Coarse-grained (CG) molecular models greatly reduce the computational cost of simulations allowing for longer and larger simulations, but come with an artificially increased acceleration of the dynamics when compared to the parent atomistic (AA) simulation. This impedes their use for the quantitative study of dynamical properties. During coarse-graining, grouping several atoms into one CG bead not only reduces the number of degrees of freedom but also reduces the roughness on the molecular surfaces, leading to the acceleration of dynamics. The RoughMob approach [M. K. Meinel and F. Müller-Plathe, J. Phys. Chem. B 126(20), 3737-3747 (2022)] quantifies this change in geometry and correlates it to the acceleration by making use of four so-called roughness volumes. This method was developed using simple one-bead CG models of a set of hydrocarbon liquids. Potentials for pure components are derived by the structure-based iterative Boltzmann inversion. In this paper, we find that, for binary mixtures of simple hydrocarbons, it is sufficient to use simple averaging rules to calculate the roughness volumes in mixtures from the roughness volumes of pure components and add a correction term quadratic in the concentration without the need to perform any calculation on AA or CG trajectories of the mixtures themselves. The acceleration factors of binary diffusion coefficients and both self-diffusion coefficients show a large dependence on the overall acceleration of the system and can be predicted a priori without the need for any AA simulations within a percentage error margin, which is comparable to routine measurement accuracies. Only if a qualitatively accurate description of the concentration dependence of the binary diffusion coefficient is desired, very few additional simulations of the pure components and the equimolar mixture are required.

Diffusion coefficients and atomic mobilities in the BCC phase of the Al–Nb–V system

Diffusion coefficients in the BCC phase of the Al–Nb–V ternary system are studied for the first time, including an assessment of the atomic mobilities. Ternary interdiffusion coefficients are obtained from the intersecting diffusion paths of several sets of diffusion couples that are annealed at both 1100 °C and 1200 °C. Existing experimental data from the pertinent binary systems are also employed for the assessments of atomic mobilities using the 1-parameter Z-Z-Z binary diffusion coefficient model developed by Zhong et al [1]. Interdiffusion coefficients in the BCC region of the Al–V system are also extracted through a forward-simulation analysis and incorporated into the mobility modeling. A complete description of diffusion in the BCC phase of the Al–Nb–V system is presented following the Binary and Cross-Binary Parameters Only (BCBPO) model developed by Zhong and Zhao [2]. Our data will be valuable input to diffusion-related simulation of refractory high entropy alloys containing aluminum.

DNS of a non-premixed CH4/O2 flame in a supercritical CO2 environment

3D Direct Numerical Simulation (DNS) is performed to investigate turbulent non-premixed methane oxy-combustion in a CO2-rich environment at supercritical conditions (300 bar). The study focuses on a shear-layer configuration typical of slot burners, where the central slot carries the fuel and the oxidant mixture O2/CO2 flows on both sides of the central jet. The simulation solves the compressible Navier–Stokes equations coupled with the translated volume formulation of the Peng–Robinson cubic equation of state (VTPR-EoS), utilizing a reduced 23-species kinetic scheme derived from the ARAMCO 2.0 complete mechanism. The extremely high pressure results in turbulent scales smaller than those observed at lower pressures. Both premixed and diffusion flame zones are identified, with heat primarily released in non-premixed rich regions, leading to a CO mass fraction of up to 0.55. The flow exhibits uphill (counter-gradient) diffusion for both CO2 and H2O, primarily influenced by the interaction of binary diffusion coefficients and individual species chemical potential gradients. Values in the range of 2.52−2.62 are obtained for the fractal dimension of temperature iso-surfaces. Mixture fraction probability density functions (PDFs) are compared with the standard presumed β−PDF, revealing an underestimation of mixing. Differently from flames at atmospheric pressures, the Dufour effect in the energy diffusion flux, is not negligible. Furthermore, fugacity coefficients must be considered in the calculation of chemical species kinetic rates.

The Role of Diffusion on Reservoir Performance in Underground Hydrogen Storage

Summary Underground hydrogen storage (UHS) has the potential to balance fluctuating sustainable energy generation and energy demand by offering large-scale seasonal energy storage. Depleted natural gas fields or underground gas storage fields are attractive for UHS as they might allow for cost-efficient hydrogen storage. The amount of cushion gas required and the purity of the backproduced hydrogen are important cost factors in UHS. This study focuses on the role of molecular diffusion within the reservoir during UHS. Although previous research has investigated various topics of UHS such as microbial activity, UHS operations, and gas mixing, the effects of diffusion within the reservoir have not been studied in detail. To evaluate the composition of the gas produced during UHS, numerical simulation was used here. The hydrogen recovery factor and methane-to-hydrogen production ratio for cases with and without diffusive mass flux were compared. A sensitivity analysis was carried out to identify important factors for UHS, including permeability contrast, vertical-to-horizontal permeability ratio, reservoir heterogeneity, binary diffusion coefficient, and pressure-dependent diffusion. Additionally, the effect of numerical dispersion on the results was evaluated. The simulations demonstrate that diffusion plays an important role in hydrogen storage in depleted gas reservoirs or underground gas storage fields. Ignoring molecular diffusion can lead to the overestimation of the hydrogen recovery factor by up to 9% during the first production cycle and underestimation of the onset of methane contamination by half of the back production cycle. For UHS operations, both the composition and amount of hydrogen are important to design facilities and determine the economics of UHS, and hence diffusion should be evaluated in UHS simulation studies.

Transport phenomena in the near-field region of Stefen flow

Stefan flow is a transport phenomenon concerning the movement of one component of a multi-component mixture that is induced by the production or removal of the component at an interface. Fick’s law is often used to describe the transport phenomena in many physical and chemical processes. However, when the system scales down to the order of molecular mean free path, the influence of interface that is not considered in Fick’s law, cannot be neglected. To predict the transport phenomena in the near-field region, the Herz-Knudsen (HK) relation is often adopted, in which the near-field region controlled by the HK relation was assumed as a zero-thickness layer. Our theoretical analysis has shown that this assumption is less physically realistic. In this study, we derive the thickness of the near-field region through the analysis of the theoretical binary diffusion coefficient and corresponding mass flux. Based on the analysis, we propose a modified Fick’s law to describe the far-field and near-field regions separately. The validity of this modified Fick’s law and its difference from Fick’s law coupled with the HK relation are demonstrated by comparing the partial pressure distributions of binary mixtures, predicted by the two versions of Fick’s law and the Direct Simulation Monte Carlo (DSMC) method, due to the deposition of one component on a cold surface. The comparison results show that the modified Fick’s law outperforms the Fick’s law coupled with the HK relation in accuracy at high deposition coefficients for H2O/N2 mixture and in stability within the range of this study. Moreover, the situations when the modified Fick’s law is required are discussed. This study provides a more molecular-level insight into the transport phenomena in the near-field region of Stefen flow.

Measurement of Effective Hydrogen-Methane Gas Diffusion Coefficients in Reservoir Rocks

Summary If hydrogen is stored in depleted gas fields, the remaining hydrocarbon gas can be used as cushion gas. The composition of the backproduced gas depends on the magnitude of mixing between the hydrocarbon gas and the hydrogen injected. One important parameter that contributes to this process of mixing is molecular diffusion. Although diffusion models are incorporated in the latest commercial reservoir simulators, effective diffusion coefficients for specific rock types, pressures, temperatures, and gas compositions are not available in the literature. Thus, laboratory measurements were performed to improve storage performance predictions for an underground hydrogen storage (UHS) project in Austria. An experimental setup was developed that enables measurements of effective multicomponent gas diffusion coefficients. Gas concentrations are detected using infrared light spectroscopy, which eliminates the necessity of gas sampling. To test the accuracy of the apparatus, binary diffusion coefficients were determined using different gases and at multiple pressures and temperatures. Effective diffusion coefficients were then determined for different rock types. Experiments were performed multiple times for quality control and to test reproducibility. The measured binary diffusion coefficients without porous media show a very good agreement with the published literature data and available correlations based on the kinetic gas theory (Chapman-Enskog, Fuller-Schettler-Giddings). Measurements of effective diffusion coefficients were performed for three different rock types that represent various facies in a UHS project in Austria. A correlation between static rock properties and effective diffusion coefficients was established and used as input to improve the numerical model of the UHS. This input is crucial for the simulation of backproduced gas composition and properties which are essential parameters for storage economics. In addition, the results show the impact of pressure on effective diffusion coefficients, which impacts UHS performance.

Determination of the Binary Diffusion Coefficients and Interaction Viscosities of the Systems Carbon Dioxide–Nitrogen and Ethane–Methane in the Dilute Gas Phase from Accurate Experimental Viscosity Data Using the Kinetic Theory of Gases

The results of viscosity measurements at moderate densities on the two gaseous mixtures carbon dioxide–nitrogen and ethane–methane including the pure gases between 253.15 K and 473.15 K, originally performed by Humberg et al. at Ruhr University Bochum, Germany, using a rotating-cylinder viscometer between 0.1 MPa and 2.0 MPa, were employed to determine the interaction viscosity, eta _{12}^{(0)}, and the product of molar density and diffusion coefficient, (rho D_{12})^{(0)}, each in the limit of zero density. The isothermal viscosity data were evaluated by those authors with density series restricted to the second order at most to derive the zero-density viscosities and initial density viscosity coefficients, eta _textrm{mix}^{(0)} and eta _textrm{mix}^{(1)}, for the mixtures, as well as, eta _i^{(0)} and eta _i^{(1)} (i=1,2), respectively, for the pure gases. Humberg et al. have already compared their eta _textrm{mix}^{(0)} and eta _i^{(0)} data for carbon dioxide–nitrogen and ethane–methane with corresponding viscosity values theoretically computed for the nonspherical potentials of the intermolecular interaction. Now we employed eta _textrm{mix}^{(0)} and eta _textrm{mix}^{(1)} as well as eta _i^{(0)} and eta _i^{(1)} in two procedures to derive eta _{12}^{(0)} values. For this, we needed A_{12}^* values (ratio between effective cross-sections of viscosity and diffusion). But the second procedure applying the initial density viscosity coefficients eta _textrm{mix}^{(1)} and eta _i^{(1)} failed to yield reasonable eta _{12}^{(0)} values. The first procedure should provide the best results when it is possible to use A_{12}^* values computed for the nonspherical potential. The effect is comparatively small if eta _{12}^{(0)} is determined. But if (rho D_{12})^{(0)} is calculated from eta _{12}^{(0)} using A_{12}^* values for the nonspherical potential, the impact is several percent. Moreover, the experimentally based eta _{12}^{(0)} and (rho D_{12})^{(0)} data agree with theoretically calculated values for the nonspherical potentials.

Revised Enskog theory for Mie fluids: Prediction of diffusion coefficients, thermal diffusion coefficients, viscosities, and thermal conductivities.

Since the 1920s, the Enskog solutions to the Boltzmann equation have provided a route to predicting the transport properties of dilute gas mixtures. At higher densities, predictions have been limited to gases of hard spheres. In this work, we present a revised Enskog theory for multicomponent mixtures of Mie fluids, where the Barker-Henderson perturbation theory is used to calculate the radial distribution function at contact. With parameters of the Mie-potentials regressed to equilibrium properties, the theory is fully predictive for transport properties. The presented framework offers a link between the Mie potential and transport properties at elevated densities, giving accurate predictions for real fluids. For mixtures of noble gases, diffusion coefficients from experiments are reproduced within ±4%. For hydrogen, the predicted self-diffusion coefficient is within 10% of experimental data up to 200 MPa and at temperatures above 171K. Binary diffusion coefficients of the CO2/CH4 mixture from simulations are reproduced within 20% at pressures up to 14.7 MPa. Except for xenon in the vicinity of the critical point, the thermal conductivity of noble gases and their mixtures is reproduced within 10% of the experimental data. For other molecules than noble gases, the temperature dependence of the thermal conductivity is under-predicted, while the density dependence appears to be correctly predicted. Predictions of the viscosity are within ±10% of the experimental data for methane, nitrogen, and argon up to 300bar, for temperatures ranging from 233 to 523K. At pressures up to 500bar and temperatures from 200 to 800K, the predictions are within ±15% of the most accurate correlation for the viscosity of air. Comparing the theory to an extensive set of measurements of thermal diffusion ratios, we find that 49% of the model predictions are within ±20% of the reported measurements. The predicted thermal diffusion factor differs by less than 15% from the simulation results of Lennard-Jones mixtures, even at densities well exceeding the critical density.

On the binary diffusion coefficients of n-alkanes in He/N2

The binary diffusion coefficients of fuel molecules in bath gasses are key parameters for accurate predictions of flame properties such as extinction strain rates. In combustion simulations, they are often calculated using the Hirschfelder-Bird-Spotz (HBS) equation, which requires the availability of effective Lennard-Jones parameters, i.e. collision diameters and well depths, which can be obtained from the intermolecular potentials of two interacting species by applying an orientation-averaging rule. Besides the HBS equation, the Green-Kubo formula can be used to obtain binary diffusion coefficients, using velocity autocorrelation and cross-correlation functions from molecular dynamics simulations. In this work, we propose a new orientation-averaging rule, called VolW-σ-ε, based on the characteristic of intermolecular potentials, and evaluate different approaches to computing the diffusion coefficients of n-alkanes in He/N2 mixtures. Several orientation-averaging rules are evaluated and compared with experimental data of n-alkanes in He and N2 and the results of molecular dynamics simulations. Finally, using the binary diffusion coefficients of n-dodecane in N2 evaluated by the VolW-σ-ε method, we reproduce previously reported experimental extinction strain rates reported for counterflow n-dodecane/N2 versus O2 jets.

Development of machine learning models for the prediction of binary diffusion coefficients of gases

Diffusion coefficient (D12) is an important transport property in the petrochemical and pharmaceutical industries for the design and optimization of processes. The process of measuring the D12 for gas mixtures via an experimental approach is time-consuming and technically challenging. Consequently, many empirical models have been developed to circumvent these challenges. Though these models exhibit good agreement with the experiment, nonetheless, improvement is still needed in terms of increasing the model performance, and the flexibility of their applications because some of these models require extensive calculations to obtain their input parameters. Motivated by this, the work presents a simple and accurate approach for the estimation of diffusion coefficient using machine learning (ML) algorithms. This study employs support vector regression (SVR), Gaussian process regression (GPR), and artificial neural networks (ANN) to estimate the D12 of molecular gas systems over a wide range of temperature (293- 313K), and pressure (0.05–12.0 MPa). The proposed ML models were built using simple descriptors such as temperature, pressure, molar masses of constituent mixtures, and mole fractions of the gases. On the testing dataset, the following overall correlation coefficients were obtained 90.7 %, 99.1 %, and 99.97 % percent for the SVR, GPR, and ANN, respectively. The ANN model did better than the other ML algorithms presented in terms of its generalization capability. The authors believe that the ANN model presented is a viable alternative for the evaluation of the binary diffusion coefficient of gases due to the simplicity of the descriptors.

The evaluation of density and diffusion properties in hydrogen/oxygen mixture modelled by Lennard-Jones fluid

This paper examines the satisfaction of the principle of corresponding states (PCS) on thepressure–density–temperature relation and the binary diffusion coefficient of hydrogen/oxygen mixture modelled as binary Lennard–Jones (LJ) fluid especially in a supercritical region. The hydrogen/oxygen mixture properties were computed by molecular dynamics simulation and compared with simulation results for a nitrogen/oxygen mixture as well as while using the Peng–Robinson (PR) equation of state (EOS) for both mixture types and a mono-component LJ-EOS. The Fuller–Schettler–Giddings model with the PR-EOS and Takahashi’s EOS were used for binary diffusion coefficient comparison. The pseudocritical point concept of a fluid mixture was applied for PCS reduction and PCS satisfaction was conducted over a wide temperature range above the pseudocritical pressure with changing hydrogen molar fraction. PCS satisfaction for hydrogen/oxygen mixture properties was confirmed at reduced temperature of 1.5 or above. At reduced temperature of 1.0 or below, the hydrogen/oxygen mixture properties disagree with those of the comparison mixture because phase separation occurs. We conclude that the properties of hydrogen/oxygen mixtures can be estimated using the pseudocritical point concept and the investigated EOSs based on the PCS in the supercritical region at reduced temperature of1.5 or above.

Thermodynamics and transport properties of valine and cysteine peptides in water

The study of thermodynamic and transport properties of amino acids gives access to knowledge about interactions between distinct molecules necessary to understand a variety of biological processes. In this work, we have performed molecular dynamics simulations of valine and cysteine peptides with lengths of (n) = 1, 2, 4, 8 & 16 monomers in an aqueous environment to estimate the solvation free energy and diffusion coefficients. We modeled our system using OPLS-AA parameter sets and TIP3P water at 310 K temperature. Solvation free energy of both the peptides have been reported using two thermodynamic integration (TI) based methods: TI and TI-CUBIC. The solvation free energy of both the peptides increases with the chain length. The estimated values using both methods are in good agreement with a statistical error of < 3%. The solvent accessible surface area (SASA) of solutes and hydrogen bonds between solute and solvent have also been presented to get more insights on solvation processes. The increase in solvation energy of both peptides with chain length is further corroborated by increase in the number of hydrogen bond (between peptide and water) and SASA with the chain length. In addition, the self diffusion coefficient of both solute and solvent along with their binary diffusion coefficient have been estimated for both the peptides. Furthermore, the effect of chain length on solvation free energy as well as diffusion coefficients have been studied.

Comparison of saturator designs for delivery of low-volatility liquid precursors

Numerous low-volatility precursors are utilized in chemical vapor deposition and atomic layer deposition processes. Such precursors are often delivered from one of two common saturator designs: a bubbler or a flow over vessel. Previous reports concerning precursor delivery from such vessels have focused primarily on continuous delivery of moderate to high volatility liquids and solids. Few reports have focused on cyclical delivery of low volatility precursors at reduced pressures. This lack of knowledge concerning such processes can be a hindrance to efficient selection of deposition conditions and vessel design. The objective of this investigation was to compare the performance of these two saturator designs for pulsed injection at reduced pressures using the low volatility liquid precursor μ2-η2-(tBu-acetylene) dicobalthexacarbonyl (CCTBA). The basis of this comparison was the measurement of CCTBA mass carryover per injection as a function of injection number, injection time, carrier gas flow rate, system pressure, and vessel idle time. The mass carryover was determined from absorbance measurements performed using a non-dispersive infrared gas analyzer. The measured mass carryover for both vessels was compared to the theoretical mass carryover determined using a simple analytical model based upon the “bubbler equation”. In the case of the bubbler, this model described the vessel performance well with knowledge of the precursor vapor pressure and vessel head space pressure. In the case of the flow over vessel, this model described the overall vessel performance poorly unless an additional vessel efficiency factor was included, a factor that is difficult to predict a priori. Furthermore, the efficiency factor was not necessarily constant for a series of injections: the efficiency factor tended to decrease from the first injection until a stable value was achieved, a value that depended on the process conditions. This limitation of the model was attributed to the specific flow dynamics associated with the flow over vessel design. Computational fluid dynamics simulations were able to reproduce the mass carryover of the flow over vessel, after estimating the CCTBA-carrier gas binary diffusion coefficient. These simulations also showed that a larger binary diffusion coefficient and a higher vapor pressure both led to an increase in mass carryover but vessel efficiency could not equal that of the bubbler. While these results were obtained with CCTBA, the general relationships between mass carryover and the various process parameters in these saturators are expected to be similar for other low-volatility precursors.

Binary Diffusion Coefficients for Short Chain Alcohols in Supercritical Carbon Dioxide—Experimental and Predictive Correlations

Experimental binary diffusion coefficients for short-chain alcohols in supercritical carbon dioxide were measured using the Taylor dispersion technique in a temperature range of 306.15 K to 331.15 K and along the 10.5 MPa isobar. The obtained diffusion coefficients were in the order of 10-8 m2 s-1. The dependence of D on temperature and solvent density was examined together with the influence of molecular size. Some classic correlation models based on the hydrodynamic and free volume theory were used to estimate the diffusion coefficients in supercritical carbon dioxide. Predicted values were generally overestimated in comparison with experimental ones and correlations were shown to be valid only in high-density regions.

Modeling of nonequilibrium processes behind a shock wave in a mixture of carbon dioxide and argon

A closed self-consistent model of a nonequilibrium flow of a mixture of carbon dioxide and argon behind the front of a plane shock wave is developed. The generalized Chapman - Enskog method is used in the three-temperature approach, taking into account various channels of vibrational relaxation in a carbon dioxide molecule. An extended system of Navier - Stokes - Fourier equations is written, consisting of the equations of conservation of mass, momentum and energy, supplemented by the diffusion equations of the mixture components and relaxation equations for the vibrational modes of the CO2 molecule. The closing relations for the stress tensor, diffusion velocity, heat flux and vibrational energy fluxes are obtained. An algorithm for calculating the coefficients of shear and bulk viscosity, thermal conductivity of various degrees of freedom, diffusion and thermal diffusion has been developed and implemented. The model was validated by comparison with experimental data for the viscosity and thermal conductivity of carbon dioxide and argon, as well as for the binary diffusion coefficient. Satisfactory agreement with the experiment was obtained. The dependence of the transport coefficients on the gas temperature, temperatures of vibrational modes and mixture composition is analyzed. The developed model is ready for use in numerical simulation of shock waves in a mixture of CO2-Ar.

Determination of diffusion coefficients of mercury atoms in various gases from longitudinal spin relaxation in magnetic gradients

We present a method to measure the binary diffusion coefficient of mercury atoms in a gas at room temperature and low pressure. It is based on the measurement of the longitudinal spin relaxation of optically pumped mercury-199 atoms in a magnetic field gradient. We provide a consistent set of diffusion coefficients for helium-3, helium-4, argon, krypton, xenon, nitrogen, carbon dioxide, oxygen, and air.