Thermal Diffusion Factor Research Articles

Transport properties of a binary mixture of CO2—N2 from the pair potential energy functions based on a semi-empirical inversion method

The potential energy surface of a CO2—N2 mixture is determined by using an inversion method, together with a new collision integral correlation [J. Phys. Chem. Ref. Data 19 1179 (1990)]. With the new invert potential, the transport properties of CO2—N2 mixture are presented in a temperature range from 273.15 K to 3273.15 K at low density by employing the Chapman—Enskog scheme and the Wang Chang—Uhlenbeck—de Boer theory, consisting of a viscosity coefficient, a thermal conductivity coefficient, a binary diffusion coefficient, and a thermal diffusion factor. The accuracy of the predicted results is estimated to be 2% for viscosity, 5% for thermal conductivity, and 10% for binary diffusion coefficient.

Segregation of an intruder in a heated granular dense gas

A recent segregation criterion [Phys. Rev. E 78, 020301(R) (2008)] based on the thermal diffusion factor Λ of an intruder in a heated granular gas described by the inelastic Enskog equation is revisited. The sign of Λ provides a criterion for the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE). The present theory incorporates two extra ingredients not accounted for by the previous theoretical attempt. First, the theory is based upon the second Sonine approximation to the transport coefficients of the mass flux of the intruder. Second, the dependence of the temperature ratio (intruder temperature over that of the host granular gas) on the solid volume fraction is taken into account in the first and second Sonine approximations. In order to check the accuracy of the Sonine approximation considered, the Enskog equation is also numerically solved by means of the direct simulation Monte Carlo method to get the kinetic diffusion coefficient D(0). The comparison between theory and simulation shows that the second Sonine approximation to D(0) yields an improvement over the first Sonine approximation when the intruder is lighter than the gas particles in the range of large inelasticity. With respect to the form of the phase diagrams for the BNE-RBNE transition, the kinetic theory results for the factor Λ indicate that while the form of these diagrams depends sensitively on the order of the Sonine approximation considered when gravity is absent, no significant differences between both Sonine solutions appear in the opposite limit (gravity dominates the thermal gradient). In the former case (no gravity), the first Sonine approximation overestimates both the RBNE region and the influence of dissipation on thermal diffusion segregation.

Thermal segregation of intruders in the Fourier state of a granular gas

A low density binary mixture of granular gases is considered within the Boltzmann kinetic theory. One component, the intruders, is taken to be dilute with respect to the other, and thermal segregation of the two species is described for a special solution to the Boltzmann equation. This solution has a macroscopic hydrodynamic representation with a constant temperature gradient and is referred to as the Fourier state. The thermal diffusion factor characterizing conditions for segregation is calculated without the usual restriction to Navier-Stokes hydrodynamics. Integral equations for the coefficients in this hydrodynamic description are calculated approximately within a Sonine polynomial expansion. Molecular dynamics simulations are reported, confirming the existence of this idealized Fourier state. Good agreement is found for the predicted and simulated thermal diffusion coefficient, while only qualitative agreement is found for the temperature ratio.

Transport properties of mixtures of rarefied gases. Hydrogen–methane system

An analysis and generalization of experimental data on transport properties based on the relations of molecular-kinetic theory and three-parameter interaction potentials of the Lennard-Jones (m–6) family have been performed for the mixture of rarefied neutral gases "hydrogen–methane." Nine parameters of the potentials have been restored in joint data processing using the weight nonlinear least-squares method. Tables of reference data for viscosity, the interdiffusion coefficient, and the thermal diffusion factor have been calculated in the temperature interval 200–1500 K. Errors of reference data in the entire interval of concentrations, including those of pure components, have been evaluated using the matrix of parametric errors.

Calculations of the thermophysical properties of binary mixtures of noble gases at low density from ab initio potentials

Interaction potentials determined ab initio from quantum mechanics were used to calculate the thermophysical properties of six binary mixtures of noble gases: helium–neon, helium–argon, helium–krypton, neon–argon, neon–krypton and argon–krypton. From the ab initio potentials, the second pressure virial coefficient, the binary diffusion coefficient and the thermal diffusion factor were computed for the considered binary mixtures at low density in the temperature range 100–5000 K employing well-established formulas in statistical thermodynamics and the kinetic theory of dilute gases. In all cases, while not as good as that for pure noble gases, close agreement between experimental data and the theoretically calculated values shows that ab initio potentials are reliable for the calculation of accurate thermophysical properties of binary mixtures of noble gases over a wide temperature range.

Thermal diffusion segregation in granular binary mixtures described by the Enskog equation

The diffusion induced by a thermal gradient in a granular binary mixture is analyzed here in the context of the (inelastic) Enskog equation. Although the Enskog equation neglects velocity correlations among particles that are about to collide, it retains the spatial correlations arising from volume exclusion effects and thus is expected to be applicable for moderate densities. In the steady state with gradients only along a given direction, a segregation criterion is obtained from the thermal diffusion factor Λ by measuring the amount of segregation parallel to the thermal gradient. As expected, the sign of the factor Λ provides a criterion for the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the parameters of the mixture (the masses and sizes of particles, concentration, solid volume fraction and coefficients of restitution). The form of the phase diagrams for the BNE/RBNE transition is illustrated in detail for several systems, with special emphasis on the significant role played by the inelasticity of collisions. In particular, an effect already found in dilute gases (segregation in a binary mixture of identical masses and sizes but different coefficients of restitution) is extended to dense systems. A comparison with recent computer simulation results reveals good qualitative agreement at the level of the thermal diffusion factor. The present analysis generalizes to arbitrary concentration previous theoretical results derived in the tracer limit case.

Thermal segregation beyond Navier–Stokes

A dilute suspension of impurities in a low-density gas is described by the Boltzmann and Boltzman–Lorentz kinetic theories. Scaling forms for the species distribution functions allow the determination of the space dependence of the hydrodynamic fields without restriction to small thermal gradients or Navier–Stokes hydrodynamics. The thermal diffusion factor characterizing segregation is identified in terms of collision integrals as a function of the mechanical properties of the particles and the temperature gradient. An evaluation of the collision integrals using Sonine polynomial approximations is discussed. The conditions for segregation both along and opposite to the temperature gradient are obtained and contrasted with the leading order Navier–Stokes approximation.

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%.

Diffusion correction and thermal diffusion factors of ions in the ionosphere and plasmasphere

Diffusion equations determining ion diffusion velocities along magnetic field lines in the multicomponent ionosphere and plasmasphere composed of ions, electrons, and neutral species are derived from Grad’s 13-moment equations for average species velocities and heat flows. The general expressions for thermal diffusion and diffusion correction factors of an ion are simplified for the following cases of a multicomponent partially ionized plasma: (1) a major ion, a minor ion, electrons, and neutral species; (2) three major O +, H +, and He + ions, electrons, and neutral species; (3) two major O + and H + ions, a minor ion, electrons, and neutral species. The ion thermal diffusion and diffusion correction factors calculated for O +, H +, and He + ions of a fully ionized plasma are approximated by the analytical formulas as functions of [O +]/[H +] while changing the ratio of [He +] to ([O +] + [H +] + [He +]) between 0.01 and 0.9. A fully ionized plasma composed of two major ion species, O + and H +, electrons, and a minor ion component, x, where x stands for NO +, N 2 + , O 2 + , H 2 + , N +, O ++, N ++, Fe +, Mg +, Na +, Ca +, Al +, and Si + is considered to calculate the thermal diffusion and diffusion correction factors of each minor ion. Analytical approximating relationships of these thermal diffusion and diffusion correction factors with the [O +]/[H +] ratio are presented for use in ionospheric models.

Generalization and calculation of the thermal diffusion factor of binary hydrogen-containing gaseous mixtures

The results of generalization of experimental data on the thermal diffusion factor α T of hydrogen-containing gaseous mixtures within the framework of similarity theory have been given. The calculated relation which makes it possible to predict the thermal diffusion factor of hydrogen-containing mixtures of nonpolar gases with a limited body of data on the substance has been obtained. The α T values of mixtures of hydrogen with inert gases, including radon Rn, and with N2, SiH4, and GeH4 in the temperature interval 100–1500 K have been calculated.

Prediction of thermophysical properties of pure noble gases

The thermophysical properties of pure helium-4, neon, argon, krypton and xenon are calculated using ab initio potentials of kinetic theory over the temperature range from 50 to 5000 K at zero-density, including the second virial coefficient, thermal diffusion coefficient and thermal diffusion factor. Comparing with results obtained by empirical potentials, the results of present work are in better agreement with experimental data and recommended values of REFPROP 8.0.

Impact of Thermodiffusion on Carbon Nanotube Growth by Chemical Vapor Deposition

Thermal diffusion, the process by which a multicomponent mixture develops a concentration gradient when exposed to a temperature gradient, has been studied in order to understand if its inclusion is warranted in the modeling of single-wall carbon nanotubes (SWNTs) synthesis by thermal chemical vapor deposition (CVD). A fully coupled reactor-scale model employing conservation of mass, momentum, species, and energy equations with detailed gas phase and surface reaction mechanisms has been utilized to describe the evolution of hydrogen and hydrocarbon feed streams as they undergo transport, as well as homogeneous and heterogeneous chemical reaction within a CVD reactor. Steady state velocity, temperature, and concentration fields within the reactor volume are determined, as well as concentrations of adsorbed species and SWNT growth rates. The effect of thermodiffusion in differing reactor conditions has been investigated to understand the impact on SWNT growth. Thermal diffusion can have a significant impact on SWNT growth, and the first approximation of the thermal diffusion factor, based on the Chapman–Enskog molecular theory, is sufficient for modeling thermophoretic behavior within a CVD reactor. This effect can be facilitatory or inhibitory, based on the thermal and mass flux conditions. The results of this investigation are useful in order to optimize model and reactor designs to promote optimal SWNT deposition rates.

Transport Properties in Gases at High Temperature and Low Pressure: Comparison of Kinetic Theory with Direct Simulation Monte Carlo

Expressions for the transport coefficients obtained from the Gross-Jackson and the Chapman–Enskog methods are used to derive explicit relations incorporating the internal energy of the molecules for pure polyatomic gases and for binary mixtures of gases. Various coefficients such as the binary diffusion, thermal conductivity, and the viscosity coefficients and the thermal diffusion factor are calculated and a comparison with the direct simulation Monte Carlo (DSMC) method is carried out. The results show that the contribution of the internal energy is important and cannot be neglected.

An exchange-Coulomb model potential energy surface for the Ne–CO interaction. II. Molecular beam scattering and bulk gas phenomena in Ne–CO mixtures

Four potential energy surfaces are of current interest for the Ne-CO interaction. Two are high-level fully ab initio surfaces obtained a decade ago using symmetry-adapted perturbation theory and supermolecule coupled-cluster methods. The other two are very recent exchange-Coulomb (XC) model potential energy surfaces constructed by using ab initio Heitler-London interaction energies and literature long range dispersion and induction energies, followed by the determination of a small number of adjustable parameters to reproduce a selected subset of pure rotational transition frequencies for the (20)Ne-(12)C(16)O van der Waals cluster. Testing of the four potential energy surfaces against a wide range of available experimental microwave, millimeter-wave, and mid-infrared Ne-CO transition frequencies indicated that the XC potential energy surfaces gave results that were generally far superior to the earlier fully ab initio surfaces. In this paper, two XC model surfaces and the two fully ab initio surfaces are tested for their abilities to reproduce experiment for a wide range of nonspectroscopic Ne-CO gas mixture properties. The properties considered here are relative integral cross sections and the angle dependence of rotational state-to-state differential cross sections, rotational relaxation rate constants for CO(v=2) in Ne-CO mixtures at T=296 K, pressure broadening of two pure rotational lines and of the rovibrational lines in the CO fundamental and first overtone transitions at 300 K, and the temperature and, where appropriate, mole fraction dependencies of the interaction second virial coefficient, the binary diffusion coefficient, the interaction viscosity, the mixture shear viscosity and thermal conductivity coefficients, and the thermal diffusion factor. The XC model potential energy surfaces give results that lie within or very nearly within the experimental uncertainties for all properties considered, while the coupled-cluster ab initio surface gives results that agree similarly well for all but one of the properties considered. When the present comparisons are combined with the ability to give accurate spectroscopic transition frequencies for the Ne-CO van der Waals complex, only the XC potential energy surfaces give results that agree well with all extant experimental data for the Ne-CO interaction.

Prediction of transport properties of O2-CO2 mixtures based on the inversion method

A new potential energy surface of O2-CO2 mixtures was obtained by means of inversion method. According to the kinetic theory of gas,the transport properties of O2-CO2 mixtures,including viscosity coefficient,thermal diffusion coefficient and thermal diffusion factor, were caluclated in the temperature range between 273.15 K and 3273.15 K at zero-density.

Dynamic thermodiffusion theory for ternary liquid mixtures

Following the non-equilibrium thermodynamics approach, we develop expressions for the calculation of the thermal diffusion coefficients in a ternary system. On the basis of some physical justifications, we approximate the net heat of transport with the activation energy of viscous flow. In parallel, we revisit the Kempers model and propose new expressions for the estimation of the thermal diffusion factors in a ternary mixture. The proposed expressions are based on a dynamic modeling approach, as they incorporate the activation energy of viscous flow, which is a fluid flow property and contains the effects of some of the parameters that govern thermodiffusion. The proposed expressions, the Kempers and Ghorayeb–Firoozabadi–Shukla models are evaluated against the experimental data. Our expression which was developed on the basis of the Kempers approach has the best performance.

Microscopic study and modeling of thermodiffusion in binary associating mixtures

Thermodiffusion in associating mixtures is a complex phenomenon, owing to the strong dependence of the molecular structure of such mixtures on concentration. In this paper, we attempt to elucidate this phenomenon and propose a qualitative mechanism for the separation of species in binary associating mixtures. A correlation between the sign change in the thermal diffusion factor and a change in the molecular structure, mixture viscosity, and the excess entropy of mixing in such mixtures is established. To quantify this correlation, we modify our recently developed dynamic model based on the Drickamer nonequilibrium thermodynamic approach [M. Eslamian and M. Z. Saghir, Phys. Rev. E 80, 011201 (2009)] and propose expressions for the estimation of thermal diffusion factor in binary associating mixtures. The prediction power of the proposed expressions, as well as other widely used models, are examined against the experimental data. The proposed theoretical expressions are self-contained and only rely on the viscosity data as input and predict a sign change in the thermal diffusion factor in associating mixtures.

Calculation of Transport Properties of CF 4+Noble Gas Mixtures

The present work is concerned with determining the viscosity, diffusion, thermal diffusion factor and thermal conductivity of five equimolar binary gas mixtures including: CF 4-He, CF 4-Ne, CF 4-Ar, CF 4-Kr, CF 4-Xe from the principle of corresponding states of viscosity by the inversion technique. The Lennard-Jones (12-6) model potential is used as the initial model potential. The calculated interaction potential energies obtained from the inversion procedure is employed to reproduce the viscosities, diffusions, thermal diffusion factors, and thermal conductivities. The accuracies of the calculated viscosity and diffusion coefficients were 1% and 4%, respectively.

Transport properties in mixtures involving carbon dioxide at low and moderate density: test of several intermolecular potential energies and comparison with experiment

It is the purpose of this paper to extract unlike intermolecular potential energies of five carbon dioxide-based binary gas mixtures including CO2–He, CO2–Ne, CO2–Ar, CO2–Kr, and CO2–Xe from viscosity data and compare the calculated potentials with other models potential energy reported in literature. Then, dilute transport properties consisting of viscosity, diffusion coefficient, thermal diffusion factor, and thermal conductivity of aforementioned mixtures are calculated from the calculated potential energies and compared with literature data. Rather accurate correlations for the viscosity coefficient of afore-cited mixtures embracing the temperature range 200 K < T < 3273.15 K is reproduced from the present unlike intermolecular potentials energy. Our estimated accuracies for the viscosity are to within ±2%. In addition, the calculated potential energies are used to present smooth correlations for other transport properties. The accuracies of the binary diffusion coefficients are of the order of ±3%. Finally, the unlike interaction energy and the calculated low density viscosity have been employed to calculate high density viscosities using Vesovic–Wakeham method.

Dynamic thermodiffusion model for binary liquid mixtures

Following the nonequilibrium thermodynamics approach, we develop a dynamic model to emulate thermo-diffusion process and propose expressions for estimating the thermal diffusion factor in binary nonassociating liquid mixtures. Here, we correlate the net heat of transport in thermodiffusion with parameters, such as the mixture temperature and pressure, the size and shape of the molecules, and mobility of the components, because the molecules have to become activated before they can move. Based on this interpretation, the net heat of transport of each component can be somehow related to the viscosity and the activation energy of viscous flow of the same component defined in Eyring's reaction-rate theory [S. Glasstone, K. J. Laidler, and H. Eyring, (McGraw-Hill, New York, 1941)]. This modeling approach is different from that of Haase and Kempers, in which thermodiffusion is considered as a function of the thermostatic properties of the mixture such as enthalpy. In simulating thermodiffusion, by correlating the net heat of transport with the activation energy of viscous flow, effects of the above mentioned parameters are accounted for, to some extent of course. The model developed here along with Haase-Kempers and Drickamer-Firoozabadi models linked with the Peng-Robinson equation of sate are evaluated against the experimental data for several recent nonassociating binary mixtures at various temperatures, pressures, and concentrations. Although the model prediction is still not perfect, the model is simple and easy to use, physically justified, and predicts the experimental data very good and much better than the existing models.