Thermal Diffusion Factor Research Articles

Calculation of the transport properties of dilute gas mixtures on the basis of model potentials. Mercury–argon system

Interatomic potentials V(Hg–Hg), V(Ar–Ar), and V(Hg–Ar) of atoms in their ground electronic state are analyzed for the technically important mercury–argon dilute gas mixture. The collision integrals are calculated for these potentials, and the transport properties of mercury, argon, and their mixture, such as, viscosity, thermal conductivity, and self-diffusion and mutual diffusion coefficients of compounds, are determined using the molecular-kinetic theory relationships. Detailed tables of properties on five isotherms within a range of 300–2000 K and mixture concentrations of 0.001–0.999 are given. Tables of the properties also contain thermal diffusion factors and Prandtl (Pr) and Schmidt (Sc) numbers. Some specific features in the behavior of properties depending on the composition are considered.

Statistical thermodynamics of thermal diffusion factors in binary hydrocarbon mixtures – an application

ABSTRACTThermal diffusion factors play key roles in the analysis of composition variation of the mixture components in hydrocarbon reservoirs and to ensure reliable formation fluid evaluation. This paper presents the statistical thermodynamics of thermal diffusion factors of binary hydrocarbon systems using the modified theory of linear transport. The theory is revised to include the effect of pressure and unlike interaction parameters in calculating the unlike collision integrals and account for the explicit effects of the intermolecular interactions, molecular mass, energy and size parameters. The dependence of the diffusion factors on temperature, pressure and composition of the mixtures is investigated in a systematic way. Comparisons of calculated results with experimental data show that the revised theory could predict the thermal diffusion factors of binary nonhydrocarbon gas mixtures and liquid hydrocarbon mixtures very well over a range of temperature and pressure including the reservoir conditions.

Determination of the potential energy surfaces of refrigerant mixtures and their gas transport coefficients

In this work, the inversion scheme was used to determine the potential energy surfaces of five polar refrigerant mixtures. The systems studied here are R123-R134a, R123-R142b, R123-R152a, R142b-R134a, and R142b-R152a. The low density transport coefficients of the refrigerant mixtures were calculated from the new invert potentials by the classical kinetic theory. The viscosity coefficient, binary diffusion coefficient, and thermal diffusion factor were computed for the temperature range from 313.15-973.15 K. The agreement with the NIST viscosity data demonstrates that the present calculated values are accurate enough to supplement experimental data over an extended temperature range. Correlations of the transport properties were also provided for the refrigerant mixtures at equimolar ratios.

Ab Initio Values of the Gas Transport Properties of Hydrogen Isotopologues and Helium–Hydrogen Mixtures at Low Density

We employed the classical kinetic theory to calculate transport properties as a function of temperature for hydrogen isotopologues and helium–hydrogen mixtures. The viscosity, thermal conductivity, diffusion coefficient, and thermal diffusion factor were computed at low density and over a wide temperature range from 298 to 2000 K. The calculation utilized the spherically symmetric versions of the latest ab initio potentials for the interactions of the like and unlike gas molecules. The computed values are generally consistent with the limited experimental data for HD, 4He–H2, 4He–D2, 4He–HD, 3He–H2, 3He–D2, H2–HD, and D2–HD. Our results provide reliable transport property data for the considered species at temperatures where experimental information is absent.

Transport coefficients of helium-argon mixture based on ab initio potential.

The viscosity, thermal conductivity, diffusion coefficient, and thermal diffusion factor of helium-argon mixtures are calculated for a wide range of temperature and for various mole fractions up to the 12th order of the Sonine polynomial expansion with an ab initio intermolecular potential. The calculated values for these transport coefficients are compared with other data available in the open literature. The comparison shows that the obtained transport coefficients of helium-argon mixture have the best accuracy for the moment.

Accurate ab initio potential for the krypton dimer and transport properties of the low-density krypton gas.

A new highly accurate potential energy curve for the krypton dimer was constructed using coupled-cluster calculations up to the singles, doubles, triples, and perturbative quadruples level, including corrections for core-core and core-valence correlation and for relativistic effects. The ab initio data points were fitted to an analytic potential which was used to compute the most important transport properties of the krypton gas. The viscosity, thermal conductivity, self-diffusion coefficient, and thermal diffusion factor were calculated by the kinetic theory at low density and temperatures from 116 to 5000 K. The comparisons with literature experimental data as well as with values from other pair potentials indicate that our new potential is superior to all previous ones. The transport property values computed in this work are recommended as standard values over the complete temperature range.

Recommended gas transport properties of argon at low density using ab initio potential

The most important transport properties of argon have been calculated using classical kinetic theory expressions in conjunction with high-quality ab initio potential energy values computed by Patkowski and Szalewicz. Dilute gas transport properties have been calculated for the viscosity, thermal conductivity, self-diffusion coefficient and thermal diffusion factor from 83 to 10,000 K. Comparisons between experimental transport property data and values presently calculated indicate that the present theoretical predictions may be employed as recommended values for this set of transport properties over a wide temperature range.

Experimental Study of Thermal Diffusion in Multicomponent Gaseous Systems

Thermal diffusion factor (TDF) measurements were performed for one quaternary, for four ternary, and for six binary gaseous systems, containing \(\hbox {H}_{2}, \, \hbox {CH}_{4}, \, \hbox {N}_{2}\), and \(\hbox {CO}_{2}\) held under atmospheric pressure and at cold- and hot-chamber temperatures of \(T_{1}\) = 280 K and \(T_{2}\) = 800 K, respectively. For the multicomponent gas mixtures, measurements were made at different values of the mole fraction of the additive. Also, the dependence of the TDF values on the mole fraction of the additive for the multicomponent mixtures was analyzed. A semi-empirical formula to calculate TDF values was proposed; this formula gives results that are in good agreement with experimental data within the respective limits of error.

The Effect of Thermal Diffusion on Decarburization Kinetics

The influence of thermal diffusion on the kinetics of decarburization of Fe-Cr-C droplets with CO2-Ar gas mixtures was investigated. With incorporation of the effect of thermal diffusion, a new correlation has been proposed to express the decarburization kinetics of levitated droplets for flows in the range of Reynolds number between 2 and 100. A thermal diffusion factor of 0.228 was evaluated for CO2-Ar gas mixtures at 1873 K (1600 °C).

Non-equilibrium molecular dynamics simulation of thermal conductivity and thermal diffusion of binary mixtures confined in a nanochannel

In this paper, direct non-equilibrium molecular dynamics simulation is developed to investigate thermal conductivity and thermal diffusion factors of confined binary mixtures of methane and some n-alkanes in a nanochannel. We used two thermal walls in different temperatures to impose temperature gradient in the system. The mixtures are confined between two parallel atomic walls, normal to temperature gradient. Simulation results show high inhomogeneity and layering in the mixtures. Thermal conductivity of mixtures increases with decreasing the channel width and increases in mixtures with high concentration of methane. Except for very small channels, confinement has minimal effect on thermal diffusion. In very narrow channels, thermal diffusion is small and it reaches a steady state value with increasing the channel width. Local velocity fields for two different channels also show different behaviors. In relatively large channels some convection patterns are observed in mixtures.

Highly accurate transport properties of helium-4, helium-3, and their binary mixtures by ab initio potential

A helium–helium interatomic potential determined from quantum–mechanical ab initio calculations by Przybytek et al. has been used in the framework of the classical kinetic theory to calculate the transport properties of helium. The viscosity, thermal conductivity, diffusion coefficient, and thermal diffusion factor were calculated for helium-4, helium-3, and their binary mixtures at low density between 100 and 10,000K. The predicted results of this work are listed in the Appendix, which are more accurate than the corresponding measured quantities over a wide temperature range.

A self-propelled thermophoretic microgear.

An asymmetric microgear will spontaneously and unidirectionally rotate if it is heated in a cool surrounding solvent. The resulting temperature gradient along the edges of the gear teeth translates in a directed thermophoretic force, which will exert a net torque on the gear. By means of computer simulations, the validity of this scenario is proved. The rotational direction and speed are dependent on gear–solvent interactions, and can be analytically related to system parameters like the thermal diffusion factor, the solvent viscosity, or the temperature difference. This microgear provides a simple way to extract net work from non-isothermal solutions, and can become a valuable tool in microfluids.

Diffusion transport coefficients for granular binary mixtures at low density: Thermal diffusion segregation

The mass flux of a low-density granular binary mixture obtained previously by solving the Boltzmann equation by means of the Chapman-Enskog method is considered further. As in the elastic case, the associated transport coefficients D, Dp, and D′ are given in terms of the solutions of a set of coupled linear integral equations which are approximately solved by considering the first and second Sonine approximations. The diffusion coefficients are explicitly obtained as functions of the coefficients of restitution and the parameters of the mixture (masses, diameters, and concentration) and their expressions hold for an arbitrary number of dimensions. In order to check the accuracy of the second Sonine correction for highly inelastic collisions, the Boltzmann equation is also numerically solved by means of the direct simulation Monte Carlo (DSMC) method to determine the mutual diffusion coefficient D in some special situations (self-diffusion problem and tracer limit). The comparison with DSMC results reveals that the second Sonine approximation to D improves the predictions made from the first Sonine approximation. We also study the granular segregation driven by a uni-directional thermal gradient. The segregation criterion is obtained from the so-called thermal diffusion factor Λ, which measures the amount of segregation parallel to the temperature gradient. The factor Λ is determined here by considering the second-order Sonine forms of the diffusion coefficients and its dependence on the coefficients of restitution is widely analyzed across the parameter space of the system. The results obtained in this paper extend previous works carried out in the tracer limit (vanishing mole fraction of one of the species) by some of the authors of the present paper.

Molecular dynamics simulation of thermodiffusion and mass diffusion in structureless and atomistic micropores

In this work, we have studied the effect of surface roughness on thermodiffusion in simple “isotopic” mixtures confined in a slit nanopore. To do so, we have performed non-equilibrium molecular dynamics simulations of Lennard–Jones binary equimolar mixtures confined in structureless (in which the interaction with the fluid is described by a Lennard–Jones 9–3 potential) and atomistic walls for various widths, from 5 to 35 times the size of a molecule, in the NP//T ensemble. For that purpose, a new algorithm is proposed in atomistic pore. Different super-critical conditions have been explored, ranging from low to moderate densities. In addition to the thermal diffusion factor, we have also estimated the mass diffusion and thermodiffusion coefficients separately. The results show that the two types of walls lead to noticeably different results. The thermal diffusion factor tends to increase in atomistic wall and slightly decrease in structureless wall when the pore width is decreasing, this being related to the average density behaviour. More precisely, both mass and thermodiffusion coefficients are weakly affected by the pore width for structureless walls, whereas both quantities largely decrease (up to 70% and 55% respectively compared to bulk fluid) when pore size decreases in the case of a rough solid surface because of the friction on the walls.

Thermal diffusion factor of Stockmayer mixtures: A non-equilibrium molecular dynamic study

Thermal diffusion factors (TDFs) in binary Stockmayer model mixtures as well as real mixtures of four refrigerants with N2 and CO have been calculated by NEMD simulations. The results of the model mixtures show that the TDF increases with the two component dipole moment ratio, however it is not a sensitive function of the ratio of the moment of inertia and the intermolecular cutoff distance. The calculated TDFs in N2/CO–refrigerants mixtures were equal for less polar refrigerants, however the TDFs of CO mixtures increase more than that of the N2 mixtures with the dipole strength of the refrigerant.

Multiproperty empirical isotropic interatomic potentials for CH4–inert gas mixtures

An approximate empirical isotropic interatomic potentials for CH4–inert gas mixtures are developed by simultaneously fitting the Exponential-Spline-Morse-Spline-van der Waals (ESMSV) potential form to viscosity, thermal conductivity, thermal diffusion factors, diffusion coefficient, interaction second pressure virial coefficient and scattering cross-section data. Quantum mechanical lineshapes of collision-induced absorption (CIA) at different temperatures for CH4–He and at T=87K for CH4–Ar are computed using theoretical values for overlap, octopole and hexadecapole mechanisms and interaction potential as input. Also, the quantum mechanical lineshapes of collision-induced light scattering (CILS) for the mixtures CH4–Ar and CH4–Xe at room temperature are calculated. The spectra of scattering consist essentially of an intense, purely translational component which includes scattering due to free pairs and bound dimers, and the other is due to the induced rotational scattering. These spectra have been interpreted by means of pair-polarizability terms, which arise from a long-range dipole-induced-dipole (DID) with small dispersion corrections and a short-range interaction mechanism involving higher-order dipole–quadrupole A and dipole–octopole E multipole polarizabilities. Good agreement between computed and experimental lineshapes of both absorption and scattering is obtained when the models of potential, interaction-induced dipole and polarizability components are used.

Multiscale Macromolecular Simulation: Role of Evolving Ensembles

Multiscale analysis provides an algorithm for the efficient simulation of macromolecular assemblies. This algorithm involves the coevolution of a quasiequilibrium probability density of atomic configurations and the Langevin dynamics of spatial coarse-grained variables denoted order parameters (OPs) characterizing nanoscale system features. In practice, implementation of the probability density involves the generation of constant OP ensembles of atomic configurations. Such ensembles are used to construct thermal forces and diffusion factors that mediate the stochastic OP dynamics. Generation of all-atom ensembles at every Langevin time step is computationally expensive. Here, multiscale computation for macromolecular systems is made more efficient by a method that self-consistently folds in ensembles of all-atom configurations constructed in an earlier step, history, of the Langevin evolution. This procedure accounts for the temporal evolution of these ensembles, accurately providing thermal forces and diffusions. It is shown that efficiency and accuracy of the OP-based simulations is increased via the integration of this historical information. Accuracy improves with the square root of the number of historical timesteps included in the calculation. As a result, CPU usage can be decreased by a factor of 3-8 without loss of accuracy. The algorithm is implemented into our existing force-field based multiscale simulation platform and demonstrated via the structural dynamics of viral capsomers.

Ab initiosimulation of transport phenomena in rarefied gases

Ab initio potentials are implemented into the direct simulation Monte Carlo (DSMC) method. Such an implementation allows us to model transport phenomena in rarefied gases without any fitting parameter of intermolecular collisions usually extracted from experimental data. Applying the method proposed by Sharipov and Strapasson [Phys. Fluids 24, 011703 (2012)], the use of ab initio potentials in the DSMC requires the same computational efforts as the widely used potentials such as hard spheres, variable hard sphere, variable soft spheres, etc. At the same time, the ab initio potentials provide more reliable results than any other one. As an example, the transport coefficients of a binary mixture He-Ar, viz., viscosity, thermal conductivity, and thermal diffusion factor, have been calculated for several values of the mole fraction.

Gaseous transport properties of hydrogen, deuterium and their binary mixtures from ab initio potential

A spherically symmetric representation of the ab initio potential, developed by K. Patkowski, W. Cencek, P. Jankowski, K. Szalewicz, J.B. Mehl, G. Garberoglio and A.H. Harvey, J. Chem. Phys. 129, 094304 (2008) [16], has been used to calculate transport properties of hydrogen, deuterium and their binary mixtures by means of the classical kinetic theory. Results are reported for viscosity, thermal conductivity, diffusion coefficient and thermal diffusion factor in the dilute-gas limit for temperatures ranging from 298 to 2000 K. Available experimental data have been investigated and compared with the theoretically calculated values to check the quality of this work. Reasonable agreements show that the high-quality potential is effective in accurately predicting transport properties of hydrogen, deuterium and their binary mixtures, which can provide useful support to experimental measurements over a wide temperature range.

Modeling Transport Properties of N2–Noble Gas Mixtures at Low and Moderate Densities

Abstract In the present paper, the unlike interaction potential energies of some nitrogen-based mixtures were determined via the inversion of reduced viscosity collision integrals and fitted to obtain analytical potential energy forms. The potentials were then applied to Schreiber et al.’s and Chapman–Enskog’s theories to calculate, respectively, the low-density thermal conductivity and other remaining transport properties of the studied mixtures. Further the calculated potential energies were applied to the Vesovic–Wakeham (VW) scheme to predict viscosity of aforementioned mixtures at moderate density. Our estimated average absolute deviation (AAD) for dilute transport properties calculated from the Chapman–Enskog (CE) method is at most to within ±1.5% for the viscosity, ±5% for the diffusion coefficient and ±25% for the thermal diffusion factor. Further, the AAD associated with the dilute thermal conductivity is of the order of ±7% using the Schreiber et al. method. As mentioned above, the calculated unlike interaction energies as well as the low-density interaction viscosity values, were employed then to predict high density viscosities using the VW scheme. The Peng–Robinson equation of state was chosen to calculate the mixture densities required by the Vesovic–Wakeham method. The obtained viscosities in the dense regime deviate from the literature data to within ±2%.