Thermal Diffusion Factor Research Articles

Diffusion-thermo and thermo-diffusion impacts on MHD natural convection flow of maxwell nanofluids over a stretching sheet

The present study carried out significant importance in its magnetic field and crosswise diffusion influenced the Maxwell nanofluid flow past a nonlinear stretching sheet. This investigation aimed to shed light on the behavior of critical parameters, particularly in the presence of thermophoresis and Brownian motion. The primary aim is to investigate the impact of thermal diffusion, diffusion-thermo, and various influencing factors on a Maxwell nanofluid near a stretching sheet in the magnetic field, and the impact of three distinct slip conditions (velocity, thermal, and solutal). The partial differential equations by the nonlinear coefficients are utilized in obtaining the most important equations. These equations are distorting to beneficial nonlinear ordinary differential equations making use of the appropriate transformations variables and transformation coefficients. To investigating the computational solutions for the reducing sets of the nonlinear ordinary differential equations, these were developing and utilized the Keller box methodology. The simulations are carried out the nanofluids velocity, temperature, concentration, skin friction coefficients, the rate of temperature transport, in addition to the rate of mass transportation, amongst previous variables. The validations of this methodology are displayed via the comparison of the present outputs through the preceding judgments into the literatures. The major conclusions drawn from this study are the concentration profiles exhibited opposing behaviours as concentration slip parameter increased. However, the temperature profile increases for Brownian motion parameter and thermophoresis parameter parameters. Secondly, concentration displayed an increasing behavior as the Soret number increased.

Applications of the kinetic theory for a model of a confined quasi-two dimensional granular mixture: Stability analysis and thermal diffusion segregation

The Boltzmann kinetic theory for a model of a confined quasi-two dimensional granular mixture derived previously [Garzó et al., “Navier–Stokes transport coefficients for a model of a confined quasi-two dimensional granular binary mixture,” Phys. Fluids 33, 023310 (2021)] is considered further to analyze two different problems. First, a linear stability analysis of the hydrodynamic equations with respect to the homogeneous steady state (HSS) is carried out to identify the conditions for stability as functions of the wave vector, the coefficients of restitution, and the parameters of the mixture. The analysis, which is based on the results obtained by solving the Boltzmann equation by means of the Chapman–Enskog method to first order in spatial gradients, takes into account the (nonlinear) dependence of the transport coefficients and the cooling rate on the coefficients of restitution and applies in principle to arbitrary values of the concentration, and the mass and diameter ratios. In contrast to the results obtained in the conventional inelastic hard sphere (IHS) model, the results show that all the hydrodynamic modes are stable so that the HSS is linearly stable with respect to long enough wavelength excitations. On the other hand, this conclusion agrees with previous stability analysis performed in earlier studies for monocomponent granular gases. As a second application, segregation induced by both a thermal gradient and gravity is studied. A segregation criterion based on the dependence of the thermal diffusion factor Λ on the parameter space of the mixture is derived. In the absence of gravity, the results indicate that Λ is always positive, and hence, the larger particles tend to accumulate near the cold plate. However, when gravity is present, our results show the transition between Λ>0 (larger particles tend to move toward the cold plate) to Λ<0 (larger particles tend to move toward the hot plate) by varying the parameters of the system (masses, sizes, composition, and coefficients of restitution). Comparison with previous results derived from the IHS model is carried out.

Exploring thermal diffusion and diffusion-thermal energy in MHD Maxwell fluid flow around a stretching cylinder

This study carries significant importance in its exploration of the consequences of thermal diffusion and diffusion-thermal energy on a Maxwell fluid near a stretching cylinder. It also considers the influence of Brownian motion and thermophoresis, alongside examining the impact of the Prandtl number and magnetohydrodynamics (MHD) and radiation into the analysis. The primary aim of this study is to investigate the impact of thermal diffusion, diffusion-thermal energy, and various influencing factors on a Maxwell fluid near a stretching cylinder. This investigation aimed to shed light on the behavior of critical parameters, particularly in the presence of Brownian motion, thermophoresis, and variations in the Prandtl number. Additionally, this study sought to adapt a Bvp4c inbuilt software in MATLAB to solve the governing equations, enabling the visualization of velocity, energy, and concentration contours. This study mainly investigated the results for the mentioned parameters for both flat plate (Curvature parameter αc = 0) and cylinder (αc = 1) on temperature, concentration, and velocity profiles. The major conclusions drawn from this study are the concentration profiles exhibited opposing behaviors as thermophoresis, Brownian motion and the Dufour effect increased. However, the temperature profile increases for these parameters. Secondly, concentration displayed an increasing behavior as the Soret number increased.

Surface morphology and topography evolution of soda-lime silica glass after 1.0 MeV Si ion bombardment

Surface pattern formation on soda-lime silica glass by 1 MeV Si ion irradiation impinging at an angle of 70° with respect to the surface normal has been studied. Modification of surfaces were analyzed for total ion fluences applied between up to ions/cm2. The surface morphology and topography were studied by scanning electron microscopy (SEM), and atomic force microscopy (AFM). These surface techniques enabled the determination of roughness, characteristic wavelengths, and correlation lengths. In addition, electron dispersive spectroscopy (EDS) scans were applied on the surface topography to study the variation of the Si content on the obtained surface patterns. From the measurement of these variables, linear and non-linear regimes were established. At linear regime, the surface morphology develops from an initial flat surface giving rise to ripples for fluences up to ions/cm2. As the ion bombardment continues surface evolve into wrinkles finalizing at cellular-like structures, growing under an anomalous scaling process. The EDS scans indicate the presence of shadowing effects. The morphological changes observed can be explained in terms of a combination of thermal mass diffusion and geometrical factors during ion irradiation, including shadowing and subsequent (secondary) surface erosion effects adapted to few MeV energies.

Mass Transfer Theory Based Analysis of Influencing Factors on Component Gradient of Near-surface Atmosphere on Venus

The atmosphere of Venus differs completely from that of Earth despite the planets’ similarity in size and mass. At Venus's surface, the atmosphere is hot and dense, with a temperature of approximately 735 K and a pressure of approximately 92 bar. The temperature profile from the Soviet VeGa-2 probe shows high instability of the near-ground potential temperature, which, according to relevant research, can be explained by the vertical gradient of N2 mole fraction. Based on the Maxwell–Stefan mass transfer theory, we propose a theoretical model of binary gas component for a quantitative discussion of influencing factors for the N2 vertical concentration gradient, which consist of temperature, gravity, specific heat ratio, mass relative factor, thermal diffusion factor, and CO2 flux. Our model shows that the 0%–3.5% N2 concentration gradient cannot be generated without CO2 flux in the near-ground atmosphere of Venus. And the result with CO2 source indicates that the 0.000001%–3.5% N2 concentration gradient at 0–7 km atmosphere can be generated by the 2.7 × 10−6 mol m−2 s−6 CO2 flux on Venusian surface, which is in agreement of gradient reckoned by VeGa-2's data. This magnitude of CO2 flux is close to the one produced by volcanic eruptions on Earth, indicating possible existence of volcanic activities on the surface of Venus. This work has provided the community a new vision to understand the influencing factors of Venusian atmospheres composition distribution.

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.

Thermodiffusion of CO2 in Water by Nonequilibrium Molecular Dynamics Simulations

The components of a fluid mixture may segregate due to the Soret effect, a coupling phenomenon in which mass flux can be induced by a thermal gradient. In this work, we evaluate systematically the thermodiffusion of the CO2-H2O mixture, and the influence of the geothermal gradient on CO2 segregation in deep saline aquifers in CO2 storage. The eHeX method, a nonequilibrium molecular dynamics simulation approach, is judiciously selected to simulate the phenomenon. At 350 K, 400 bar, and CO2 mole fraction of 0.02 (aquifer conditions), CO2 accumulates on the cold side, and the thermal diffusion factor is close to 1 in a number of force fields. The lower the temperature, the higher is the separation and the thermal diffusion factor. In colder regions, water self-association is stronger, whereas the CO2-H2O cross-association and the CO2-CO2 interactions enhance at higher temperatures. Thermodiffusion and gravitational segregation have opposite effects on CO2 segregation. At typical subsurface conditions, the Soret effect is more pronounced than gravity segregation, and CO2 concentrates in the top (colder region). Our work sets the stage to model the effect of electrolytes on CO2 segregation in subsurface aquifers and other areas of interest.

Predicting thermodiffusion in simple binary fluid mixtures.

The predictive capabilities of some existing theoretical models to quantify thermodiffusion have been investigated in this work. To do so, the tests have been performed on two model fluids, the hard-sphere and the Lennard-Jones (including spheres and dimers) ones, exploring different mixtures and thermodynamic conditions thanks to extensive molecular simulations. It has been confirmed that the thermal diffusion factor should be expressed as the sum of one term related to the isotope effect and one term related to the "chemical" effects and that a kinetic term is required to quantify thermodiffusion from the gas state to the liquid state. In addition, regarding the isotope effects, it has been obtained that none of the available theoretical models are able to yield a reasonable prediction relatively to the molecular simulations results and that the moment of inertia contribution is one order of magnitude smaller than the mass contribution in the liquid state. Finally, concerning the chemical effects, it has been shown the Shukla and Firoozabadi model, complemented with a kinetic term, is probably the most reasonable option to estimate the chemical contribution to the thermal diffusion factor, even if it fails in capturing the effect of the asymmetry in size and in shape between the species. Overall, this works confirms that there is still a lack of a generic model able to predict accurately thermal diffusion factors, or equivalently Soret coefficient, in simple binary mixtures from the gas state to the liquid state.

Consolidated theory of fluid thermodiffusion

AbstractWe present the Onsager–Stefan–Maxwell thermodiffusion equations, which account for the Soret and Dufour effects in multicomponent fluids. Unlike transport laws derived from kinetic theory, this framework preserves the structure of the isothermal Stefan–Maxwell equations, separating the thermodynamic forces that drive diffusion from the force that drives heat flow. The Onsager–Stefan–Maxwell transport‐coefficient matrix is symmetric, and the second law of thermodynamics imbues it with simple spectral characteristics. This new approach allows for heat to be considered as a pseudo‐species and proves equivalent to both the intuitive extension of Fick's law and the generalized Stefan–Maxwell equations popularized by Bird, Stewart, and Lightfoot. A general inversion process facilitates the unique formulation of flux‐explicit transport equations relative to any choice of convective reference velocity. Stefan–Maxwell diffusivities and thermal diffusion factors are tabulated for gaseous mixtures containing helium, argon, neon, krypton, and xenon. The framework is deployed to perform numerical simulations of steady three‐dimensional thermodiffusion in a ternary gas.

Transport properties of the binary gas mixtures containing CO2, N2, SF6, and CF4 at low density

The transport properties at low density are investigated in the framework of the kinetic theory of gases for five binary mixtures composed of CO2, N2, SF6, and CF4, which are of great interest to the electric power industry and are not available in the literature. The Lennard-Jones (12–6) potentials recommended in the literature are used to model the interactions between like molecules, and the Lorentz–Berthelot combining rules are employed to further describe the unlike interactions. The viscosity, binary diffusion coefficient, and thermal diffusion factor are computed for CO2–SF6, CO2–CF4, N2–SF6, N2–CF4, and SF6–CF4. The experimental data are available for the viscosity and diffusion coefficient of the studied systems over a much limited temperature range, and reasonable agreement is found between the experimental data and our calculated values. The new transport property values of the five binary mixtures are tabulated in the supplementary material, covering a very wide temperature range from 300 to 30 000 K.

Contribution of internal degree of freedom of soft molecules to Soret effect.

We study the Soret effect in binary dimer-monomer mixtures using nonequilibrium molecular dynamics simulations and investigate the pure contribution of the internal degree of freedom of flexible molecules to the Soret effect. We observe that the thermal diffusion factor tends to decrease and change its sign as the molecules become softer. We propose two possible mechanisms for our observations: change of the molecule structures with the temperature, causing bulkier molecules to migrate to the hotter region, and asymmetry of the restitution between rigid and flexible molecules, due to which flexible molecules show larger restitution when placed at the hotter region.

Transport coefficients of multicomponent mixtures of noble gases based on ab initio potentials: Diffusion coefficients and thermal diffusion factors

Diffusion coefficients and thermal diffusion factors of binary, ternary, and quaternary mixtures of helium, neon, argon, and krypton at low density are computed for wide ranges of temperatures and molar fractions, applying the Chapman–Enskog method. Two definitions of the diffusion coefficients are discussed, and a general relation between them is obtained. Ab initio interatomic potentials are employed in order to calculate the omega-integrals being part of the expression of the reported quantities. The relative numerical errors of the diffusion coefficients do not exceed the value of 5 × 10−5 being even smaller in some cases. The uncertainties of diffusion coefficients due to the interatomic potential vary between 4 × 10−4 and 6 × 10−3. The numerical error and uncertainty due to the potential of the thermal diffusion factors are estimated as 10−4 and 3 × 10−3, respectively. It is shown that the present results for binary mixtures are more accurate than any other available in the literature, while the results for ternary and quaternary mixtures are reported for the first time.

Impacts of hydrogen-addition on methanol-air laminar burning coupled with pressures variation effects

The effect of hydrogen addition on the methanol laminar flames under various pressures was investigated experimentally and kinetically. A constant volume chamber was used to perform the experiments. The flame propagation was recorded by a schlieren system and a high-speed camera. The CHEMKIN was used to calculate the detailed reaction process. The initial pressure was changed from 1 to 3 bar, and the hydrogen mole fraction was varied from 0 to 0.8. The experimental results show that the laminar burning velocity is increased when adding more hydrogen and lowing initial pressure. When improving hydrogen fraction and initial pressure, Markstein length is decreased. The hydrodynamic instability is enhanced under elevated pressure. The hydrodynamic factor destabilizes the flames of rich-fuel mixtures with less hydrogen blended. When adding more hydrogen, the thermal-diffusion factor contributes most to the flame instability. Almost all main reactions tend to be more sensitive under higher pressure, and blending hydrogen provides more promotion to reactions with the positive sensitivity coefficient. The multiplication of H atoms caused by hydrogen introducing is capable of the enhancement of burning velocity, and the obvious consumption of free radicals due to the improvement of initial pressure results in the inhibition of flame propagation.

Transport coefficients of argon and its mixtures with helium and neon at low density based ab initio potentials

The transport coefficients, such as viscosity, thermal conductivity, diffusion coefficient and thermal diffusion factor of helium-argon and neon-argon mixtures at low density are calculated for a wide range of temperature applying the quantum approach to the interatomic interaction. Viscosity and thermal conductivity of pure argon are also analyzed in the frame of the quantum approach. The Chapman-Enskog method is employed considering the 10th order of Sonine polynomial expansion. Ab initio potentials for interatomic interactions are used to calculate the omega-integrals. The relative numerical errors of the present results depend on the temperature and vary from one coefficient to other. At the room temperature, this error has the order of 10−5 for the thermal diffusion factor and 10−6 for the other coefficients. In most of cases, the relative uncertainty related to the interatomic potential is one order higher than the numerical error. It was shown that the influence of the quantum effects on the transport coefficients of argon has the order of experimental uncertainty. The thermal diffusion factor of the helium-argon mixture changes its own sign at low temperature, while the same coefficient of the neon-argon mixture is always negative.

Optimization of the photovoltaic-thermoelectric hybrid system with and without optical concentrator

The photovoltaic-thermoelectric coupled system has drawn widespread attention in recent years due to its potential of utilization of full-spectrum solar energy. The output power of thermoelectric (TE) is usually much less than that of photovoltaic (PV), because the temperature difference of TE module is usually very small. Thus, the optical concentrating method has been used to increase the temperature difference, but it increases complexity of the structure and extra cost for the sunlight tracking system. Another practical way is using the thermal concentrating method to increase the heat flux of the TE module. However, for there two PV-TE coupled systems i.e. optical and thermal concentrating systems, there exists a confrontation between the PV cell and the TE module. The efficiency of PV cell decreases with the increasing temperature, while the performance of the TE module increases with the increasing temperature difference. In some conditions, the total efficiency of the PV-TE coupled system may be even lower than that without TE module. Therefore, it is necessary to investigate the optimal combination mode of PV cell and TE module for the coupled system. In this paper, a thermodynamic model based on energy-balanced equation is established to investigate the structural optimization and efficiency improvement of PV-TE coupled power generation system, which considers the effects of the thermal concentration factor, the length of thermocouples, the loading resistance of TE module and thermal diffusion factor. The influence rules of these factors on power generation efficiency of PV-TE coupled system without and with concentrator are also theoretically analyzed. (1) For the PV-TE coupled system without concentrator, the influences of thermal concentration factor, the length of thermocouples and the ratio of loading resistance to the internal resistance of TE module on the total efficiency of PV-TE coupled system are analyzed under four efficiency temperature coefficients of PV cells ( β ref =0.001, 0.002, 0.003, 0.004 K−1). It is found that, when the figure of merit of TE module Z is 4×10−3 K−1 and β ref is 0.001 K−1, the total efficiency increases initially and then decreases with the increases of the thermal concentration factor, the length of thermocouples and the ratio of loading resistance to the internal resistance of TE module. Therefore, there exist optimal values of thermal concentration factor, length of thermocouples and loading resistance of TE module to maximize the total efficiency. (2) For the PV-TE coupled system with concentrator, the influence of thermal diffusion factor on the total efficiency of PV-TE coupled system under five efficiency temperature coefficients of PV cells ( β ref=0.001, 0.0015, 0.002, 0.0025, 0.003 K−1) is studied for the figure of merit of TE module Z =2.545×10−3 K−1 and Z = 4×10−3 K−1. The results shown that, for the cases of Z =2.545×10−3 K−1, β ref= 0.001 K−1; Z = 4×10−3 K−1, β ref= 0.001 K−1; Z = 4×10−3 K−1, β ref= 0.0015 K−1, the total efficiency decreases as the thermal diffusion factor increases. While for other cases, the total efficiency increases significantly as the thermal diffusion factor increases. It has also shown that the increases of efficiency caused by the increase in thermal diffusion factor becomes small when the thermal diffusion factor is over 5.12. The reason is that the heat transfer becomes fast when the thermal diffusion factor becomes larger, which leads to the increase of temperature of the PV cell and the hot side of the TE becomes small as the thermal diffusion factor is over 5.12. Based on the above results, it is suggested that an optimal thermal diffusion around 3.0 can have a better balance of both cost and total efficiency of the PV-TE coupled system with concentrator.

Semi Empirical Calculation of Intermolecular Potentials and Transport Properties of Some Binary and Ternary Industrial Refrigerant Mixtures

In this study the intermolecular potential energies of some environment-friendly industrial HFC refrigerants were obtained through the inversion method which is based on the corresponding states principle. These potentials were later employed in calculation of transport properties (viscosity, diffusion, thermal conductivity and thermal diffusion factor) of some binary and ternary refrigerant mixtures, in the low density region. Predicted transport properties were compared with the available literature data and gave rise to the acceptable agreement. On the other hand, the interaction potential was fitted to an analytical form, and the calculated low density transport properties were also fitted to the fairly exact equations. In the case of R410A and R421B mixtures, high density viscosity values were also calculated through the Vesovic-Wakeham method. Due to lack of experimental values on high density viscosities of these two mixtures, we could only compare calculated high density viscosities for other available molar compositions of R124-R134a and R125-R32 binary mixtures, with literature data, while again acceptable accordance was observed.

Elemental and isotopic fractionation of noble gases in gas and oil under reservoir conditions: Impact of thermodiffusion⋆.

Noble gases, and the way they fractionate, is a promising approach to better constrain origin, migration and initial state distributions of fluids in gas and oil reservoirs. Thermodiffusion, is one of the phenomena that may lead to isotope and elemental fractionation of noble gases. However, this effect, assumed to be small, has not been quantified, nor measured, in oil and gas under reservoir conditions. Thus, in this work, molecular dynamics simulations have been performed to compute the thermal diffusion factors of noble gases, in a dense gas (methane) and in an oil (n-hexane) under high pressures. Interestingly, it has been found that thermal diffusion factors, associated to both isotopic (36Ar, 40Ar) and elemental fractionations of noble gases (4He, 20Ne, 40Ar, 84Kr and 131Xe) in gas and oil, could be expressed as linear functions of the reduced masses. Regarding the amplitude of the phenomena, it has been found that, in a stationary 1D oil or gas fluid column, thermodiffusion due to a typical geothermal gradient has an impact on noble gas isotopic and elemental fractionation which is of the same order of magnitude than gravity segregation, but opposite in sign. In addition, the relative impact of thermodiffusion on isotopic and elemental fractionations depends on the fluid type which is another interesting feature. Thus, these first numerical results on isotopic and elemental fractionation of noble gases by thermodiffusion in simple pure gas and oil emphasize their interest as natural tracers that could be used to improve the pre-exploitation description of oil and gas reservoirs.

Determination of the potential energy surfaces of some hydrocarbon refrigerants and their gas transport properties via semi-empirically based assessment

Abstract Effective and isotropic potentials of three hydrocarbon refrigerants were determined from an iterative inversion procedure, including ethylene (R1150), isobutane (R600a), and neopentane (R601b). By employing the inverted potentials, predictions of transport properties were performed with the aid of the kinetic theory of dilute gases. The viscosity coefficient, self-diffusion coefficient, and thermal diffusion factor of pure R1150, R600a, and R601b were presented over the temperature range from 273.15 K to 973.15 K at low density. Comparisons of the theoretically calculated values with the literature data were discussed. It is shown that the potentials obtained by the inversion scheme were able to predict accurate transport properties for these slightly polar ozone-safe hydrocarbon refrigerants.

Transport coefficients of helium-neon mixtures at low density computed from ab initio potentials.

The viscosity, thermal conductivity, diffusion coefficient, and thermal diffusion factor of helium-neon mixtures at low density are calculated for a wide range of temperature and for various molar fractions. The Chapman-Enskog method is employed considering the 10th order of the Sonine polynomial expansion. Ab initio potentials for intermolecular interactions are used to calculate the omega-integrals. The relative numerical error of the present results obtained for the potentials used here is less than 7 × 10-5 for the thermal diffusion factor and 2 × 10-5 for all the other coefficients. Since each employed potential has a different accuracy, the uncertainty related to such accuracies was analyzed, considering the contribution of each potential uncertainty. It was found that the total uncertainty due to the potentials is larger than the numerical error and it varies depending on the temperature and molar fraction. A comparison of the calculated transport coefficients with those available in the open literature shows that the present calculations provide the most accurate values currently available for the transport coefficients of helium-neon binary mixtures at low density.

Thermophoresis of a Brownian particle driven by inhomogeneous thermal fluctuation

Brownian motion of a spherical particle induced by the interaction with surrounding molecules is considered. If the particle is larger than the molecules and the temperature of surrounding media is spatially non-uniform, the interaction between an individual molecule and the particle is also position-dependent. That is, the particle is subject to inhomogeneous thermal fluctuation. In this paper, we investigate the contribution of the inhomogeneous thermal fluctuation to the thermophoresis, i.e., the Soret coefficient or thermal diffusion factor. The problem is simplified by assuming a hard-sphere potential between the particle and the surrounding molecules and is investigated using the kinetic theory, namely, we consider a linear Boltzmann-type equation for the velocity distribution function of the particle. Using the perturbation analysis with respect to the square root of mass ratio between the molecule and the particle, the drift-diffusion equation of the particle is derived. It is found that the Soret coefficient, or thermal diffusion factor, is dependent on the mass ratio and the excluded volume of the particle. In particular, when the ratio of the mass density of the particle to that of the surrounding media decreases, the Soret coefficient also decreases and may take negative value. The present result well describes the mass-dependency of thermal diffusion factor obtained by the molecular dynamics simulation carried out in an existing study and the one in the present study, where soft potentials of Lennard-Jones-type are used instead of hard-sphere potential.