Kinetic Theory Of Transport Processes Research Articles

Thermal conductivity of two-dimensional group IV-element thermocrystals

A thermocrystal is a type of periodic structure bandgap material that can control heat flux transmission and reflection. In this paper, we use and improve a model based on the kinetic theory of transport processes to calculate the corresponding thermal spectra, dispersion relations and thermal transmission losses of two-dimensional thermocrystals with different film thicknesses, different lattice parameters, different modes, and linear defect structure. The results show that the thermal conduction can be reduced by approximately 19.6% using bandgap materials.

Kinetic theory of transport processes in partially ionized reactive plasma, II: Electron transport properties

Abstract The previously obtained in (Zhdanov and Stepanenko, 2016) general transport equations for partially ionized reactive plasma are employed for analysis of electron transport properties in molecular and atomic plasmas. We account for both elastic and inelastic interaction channels of electrons with atoms and molecules of plasma and also the processes of electron impact ionization of neutral particles and three-body ion–electron recombination. The system of scalar transport equations for electrons is discussed and the expressions for non-equilibrium corrections to electron ionization and recombination rates and the diagonal part of the electron pressure tensor are derived. Special attention is paid to analysis of electron energy relaxation during collisions with plasma particles having internal degrees of freedom and the expression for the electron coefficient of inelastic energy losses is deduced. We also derive the expressions for electron vector and tensorial transport fluxes and the corresponding transport coefficients for partially ionized reactive plasma, which represent a generalization of the well-known results obtained by Devoto (1967). The results of numerical evaluation of contribution from electron inelastic collisions with neutral particles to electron transport properties are presented for a series of molecular and atomic gases.

Kinetic theory of transport processes in partially ionized reactive plasma, I: General transport equations

In this paper we derive the set of general transport equations for multicomponent partially ionized reactive plasma in the presence of electric and magnetic fields taking into account the internal degrees of freedom and electronic excitation of plasma particles. Our starting point is a generalized Boltzmann equation with the collision integral in the Wang-Chang and Uhlenbeck form and a reactive collision integral. We obtain a set of conservation equations for such plasma and employ a linearized variant of Grad’s moment method to derive the system of moment (or transport) equations for the plasma species nonequilibrium parameters. Full and reduced transport equations, resulting from the linearized system of moment equations, are presented, which can be used to obtain transport relations and expressions for transport coefficients of electrons and heavy plasma particles (molecules, atoms and ions) in partially ionized reactive plasma.

Thermal energy transport model for macro-to-nanograin polycrystalline semiconductors

Understanding thermal energy transport in polycrystalline semiconductors is important for the efficiency of electronic devices and thermoelectric materials. In this paper, we study the reduction of the transport of thermal energy in polycrystalline semiconductors generated by the shortening of the phonon mean free paths due to grain boundary scattering. We calculate the reduction of the thermal conductivity in polycrystals, from macro-to-nanograin sizes and different temperatures, by using a theoretical approach based on the kinetic theory of transport processes. The approach involves an exact expression for the reduction of the phonon mean free paths that includes their directional, frequency, and polarization dependence. By comparing the results of our model for the reduced thermal conductivity of the grain against the thermal boundary Kapitza resistance calculated by others, we find that the thermal conductivity of polycrystalline Si and SiC materials is dominated by the reduced thermal conductivity of the grain. We also show that in order to accurately calculate the thermal conductivity, the proportion of heat transported by transverse and longitudinal phonons must be correctly taken into account. By using the model, we study grain boundary scattering effects on the reduction of the thermal conductivity of polycrystalline silicon and silicon carbide. The calculated results are compared with experiments at different temperatures and grain sizes without using free adjustable variables (e.g., defects concentration) or phenomenological formulas to account for the reduced thermal conductivity of the grain.

Micro to nano scale thermal energy conduction in semiconductor thin films

We study the effects of phonon boundary scattering on the transport of thermal energy in semiconductor thin films across multiple length scales and temperatures. We use a model based on the kinetic theory of transport processes that accurately calculates the reduction of the phonon mean free paths by including the effects of spatial location and propagation direction of phonons. We investigate how the effective phonon mean free paths and the resultant thermal conductivities are reduced by the film length scale and surface roughness. The thermal conductivities of silicon and germanium thin films are calculated for temperatures between 4 K and 500 K and thicknesses from nano to micro and good agreement is obtained with experimental measurements. The theoretical study in this paper helps to understand and quantitatively predict the transport of thermal energy in nanoscale materials, which can be used to improve the efficiency of optoelectronic devices and thermoelectric materials.

The Kinetic Theory of Transport Processes in Turbulent Media of Moderate Density

ABSTRACT: The purpose of this paper is to develop the kinetic theory of transport processes (energy, momentum and mass transfer) in turbulent media of moderate density by methods of statistical mechanics and to determine their equilibrium and non‐equilibrium properties. New analytical and evaluated expressions for turbulent transport coefficients have been founded. Hydrodynamic equations of Euler and Navier‐Stokes type are obtained from kinetic equations by multiplying on additive invariants and integrating them on the particle coordinates.

Kinetic theory of transport processes in weakly ionized gases

A consistent method for the treatment of a plasma of arbitrary degree of ionization is presented. This method consists of a perturbation expansion in the framework of the multiple time scales formalism. Here the results are presented for a weakly ionized gas where elastic electron-atom collisions dominate. It appears that an isotropic correction to the zeroth order Maxwellian electron distribution function is necessary. Calculated electron transport coefficients are compared with the Frost mixture rule and with other calculations.

Semiclassical evaluation of the temperature dependences of some kinetic cross sections for nonspherical molecules

By using semiclassical (WKB) wavefunctions and the distorted wave approximation, we obtain the temperature dependences of σ (0001) and σ(02) appearing in the kinetic theory of transport processes of nonspherical molecules. Contributions from reorientation and energetically inelastic collisions are treated which lead to good agreement between the theoretical and experimental temperature dependences for some diatomic molecules.

The kinetic theory of transport processes in adsorbed gases

The interaction of adsorbed molecules with molecules of the underlying solid undergoing thermal oscillations is discussed and calculated. The friction coefficient for the adsorbed molecules has been evaluated by means of some approximate formulae and compared with the experimental data. The kinetic equations describing a non-uniform state of adsorbed gas has been solved by the Chapman-Enskog perturbation method. The phenomena of surface diffusion, thermal diffusion, thermal conduction and viscosity are discussed on the basis of the second approximation of this method. The application of this theory to the separation of components of adsorbed gas by surface flow is described in detail. The theory of surface separation of isotopes is also discussed and compared with experimental data.