Heat transfer to nonspherical particles in a rarefied plasma flow

The interaction of a nonspherical metallic or nonmetallic particle with a rarefied thermal plasma flow is considered. Heat transfer to a particle of arbitrary shape with an extremely thin plasma sheath due to, respectively, gas molecules, electrons, and ions is described. Analytical expressions are derived for charge and heat fluxes in the particular case of a spheroidal metallic or nonmetallic particle in a subsonic plasma flow. It has been shown that the intensity of heat exchange is greatly influenced by gas ionization, charge transfer processes, and particle shape, velocity, and orientation in the plasma flow.     

Drag force acting on an evaporating particle immersed in a rarefied plasma flow

Analytical expressions are presented for the drag force acting on an evaporating or nonevaporating particle immersed in a plasma flow for the extreme case of free-molecule flow regime and thin plasma .sheath. It is shown that the drag force on a spherical particle is proportional to the square of the particle radius and to the relative velocity between the particle and the bulk plasma at low speed ratios. The existence of a relative velocity between the particle and the plasma results in a nonuniform heat flux distribution with its rnaximum value at the frontal stagnation point of tire sphere. This nonuniform distribution of the local heat fux density causes a nonuniforrn distribution of the local evaporated-mass flux and vapor reaction force around the surface of an evaporating particle, and thus induces an additional force on the particle. Consequently, the drag force acting on art evaporating particle is always greater than that on a nonevaporating one. This additional drag force due to particle evaporation is more significant for nonmetallic particles and for particle materials with lower latent heat of evaporation and lower vapor molecular mass. It increases with increasing plasma temperature and with decreasing gas pressure at the high plasma temperatures associated with appreciable gas ionization. The drag ratio increases with increasing electron/heavy-particle temperature ratio at high electron temperatures for a two-temperature plasma.     

Experimental study of effective particle heating by a thermal plasma flow confined in a porous ceramic tube

The heating of a single alumina particle (1 mm diameter) was experimentally investigated using a thermal argon plasma flow confined in a tube. Two kinds of tube were used; a porous ceramic tube (PCT) with a transpiration gas and a water-cooled copper tube (WCT). The temperature and velocity of the particle heated in a thermal plasma flow were measured at the exit of the tube by the calorimetric and optical method, respectively. The plasma temperature and velocity at the exit of the tube were also measured. The heating rate of a particle was estimated from these experimental results. According to the results, the heating rate of a particle is higher for PCT with a small flow rate of transpiration gas than for WCT. Therefore, PCT is effective for the particle heating.Notation A cross-sectional area - Bi Biot number - C constant - c _p specific heat - D diameter - h heat transfer coefficient - k thermal conductivity - L length of tube - l distance for heat conduction loss - M mass - m flow rate of plasma jet gas - Nu Nusselt number - P pressure - Pr Prandtl number - Q heat transfer rate - Q _p total heat delivered to the particle - r radial distance - T plasma temperature - T _p particle temperature - T temperature rise - t time - U plasma velocity - U _p particle velocity - x axial distance - density - viscosity - residence time of the particle - a atmospheric (static) - Ar argon - b bulk - c centerline - cond conduction - cu probe - f film - i entrance of the tube - free stream - loss heat transferred to the wall of the tube - p particle - r room - rad radiation - t total - W wall, sphere surface - wa water - 0 exit of the tube     

Particle dynamics and particle heat and mass transfer in thermal plasmas. Part II. Particle heat and mass transfer in thermal plasmas

This paper is concerned with a review of heat and mass transfer between thermal plasmas and particulate matter. In this situation various effects which are not present in ordinary heat and mass transfer have to be considered, including unsteady conditions, modified convective heat transfer due to strongly varying plasma properties, radiation, internal conduction, particle shape, vaporization and evaporation, noncontinuum conditions, and particle charging. The results indicate that (i) convective heat transfer coefficients have to be modified due to strongly varying plasma properties; (ii) vaporization, defined as a mass transfer process corresponding to particle surface temperatures below the boiling point, describes a different particle heating history than that of the evaporation process which, however, is not a critical control mechanism for interphase mass transfer of particles injected into thermal plasmas; (iii) particle heat transfer under noncontinuum conditions is governed by individual contributions from the species in the plasma (electrons, ions, neutral species) and by particle charging effects.     

Thermophoretic force acting on an evaporating particle suspended in a rarefied plasma

Analytical results of the thermophoretic force on an evaporating spherical particle immersed in a rarefied plasma with a large temperature gradient are presented for the extreme case of free-molecule regime and thin plasma sheath. It has been shown that the existence of a temperature gradient in the plasma causes a nonuniform distribution of the local heat flux density on the sphere surface with its maximum value at the fore-stagnation point of the sphere, although the total heal flux to the whole particle is independent of the temperature gradient existing in the plasma. This nonuniform-distribution of the local heat flux density causes a nonuniform distribution of the. local evaporated-mass flux and related reaction force around the surface of an evaporating particle, and thus causes an additional force on the particle. Calculated results show that the thermophoretic force on an evaporating particle may substantially exceed that on a nonevaporating one, especially for the case of a metallic particle (with infinite electric conductivity). The effect of evaporation on the thermophoretic force is more pronounced as the evaporation latent heat of the particle material is comparatively low and as high plasma temperatures are involved.     

Heat transfer from a rarefied plasma flow to a metallic or nonmetallic particle

Heat transfer from a plasma flow to a metallic or nonmetallic spherical particle is studied in this paper for the extreme case of free-molecule flow regime. Analytical expressions are derived for the heat flux due to, respectively, atoms, ions, and electrons and for the floating potential on the sphere exposed to a two-temperature plasma flow. It has been shown that the local or average heat flux density over the whole sphere is independent of the sphere radius and approximately in direct proportion to the gas pressure. The presence of a macroscopic relative velocity between the plasma and the sphere causes substantially nonuniform distributions of the local heat flux and enhances the total heat flux to the sphere. The heat flux is also enhanced by the gas ionization. Appreciable difference between metallic and nonmetallic spheres is found in the distributions along the oncoming flow direction of the floating potential and of the local heat flux densities due to ions and electrons. The total heat flux to the whole sphere is, however, almost the same for these different spheres. For a fixed value of the electron temperature, the heat flux decreases with increasing temperature ratio T_e/T_h.     

Heat transfer to a single particle exposed to a thermal plasma

This paper is concerned with an analytical study of the heat and mass transfer process of a single particle exposed to a thermal plasma, with emphasis on the effects which evaporation imposes on heat transfer from the plasma to the particle. The results refer mainly to an atmospheric-pressure argon plasma and, for comparison purposes, an argon-hydrogen mixture and a nitrogen plasma are also considered in a temperature range from 3000 to 16,000 K. Interactions with water droplets, alumina, tungsten, and graphite particles are considered in a range of small Reynolds numbers typical for plasma processing of fine powders. Comparisons between exact solutions of the governing equations and approximate solutions indicate the parameter range for which approximate solutions are valid. The time required for complete evaporation of a given particle can be determined from calculated values of the vaporization constant. This constant is mainly determined by the boiling (or sublimation) temperature of the particles and the density of the condensed phase. Evaporation severely reduces heat transfer to a particle and, in general, this effect is more pronounced for materials with low latent heat of evaporation.     

Progress of laser ionization mass spectrometry for elemental analysis — A review of the past decade

Mass spectrometry using a laser ionization source has played a significant role in elemental analysis. Three types of techniques are widely used: high irradiance laser ionization mass spectrometry is capable of rapid determination of elements in solids; single particle mass spectrometry is a powerful tool for single particle characterization; and resonance ionization mass spectrometry is applied for isotope ratio measurements with high sensitivity and selectivity. In this review, the main features of the laser ablation process and plasma characterization by mass spectrometry are summarized. Applications of these three techniques for elemental analysis are discussed.     

Effect of particle charging on momentum and heat transfer from rarefied plasma flow

The features of interaction of a spherical metallic particle with a rarefied thermal plasma flow due to the presence o charges-electrons and ions in the gaseous phase-are considered. Analytical expressions describing charge, momentum, and energy exchange between the plasma and the particle für the cases of strong and weak Debye screening are obtained. It is illustrated that the efficiency of particle heating in the plasma considerably grows as compared with a hot molecular gas due to participation of electrons and ions in file transfer processes.     

Behavior of particulates in thermal plasma flows

Injection of particulate matter into a thermal plasma represents one of the approaches used in thermal plasma processing. The injected particles are usually treated as a dispersed phase, governed by the equation of motion and the rate equations for heat and mass transfer in Lagrangian coordinates. A stochastic approach is introduced to take particle dispersion into account due to turbulent fluctuations by randomly sampling instantaneous flow fields. Three-dimensional effects are also considered which are mainly due to particle injection and the presence of a swirl component. A modified approach for investigating noncontinuum effects on plasma-particle heat transfer is proposed, incorporating both electric and aerodynamic effects on the boundary layer around a particle immersed into a thermal plasma. Comparisons of theoretical predictions based on the present model with available experimental data are, in general, in reasonable agreement.     

In-Flight Spheroidization of Alumina Powders in Ar–H<Subscript>2</Subscript> and Ar–N<Subscript>2</Subscript> Induction Plasmas

In-flight spheroidization of alumina powders in Ar–H₂ (H₂–7.6%, vol/vol) and Ar–N₂ (N₂–13.0%, vol/vol) RF induction plasmas was investigated numerically and experimentally. The mathematical model for the plasma flows incorporates the k– turbulence model, and that for particles is the Particle-Source-in-Cell (PSI-Cell) model. Experimental results demonstrate that spheroidized alumina particles are produced in both Ar–H₂ and Ar–N₂ RF plasmas, with different particle size distributions and crystal phases. Agreement between the predicted and measured particle size distributions is satisfactory under high particle feed rate conditions, while the results obtained for the Ar–H₂ plasma are better than those for the Ar–N₂ plasma. The discrepancy occurring in low feed rate conditions suggests that particle evaporation is an important factor affecting the plasma–particle heat transfer.     

Unsteady heating of metallic particles in a rarefied plasma

Analytical results are presented concerning the unsteady heating of a metallic spherical particle innnersed in a rarefied plasma. The results show that the tinte periods required for the solid-phase heating, melting, liquid-phase heating, and evaporation are all proportional to the particle radius. For estimating the time needed for the solid-phase heating and that for the melting, the additional heat transfer rmechanism due to the thermionic emission front the particle surface is usually negligible since the surface temperatures of the particle heated in the plasma are, in general, compartively low during those heating steps. Thermionic emission assumes its effect only as the higher surface temperatures of the heated particle are involved (e.g., higher than 4000 K), while radiation loss shows its effects at much lower wall temperatures. As the plasma temperature is comparatively low, radiation heat loss may restrict the surface temperature of a particle to such a low value that the effect of thermionic emission on the overall heating time can he neglected and complete evaporation of refractor y metallic particles becomes impossible. The uncertainty in the calculation of the effect of thermionic emission is associated with the choice of the value of the effective work function for the particle material.     

Modeling of the plasma sintering process at reduced pressures

Numerical simulation of the thermal behavior of sintering specimen under RF plasma conditions at reduced pressure is considered. A two-dimensional approach is adopted for describing flow, temperature, and electromagnetic fields in the reactor with appropriate boundary conditions. Slip boundary conditions are imposed for the velocity field at the sample surface and at the wall of the reactor, and corresponding jump boundary conditions are specified for the temperature field. Simple kinetic theory is employed for the calculation of the heat flux from the plasma to the specimen. The so-called capture-radiative-cascade model is adopted for ionization and recombination processes. The results indicate that ion-electron surface recombination is the dominant heat transfer mechanism to the sintering specimen under reduced pressure conditions.     

Particle behavior in thermal plasmas

In this overview, effects exerted on the motion and on heat and mass transfer of particulates injected into a thermal plasma are discussed, including an assessment of their relative importance in the context of thermal plasma processing of materials. Results of computer experiments are shown for particle sizes ranging from 5–50 μm, and for alumina and tungsten as sample materials. The results indicate that (i) the correction terms required for the viscous drag and the convective heat transfer due to strongly varying properties are the most important factors; (ii) noncontinuum effects are important for particle sizes <10 μm at atmospheric pressure, and these effects will be enhanced for smaller particles and/or reduced pressures; (iii) the Basset history term is negligible, unless relatively large and light particles are considered over long processing distances; (iv) thermophoresis is not crucial for the injection of particles into thermal plasmas; (v) turbulent dispersion becomes important for particle <10 μm in diameter; and (vi) vaporization describes a different particle heating history than that of the evaporation process which, however, is not a critical control mechanism for interphase mass transfer of particles injected into thermal plasmas.     

Gold colloid analysis by inductively coupled plasma-mass spectrometry in a single particle mode

Analysis in a single particle mode of gold colloids in water has been performed by inductively coupled plasma-mass spectrometry (ICP-MS). The signal induced by the flash of ions due to the ionization of a colloid in the plasma torch can be measured for the ions ¹⁹⁷Au⁺ by the mass spectrometer without interferences. The intensity of the MS signal is recorded in time scan. The recorded peak distributions were analysed as a function of the colloid size for five monodisperse colloids (80-250 nm). This study describes the experimental conditions to analyse gold colloids in a single particle mode. The size detection limit is around 25 nm corresponding to 0.15 fg colloids and one particle per ml may be detected during a 1 min time scan within standard procedure.     

Influence of the particle size distribution on the CRTA curves for the solid-state reactions of interface shrinkage type

The kinetic curves at infinite temperature for the solid-state reactions of the interface shrinkage type were drawn theoretically by taking account the particle size distribution in the sample mixture. The CRTA curves for the reactions with the particle size distribution can be drawn by utilizing the universal kinetic curves at infinite temperature. The proper kinetic treatment for the CRTA curves with the particle size distribution is discussed in connection with the property of the kinetic equation with respect to the particle size distribution. The present kinetic consideration is taken as a simulation for the reactions with a certain distribution in among the reactant particles, produced preferably by the mass and heat transfer phenomena during the thermoanalytical measurements. The merit of the rate jump method by a single cyclic CRTA curve is also discussed on the basis of the present results.     

Thermophoretic force on a metallic or nonmetallic particle immersed into a rarefied Plasma

Analytical results of the thermophoretic force on a metallic or nonmetallic spherical particle immersed into a rarefied plasma with a heat flux within the plasma are presented for the extreme case of free-molecule regime and thin plasma sheath. It has been shown that the thermophoresis is predominantly caused by atoms at low plasma temperatures with negligible gas ionization, while it is mainly due to ions and electrons at high plasma temperatures with great degree of ionization. The ion flux incident to a particle is constant on the whole sphere surface, while the electron flux to the metallic sphere is dependent on the -position with slightly greater value at the fore stagnation point. Consequently, there is a small difference between the metallic and nonmetallic spheres in their -distributions of the floating potential on the surface, which causes the thermophoretic force on a nonmetallic sphere to be appreciably greater than that on a metallic sphere at high plasma temperatures. Expressions for the total thermophoretic force on a metallic sphere and its components due to, respectively, atoms, ions, and electrons have been given in a closed form. Calculated results are also presented on the effects of pressure and of electron/heavy-particle temperature ratio. These results can be understood based on the variation of atom, ion, and electron thermal conductivities with the gas pressure, the temperature, and the temperature ratio.     

Comparison of Simple Particle-Radiation Coupling Models Applied on a Plasma Black Process

The effect of soot formation on the radiative heat transfer inside a plasma reactor for carbon black synthesis has been modelled. For this purpose, three methods to quantify the soot volume fraction have been tested and evaluated: (1) Assuming local thermodynamic equilibrium, (2) assuming instantaneous conversion of the hydrocarbon and (3) using a single-step soot model. These approaches have been studied using a two-dimensional axis-symmetric and a three-dimensional steady computational fluid dynamics (CFD) model based on the commercial software FLUENT (v.5.6). The CFD model includes turbulence effects (by standard k– model), an electric arc sub-model to describe the time-average and spatial-average Lorentz forces and ohmic heating generated by the three-phase power-supply, methane transport in a nitrogen plasma and radiation calculations. The calculations show that for the simulated operating conditions the resulting temperature distributions obtained are very similar with the three methods in spite of major differences in the treatment of particle formation in the different methods.