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.     

Nusselt number correlations for heat transfer to small spheres in thermal plasma flows

Seven different equations predicting heat transfer rates to small spheres in plasma flows are examined considering argon and nitrogan as plasma gases from 300 to 21,000 K at 1 atm. For argon there is a general consensus up to 9000 K, beyond which wide deviations in behavior occur. For nitrogen, the seven correlations are in good agreement up to 4000 K, but show substantial deviations beyond this value. Comparisons with the sparsely available experimental data are made for argon from 300 to 17,000 K and for nitrogen up to 5500 K. Disagreement between the various correlations and experiment can exceed one order of magnitude.     

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.     

Behavior of small particles in a thermal plasma flow

In this paper computational results are presented which reveal the effects of the Knudsen number on heat transfer and drag of small particles in a flowing thermal argon plasma. The Knudsen number is restricted to moderate values so that temperature jump and velocity slip conditions may be employed, and for the governing equations the continuum approach remains valid. It is shown that the ratio of the heat fluxes with and without the Knudsen effect is almost identical to the ratio obtained by the authors for the case of pure heat conduction. This fact is very important for modeling of the behavior of particles injected into an actual plasma reactor when the Knudsen effect has to be taken into account.On leave from the Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R.C.     

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.     

Heat transfer to a particle under plasma conditions with vapor contamination from the particle

Heat transfer to a copper particle immersed into an argon plasma is considered in this paper, including the effects of contamination of the plasma (transport coefficients) by copper vapor from the particle. Except for cases of high plasma temperatures, the vapor content in the plasma is shown to have a considerable influence on heat transfer to a nonevaporating particle, and, to a lesser extent, on heat transfer to an evaporating particle. Evaporation itself reduces heat transfer to a particle substantially as shown in a previous paper [Xi Chen and E. Pfender, Plasma Chem. Plasma Process.,2, 185 (1982)]. Comparisons of the calculated results with those based on a method suggested in the above reference show that the simplified assumptions employed, i.e., that the surface temperature is equal to the boiling point and that plasma properties based on a fixed composition are applicable, can be employed to simplify calculations for many cases. This study reveals that a considerable portion of a particle must be vaporized before a steady concentration distribution is established around the particle.Nomenclature C _p specific heat at constant pressure - D diffusion coefficient of copper in the mixture - D _a diffusion coefficient of copper atoms in the mixture - D _i ambipolar diffusion coefficient of copper ions in the mixture - f mass fraction of copper in the mixture - f _a mass fraction of copper atoms in the mixture - f _i mass fraction of copper ions in the mixture - f mass fraction of copper in the plasma far away from the particle - f _s mass fraction of copper at the particle surface - G total mass flow rate due to evaporation - G _a mass flow rate of copper atoms - G _i mass flow rate of copper ions - H function defined in Eq. (19) - h specific enthalpy - h _s specify enthalpy at the particle surface - h specific enthalpy corresponding toT andf - k thermal conductivity - L latent heat of evaporation - M ₁ molecular weight of argon (M ₁=39.99) - M ₂ molecular weight of copper (M ₂=63.55) - p ₀ pressure of the gas mixture - p _s partial pressure of copper vapor at the particle surface - Q ₀ heat flux to a particle without evaporation - Q ₁ heat flux to a particle with evaporation - R gas constant - r radical coordinate - r _s particle radius - S heat conduction potential defined in Eq. (4) - S _s surface value ofS, corresponding toT _s andf _s - S free-stream value ofS, corresponding toT andf - T temperature - T _b boiling temperature of particle material - T _s particle surface temperature - T plasma temperature - density - T temperature step for numerical integration     

A study of chromic oxide decomposition in an RF argon plasma

Vapor-phase thermal decomposition of chromic oxide in an rf argon plasma was studied using a new experimental system. Homogeneous and heterogeneous modes of reaction were compared, the overall process efficiency being substantially higher for the process carried out entirely in the vapor phase. Reaction products were collected along the reactor wall and studied by chemical methods as well as SEM, X-ray, and IR absorption. The collected powder was highly reactive, fine-grained, and of semiamorphous nature, the average particle size being well below 100 nm. Temperature profiles recorded below the coupling coil by spectroscopic methods were typical of an rf plasma, showing maxima slightly exceeding 5000 K, with the presence of off-axis peaks. Local Cr contents and concentration ratio (Cr)/(Cr₂O₃) in the plasma were determined from the deposition data obtained. A diffusion process was assumed for the wall-deposit buildup. The results obtained confirmed the advantages of using plasma vapor-phase systems, these being higher-efficiency processes and more reliable models than those obtained in the case of gas-solid plasma reactors, where solid particles are injected into the plasma. The thermal decomposition conversion of Cr₂O₃ into Cr was about 8 times higher in the homogeneous gas phase than in the plasma solid phase, all other conditions being equal.Nomenclature c velocity of light, cm × s^–1 - C _Cr ^m metallic Cr content, % by wt. - C _Cr ^t total Cr content, % by wt. - D species diffusivity, cm² · s^–1 - E energy of excited level, eV - f oscillator strength - F rate of species deposition, mol · cm^–2 · s^–1 - g statistical weight - h Planck's constant, J · s^–1 - I radial emission intensity for a given spectral line at a given radius in the plasma, W · sr^–1 · cm^–3 - k Boltzmann's constant, J · K^–1 - l length of collected deposit, cm - m mass of collected deposit, g - M molar weight of Cr - M _Ar ^a molar flow of axial argon, mmol · s^–1 - M _Ar ^p molar flow of peripheral argon, mmol · s^–1 - M _{Cr 2}O₃ molar flow of evaporated Cr₂O₃, mmol · s^–1 - Cr(I) concentration, cm^–3 - Q _T partition function at temperatureT - r reaction radius, cm - R radius of quartz tube, cm - t duration of deposition, s - T temperature, K - total extent of Cr₂O₃ decomposition into Cr, % - Z position of a plane normal to the plasma axis downward the lower turn of rf coil, cm Greek Letters molar ratio of Cr and Cr₂O₃ in deposit - wavelength, nm - species concentration, mol · cm^–3     

Heat transfer from a transferred-arc plasma to a cylindrical enclosure

Hear-transfer rates from an axially enclosed transferred arc to a surrounding water-cooled cylindrical sleeve, 15 cm high, were measured. The arc (argon or nitrogen) was struck between a movable cathode within the sleeve and a bath of molten copper below the sleeve, serving as anode. The distance from the bottom of the sleeve to the surface of the molten copper (L _o) was constant. Variables studied were the diameterD of the sleeve (5, 7.5. and 10 cm), the length of the arc within the sleeveL (5, 10, and 15 cm), the currentI (200, 250, and 300 A) and a tangential flow of gas or vortex within the sleeve (0, ?0, and 50 liters/min). The total power transferred to the sleeve,P _s was measured caloronetrically and was the sure ofP _r the effective power radiated by the arc of lengthL within the sleeve.P _a, the power radiated into the sleeve from the arc of length L_o below the sleeve, andP _o , the power radiated from the melt surface (a constant of small value), minusP _a , the power lost by convection from the sleeve (negligible, except for a strong vortex). BothP _r andP _o were found to be equal to the product of the Joule heat released within their respective arc lengths, IV_gL and IV_g0L₀ (where V_g and V_g0 are the voltage gradients), and dimenonless efliciency factors, η_r and η₀. which are functions ofL/D andL ₀ /D, respectively, for each gas, regardless of the geometry of the sleeve, the current, and the strength of the vortex.     

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.     

Dependence of the self-bias on the plasma parameters and on the electrode areas in RF plasma reactors

From the current-voltage characteristics for the collisionless sheath the dependence of the self-bias on the plasma parameters (electron temperature, ratio of electron temperatures and electron densities at the two electrodes), on the applied external voltage, and on the ratio of the electrode areas is investigated. Sinusoidal (is well as periodic rectangular and triangular time dependences of the voltage are considered. The integral equation for the self bias voltage is solved numerically. For large external RF voltages in comparison to the floating potential, simple analytical formulas result for the dependence of the bias voltage on the plasma parameters and the dimensions of the electrodes, which can be useful in practice.     

质量、热量传递过程中的Marangoni效应*

由质量、热量传递引发,表面张力梯度驱动的Marangoni效应不但对化学工程、材料工程和热能工程等领域里的一系列过程具有重要的影响,而且具有非线性耗散系统理论研究的一个具有实际意义的课题。对Marangoni效应的实验及理论研究有助于增进对微观传热、传质机理的理解,它的合理利用也可以提高某些过程的效率。迄今为止,对Marangoni效应的认识还不能满足理论研究和工程应用的要求。按期在各相关领域内对Marangoni的研究十分活跃,本文回顾了这些研究成果。     

Modeling heat and mass transfer in the gas-phase chemical deposition of polycrystalline ZnSe layers

Heat and mass transfer in the gas-phase deposition of zinc selenide in the zinchydrogen selenide—argon system with separate injection of reagents into a reactor by local jets has been studied. The effects of technological parameters, design, and the geometric dimensions of the reactor on the distribution of the deposition rates of the zinc selenide layers formed have been considered.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1625–1631, July, 1996.     

Hydrodynamics and heat transfer in a plasma spouted bed reactor

The literature reveals very little intformation about plasma spouted bed hydrodynamics. Spouting of corindon particles with diameters ranging from 0.4 to 3.36 mm with argon plasma was conducted in a 90-mm-diameter column in the temperature range 300–1300°C. It was found that the maximum spoutable height (H_m) decreases with increasing particle diameter and decreasing mean bed temperature. A relation between the inlet plasma velocity and H_m is proposed. Concerning heat transport phenomena in the annulus, measurements and calculations indicate a large axial diffusivity but a poor radial mixing. Typical values of D_z and D_r are proposed on the basis of an identification procedure.Notation Ar Archimede number - Ar d ³ p (p — f) _f g ² - C_p specific heat - d_p particle diameter - d_e core diameter (or spout diameter) - D_i fluid inlet orifice diameter - D_e column diameter - D_r and D_z radial and axial diffusivity, respectively - g acceleration due to gravity - H packed static bed height - H_b bed height - H_m maximum spoutable bed height - P power     

Knudsen effect on plasma-particle mass transfer. I. Formulation and application to self-diffusion

The Knudsen effect on mass transfer between a plasma gas and a small particle is investigated. A predictive model is developed by incorporating the Z-potential approach into the jump theory. The predictions of the model are explored through a case study. The results indicate that the Knudsen effect is significant and depends strongly on the particle size and the surface conditions. The plasma and the particle surface temperatures are also found to be determining factors. Under certain conditions, it is observed that the Knudsen effect can enhance the plasma-particle mass transfer, contrary to the predictions of the previous near-isothermal models.     

Influence of the Electromagnetic Forces on Momentum and Heat Transfer in a 3-Phase ac Plasma Reactor

A new 3-phase ac plasma reactor has been developed within the framework of research on hydrocarbon cracking for the production of carbon black and hydrogen. ^(1,2) One of the main characteristics of the system is related to the 3-phase, 50 Hz ac current plasma generator which induces a very particular arc motion affecting the heat and mass transfer inside the reactor. In a first step, the general flow inside the reactor in the absence of hydrocarbon injection has been studied. A simplified approach to characterize the heat and mass transfer inside the reactor is presented in this paper. The arc zone analysis is carried out simultaneously by a theoretical analysis of the electromagnetic forces and by an ultrahigh-speed cine-camera analysis. The flow in the reactor is modeled with a CFD commercial code. Results are compared with experimental temperature measurements.     

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.     

Heat transfer coefficient and pressure drop during refrigerant R-134a condensation in a plate heat exchanger

The condensation heat transfer coefficient and the two-phase pressure drop of refrigerant R-134a in a vertical plate heat exchanger were investigated experimentally. The area of the plate was divided into several segments along the vertical axis. For each of the segments, local values of the heat transfer coefficient and frictional pressure drop were calculated and presented as a function of the mean vapor quality in the segment. Owing to the thermocouples installed along the plate surface, it was possible to determine the temperature distribution and vapor quality profile inside the plate. The influences of the mass flux and the heat flux on the heat transfer coefficient and the pressure drop were also taken into account and a comparison with previously published experimental data and literature correlations was carried out. Presented at the 34th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 21–25 May 2007.     

Enhancement of the heat and mass transfer in compact zeolite layers

Heat and mass transfer during the adsorption of water on zeolite has been studied both theoretically and experimentally. A dynamic simulation model of a zeolite layer has been developed to estimate the predominant transport resistances and calculations were carried out to assist the simultaneous experimental investigations. On one hand, a metallic matrix was added to the compact zeolite layer to improve the heat transfer. On the other hand, pore-forming materials such as melamine or tartaric acid were used. These organic components are removed during drying of the zeolite so that the mass transfer inside the zeolite is significantly enhanced compared to a granulated zeolite bed. The experimental investigations show that the theoretically deduced possibilities of improving the adsorption process can be realized in the manufactured zeolites.The investigations described here are of interest for the development of adsorption heat pumps. Due to the thermodynamic characteristics the adsorption system zeolite-water is a promising working pair for this application. The investigations show that the main shortcoming of these machines, the thermal output, can be increased significantly.     

Experimental studies of charge transfer reactions between argon and the third row metals calcium through copper in the inductively coupled plasma

The effect of charge transfer reactions on analyte excitation and ionization in the inductively coupled plasma was studied by two independent techniques. In one technique, pulsed lasers were used to either deplete the ground state of neutral analyte atoms or enhance the population of selected states of the singly charged ion. In both cases the perturbed species were collision partners with argon in potential charge transfer reactions. The effects of charge transfer collisions could be detected in the form of changes in emission from product species. In the second technique, a simple correlation method was used to detect the link via charge transfer of neutral atom ground states and highly excited ionic levels. In the presence of charge transfer collisions, the populations of such linked levels show strong positive correlations. The two techniques were used to study the effects of charge transfer reactions on the third row elements Ca–Cu. With the exception of Cr and Mn, all of the elements studied showed positive evidence of excitation and ionization by charge transfer collision with argon.     

Polymerization of mono‐, Di‐, and trichloroethyl methacrylates: A study in chain transfer

Bulk free radical polymerization of the monomer series CH₂ = C(CH₃)C(O)OCH₂CH_3‐n Cl_n , n = 1, 2, 3, yields an unexpectedly crosslinked product with a crosslink density that increases with decreasing chlorine content of the respective monomer (n = 3 < n = 2 < n = 1). This chlorine substituent effect is investigated by correlation with chain transfer constant measurements for four homologous series of chloroalkyl compounds (chloroethyl acetates (CH₃C(O)OCH₂CH_3‐n Cl_n , n = 1,2,3); chloromethanes (CH_4‐n Cl_n , n = 2,3,4) and CD₂Cl₂ and CDCl₃ analogs; butyl chloride isomers (n‐ , iso‐ , sec‐, tert‐) and tert‐C₄D₉Cl analog; and nine chloroethanes (C₂H_{n ?6}Cl_n , n = 1–6)) in a methyl methacrylate polymerization. The pattern conveyed by the magnitude of chain transfer constants and deuterium isotope effects is consistent with a vicinal chlorine effect (i.e., chlorine activation of a vicinal hydrogen for abstraction) to account for the relative activities of the four series of model compounds and for the propensity of the chloroethyl methacrylates to crosslink in a bulk free radical polymerization. The chloroalkyl moiety's contribution to chain transfer is relatively modest (≤10^?4), but, when incorporated as a monomer pendant group in free radical polymerizations, it is effective in broadening molecular weight to the extent of resulting in a crosslinked polymer. Published 2016.^? J. Polym. Sci., Part A: Polym. Chem. 2017 , 55 , 93–106