Ordinary Diffusion Coefficients Research Articles

Dehumidification Analysis of Rotary Solid Desiccant Wheel System for different Surface Materials

In recent decades, desiccant dehumidification has been given much interest in the air conditioning industry area. Compared to the conventional vapour compression air conditioning system, desiccant dehumidification has various advantages, including separate humidity and temperature control. In this paper, the analysis of the Rotary Solid Desiccant Wheel System has been performed. Here, we have studied three diffusion coefficients: Ordinary, Knudsen and Surface diffusion coefficients for Rotary Solid Desiccant Wheel System. Also, the analysis has been performed for three different solid desiccant materials: Silica Gel, Molecular Sieve and Activated Alumina to incorporate and to study the effect of pore size on moisture transport and to examine the impact of Tortuosity factor on moisture transport phenomenon. This analysis can correctly select the best desiccant material suitable for the desiccant dehumidification industry.

Investigation of transient metal vapour transport processes in helium arc welding by imaging spectroscopy

In order to understand the transient transport mechanisms of metal vapour in an arc plasma, imaging spectroscopy was performed for helium arc plasmas burning on pure metals. The measured images were converted into the spectral intensity distributions at the central cross-section of the arc plasma by image processing and Abel inversion. The transient transport process of metal vapours inside the arc plasma are discussed in terms of the diffusion coefficients of metal vapour. The metal vapour generated from the weld pool surface was transported into the arc plasma and to the region near the tungsten electrode within a few seconds. As time passed, the metal vapour spectral intensities gradually increased near the weld pool surface, near the electrode and in the intermediate region. In contrast, the He I spectral intensity was weak and the He I distribution shrunk toward the centre of the arc. This is because the helium arc plasma was cooled by the strong radiation from metal vapour. For an arc burning on pure chromium, chromium ions reached to centre of the arc after about 40 s. In contrast, on pure iron, iron ions did not reach to the centre of the arc. This is because the helium arc plasma on pure chromium was cooled to a temperature at which the electric field and ordinary diffusion coefficients of chromium are largest, whereas the temperature of the plasma on pure iron remained high. Two factors contributed to this; the higher boiling point of iron, which reduces the iron vapour concentration, and the lower radiative emission coefficient of iron.

Effects of Ultrasonic Vibration on the Transport Coefficients in Plasma Arc Welding

In ultrasound assisted plasma arc welding (U-PAW), the exerted ultrasonic vibration on the tungsten electrode interacts with the plasma arc and changes its heat-pressure characteristics. It is of great significance to investigate the underlying interaction mechanism. In this study, the calculation method of transport coefficients in U-PAW is developed. Translational thermal conductivity (including electrons thermal conductivity and the thermal conductivity of heavy particles) and electrical conductivity are calculated by considering the second-order approximation of Maxwell velocity distribution function, while the method of Butler et al. is adopted to calculate the reaction thermal conductivity in U-PAW. The effective value of the ultrasound velocity gradient tensor is employed to describe the effects of ultrasonic vibration on transport coefficients in ultrasound assisted plasma arc. The calculation results show that when the ultrasound is applied, the thermal conductivity of heavy particles in the plasma increases significantly and the electron thermal conductivity increases within some extent. The thermal conductivity of the reaction also increased to a great extent, and the electrical conductivity decreases a little bit. Although the thermal diffusion coefficient also has some increase, but the ordinary diffusion coefficient is obviously reduced due to the application of the ultrasound. With the updated transport coefficients, the plasma arc pressure on the anode surface is numerically computed, and the predicted pressures of PAW and U-PAW can be consistent with the measured ones.

Numerical simulation of mixture gas arc of Ar-O<sub>2</sub>

Mixture gas arcs are used extensively in welding manufacturing. A two-dimensional steady mathematical model for Ar-O<sub>2</sub> mixture gas arc is developed to understand further the heat and mass transfer of the mixture gas arc. The model is based on the assumption of local thermodynamic equilibrium, and the thermodynamic parameters and transport coefficients are dependent on both the temperature and the oxygen content. In the present model, the diffusion between the argon species and oxygen species is depicted by the approach of the combined diffusion coefficient, i. e. the mixture gas arc is simplified into two different species, and the diffusion between them is formulated by combined ordinary diffusion coefficient and combined temperature diffusion coefficient; the oxygen distribution and its influence on the temperature and flow field of the arc are investigated for two different current conditions. It is shown that the oxygen species presents significant non-uniform distribution for argon gas mixed with 5% oxygen; the oxygen content is higher than that in mixed shielding gas in the regions close to the electrodes and arc axis, while its content is lower than that of the mixed shielding gas in other regions. For high current, oxygen concentrates more to the flat anode, while it concentrates more to tungsten cathode for low current. For both cases, oxygen content is inhomogeneous in the region 0.1 mm above the anode. The 5% oxygen mixed in argon constricts the arc plasma to some extent and thus raises the arc temperature as well as the plasma flow velocity.

A computational model of gas tungsten arc welding of stainless steel: the importance of considering the different metal vapours simultaneously

A 2D computational model of the mixing of multiple metal vapours into a helium arc in gas tungsten arc welding of stainless steel is presented. The combined diffusion coefficient method, extended to three-gas mixtures, is used to treat helium–chromium–iron and helium–manganese–iron plasmas. It is found that all metal vapours penetrate to the arc centre and reach the cathode, with iron vapour confined near the cathode tip, while chromium and manganese vapours accumulate about 1.5 mm above the tip. The predicted distributions of chromium, manganese and iron show reasonable agreement with published photographic images and radial distributions of atomic line emission intensities. The results are also consistent with published measurements of the deposition of the metals on the cathode surface. A detailed examination of the influence of the different diffusion coefficients, net emission coefficients and vapour pressures of the metals on the metal vapour transport in the arc plasma is presented. It is shown that cataphoresis (diffusion due to applied electric fields) leads to the penetration of the metal vapours into the arc. The different distribution of iron vapour from those of chromium and manganese vapours near the cathode is strongly influenced by the lower ordinary diffusion coefficients of iron at low temperatures. Radiative emission is found to be important since it leads to cooling of the arc, which decreases the influence of cataphoresis. The vapour pressure only influences the concentration of the metal vapour close to the workpiece. Results for the two-gas helium–chromium and helium–iron systems are compared to those for the three-gas helium–chromium–iron system. It is shown that it is important to consider the different metal vapours simultaneously to obtain an accurate calculation of the metal vapour and arc temperature distributions.

Combined Diffusion Coefficients in CO2 Thermal Plasmas Contaminated with Cu, Fe or Al

Our work aims at the computation of combined diffusion coefficients in CO2–metal (Cu, Fe, Al) mixtures at a temperature interval of 2000–30,000 K at 0.1 MPa and aims at the investigation of the impact of the concentration and nature of metal vapor (Cu, Fe, Al) on diffusion phenomena. The combined diffusion coefficients have four components, more specifically, combined ordinary diffusion coefficient, combined electric field diffusion coefficient, combined temperature diffusion coefficient and combined pressure diffusion coefficient due to the gradients of the species densities, applied electrical field temperature and pressure. The results indicate that, for Cu and Fe, the combined diffusion coefficients are quite identical under the condition of same metal concentrations (1 and 10% mass concentration). Compared with Cu and Fe under the same metal concentrations (1 and 10%), Al results in a larger enhancement of combined electric field and ordinary diffusion coefficients while smaller enhancement of combined temperature diffusion coefficients. All the combined diffusion coefficients exhibit an upward trend with metal concentrations except for combined electric field, temperature and pressure diffusion coefficients. These three mentioned coefficients are attenuated by the metal vapor above the certain concentration such as, in the case of combined temperature diffusion coefficients, 70% Cu, 70% Fe and 50% Al for CO2–Cu, CO2–Fe and CO2–Al mixtures respectively. Namely, compared with Cu and Fe, less quantity of Al is required to achieve the maximum of combined diffusion coefficients. Maximum peaks for the combined coefficients are shifted to the higher temperature with increasing metal concentrations.

Thermodynamic properties and transport coefficients of two-temperature helium thermal plasmas

Helium thermal plasmas are in widespread use in arc welding and many other industrial applications. Simulation of these processes relies on accurate plasma property data, such as plasma composition, thermodynamic properties and transport coefficients. Departures from LTE (local thermodynamic equilibrium) generally occur in some regions of helium plasmas. In this paper, properties are calculated allowing for different values of the electron temperature, Te, and heavy-species temperature, Th, at atmospheric pressure from 300 K to 30 000 K. The plasma composition is first calculated using the mass action law, and the two-temperature thermodynamic properties are then derived. The viscosity, diffusion coefficients, electrical conductivity and thermal conductivity of the two-temperature helium thermal plasma are obtained using a recently-developed method that retains coupling between electrons and heavy species by including the electron–heavy-species collision term in the heavy-species Boltzmann equation. It is shown that the viscosity and the diffusion coefficients strongly depend on non-equilibrium ratio θ (), through the plasma composition and the collision integrals. The electrical conductivity, which depends on the electron number density and ordinary diffusion coefficients, and the thermal conductivity have similar dependencies. The choice of definition of the Debye length is shown to affect the electrical conductivity significantly for θ > 1. By comparing with literature data, it is shown that the coupling between electrons and heavy species has a significant influence on the electrical conductivity, but not on the viscosity. Plasma properties are tabulated in the supplementary data.

Calculation of combined diffusion coefficients in SF6-Cu mixtures

Diffusion coefficients play an important role in the description of the transport of metal vapours in gas mixtures. This paper is devoted to the calculation of four combined diffusion coefficients, namely, the combined ordinary diffusion coefficient, combined electric field diffusion coefficient, combined temperature diffusion coefficient, and combined pressure diffusion coefficient in SF6-Cu mixtures at temperatures up to 30 000 K. These four coefficients describe diffusion due to composition gradients, applied electric fields, temperature gradients, and pressure gradients, respectively. The influence of copper fluoride and sulfide species on the diffusion coefficients is shown to be negligible. The effect of copper proportion and gas pressures on these diffusion coefficients is investigated. It is shown that increasing the proportion of copper generally increases the magnitude of the four diffusion coefficients, except for copper mole fractions of 90% or more. It is further found that increasing the pressure reduces the magnitude of the coefficients, except for the combined temperature diffusion coefficient, and shifts the maximum of all four coefficients towards higher temperatures. The results presented in this paper can be applied to the simulation of high-voltage circuit breaker arcs.

Numerical solution of multi-component species transport in gases at any total number of components

In Böttcher [K. Böttcher, Numerical solution of a multi-component species transport problem combining diffusion and fluid flow as engineering benchmark, Int. J. Heat Mass Transfer 53 (1–3) (2010) pp. 231–240], one of us described an implementation of ternary multi-component species transport by diffusion and convection and presented benchmark cases and simulation results for these cases computed with software ENTWIFE. In this paper, an implementation of the Stefan–Maxwell equation into the ANSYS CFX software is described in combination with a procedure to numerically calculate the ordinary multi-component diffusion coefficients in gases at any total number of components. Finally, the benchmark for ternary mixtures is extended to a quarternary one. A comparsion to the benchmark results of Böttcher revealed an implementation mistake in Böttcher’s paper leading to wrong results in case of largely different molar masses. The correct benchmark results are presented here and furthermore compared to two different kinds of effective binary diffusion approaches in multi-component gas mixtures.

Transport coefficients of plasmas in mixtures of nitrogen and hydrogen

Calculated values of the viscosity, thermal conductivity and electrical conductivity of nitrogen and mixtures of nitrogen and hydrogen, including ammonia and hydrazine, at high temperatures are presented. Combined ordinary, pressure, temperature and electric field diffusion coefficients are also given for the mixtures. The calculations, which assume local thermodynamic equilibrium, are performed for plasmas in the temperature range from 300 to 30,000K and the pressure range from 0.1 to 5atm. The results are compared with those of previously published studies. Reasonable and in some cases very good agreement is found; those discrepancies that exist are attributed to the improved values of the some of the collision integrals used here. Different mixing rules are tested, with two found to give very good results: that of Yun et al. [K.-S. Yun, S. Weissman, E.A. Mason, Phys. Fluids 5 (1962) 672] for the viscosity and thermal conductivity, and a simple interpolation weighted by mole fraction for the electrical conductivity.

Measurement of Knudsen and Effective Ordinary Diffusion Coefficients in Solid Oxide Fuel Cell Anodes Fabricated by Atmospheric Plasma Spraying Using Powder, Suspension, and Solution Precursor Feedstocks

Ni and yttria-stabilized zirconia electrode layers were fabricated by atmospheric plasma spraying using powder, suspension, and solution precursor feedstocks. Permeability measurements were used to evaluate the Knudsen diffusion coefficients for N2. It was demonstrated that the forced flow behavior for a second gas, e.g. Ar, may be determined based on the microstructural parameters obtained using N2. Graham's diffusion cell was used to obtain effective ordinary diffusion coefficients for the H2/N2 system. The values obtained for the three plasma sprayed coatings did not differ significantly. Further work is required to satisfactorily separate the diffusion coefficients for the coatings from the measured results on the support and coating combinations.

Two-temperature thermodynamic and transport properties of carbon–oxygen plasmas

Thermodynamic and transport properties of different carbon–oxygen plasmas mixtures are presented for both thermal equilibrium and non-equilibrium conditions: to the knowledge of the authors, the latter data have not been reported in the literature. The calculations of transport properties are carried out using the Chapman–Enskog method up to the third order; properties for plasmas out of equilibrium have been obtained using both the two-temperature theory developed by Rat et al and a simplified theory by Devoto, that neglects the coupling between electrons and heavy particles; it is shown that for carbon–oxygen mixtures no differences between results obtained using these two theories can be appreciated for thermal and electrical conductivities; some discrepancies have been found for ordinary diffusion coefficients of the type electron-heavy particle. Moreover, local thermodynamic equilibrium results for transport properties obtained using Lennard-Jones potentials have been compared with results obtained using more recent potential data and with available results reported in the literature. Results for composition, mass density, specific heat, thermal conductivity, electrical conductivity and viscosity of atmospheric pressure plasmas in the electron temperature range 300–30 000 K are reported.

Calculation of diffusion coefficients in air–metal thermal plasmas

This paper presents the combined diffusion coefficients of metal vapours (silver, copper and iron) in air thermal plasmas for temperatures ranging from 300 to 30 000 K. The theory used to calculate these coefficients is remembered and validated by comparison with the literature values in several cases such as Ar–He, Ar–Cu and N2–O2 mixtures. The results are discussed showing the influences of the metal concentration, of the vapour nature and of the pressure. The results show rather similar behaviour for the three metals. The maximum values of the combined ordinary diffusion coefficient in the evolution with temperature are obtained for temperature around 10 000 K but this peak is shifted to the highest temperatures when the metal proportion increases. Another result shows that the diffusion coefficient decreases when pressure increases.

Transport properties in non-equilibrium argon, copper and argon–copper thermal plasmas

We present calculated values of transport properties (viscosity, thermal and electrical conductivities) of argon, copper and argon–copper thermal plasmas at equilibrium and non-equilibrium. In addition, combined ordinary and thermal diffusion coefficients, as defined by Murphy, are also given. The calculations are performed in the temperature range 300–25 000 K and at atmospheric pressure.For all these calculations, we use a recent theory developed by Rat to determine the transport properties like, for example, viscosity or combined diffusion coefficients in non-equilibrium plasma (note that equilibrium is only a specific case). We also take great care in evaluating the collision integrals necessary to calculate the transport coefficients (especially the Cu–X interactions). At equilibrium, our results are compared with published values obtained theoretically and experimentally. Moreover, to our knowledge, there are no accessible data for these non-equilibrium argon–copper plasmas.

TWO-TEMPERATURE COMBINED DIFFUSION COEFFICIENTS IN ARGON-HELIUM THERMAL PLASMAS

From the derivation of two-temperature diffusion number fluxes of species proposed by Rat et al and that of ambipolar diffusion coefficients, combined diffusion coefficients introduced by Murphy at equilibrium are extended to non-equilibrium thermal plasmas, where the kinetic temperature of electrons Te is different from that of heavy species Th. Two-temperature ordinary and thermal combined diffusion coefficients are calculated in an argon-helium plasma at atmospheric pressure up to 30,000 К. Plasma composition is obtained using a non-equilibrium constant method. The dependence on the electron temperature of combined diffusion coefficients is analyzed for different mole percentages of argon in the mixture and for different values of the non-equilibrium parameter q = Te/Th Similar behaviors to those obtained at equilibrium are highlighted with a decrease in the combined diffusion coefficients, at fixed electron temperature, as q increases.

Isotopic Approximations to Thermal Diffusion Factor and Ordinary Diffusion Coefficient in a Mixture of More than 4 Components

Isotopic approximations to thermal diffusion factors in mixtures of more than 4 components were derived in the case where a gas mixture consists of isotopes and squares of relative mass differences among the isotopes are small enough to be negligible. Approximate solutions of a set of υ-simultaneous equations by which the factor is expressed were given on the analogy of those in 3-component mixture, and they were ensured to satisfy the equations approximately. The obtained approximations to the factors were the same as those to binary thermal diffusion factors. The same procedure led to approximate expressions to ordinary diffusion coefficients.

Isotopic Approximations to Thermal Diffusion Factor and Ordinary Diffusion Coefficient in a Mixture of More than 4 Components.

Isotopic approximations to thermal diffusion factors in mixtures of more than 4 components were derived in the case where a gas mixture consists of isotopes and squares of relative mass differences among the isotopes are small enough to be negligible. Approximate solutions of a set of υ-simultaneous equations by which the factor is expressed were given on the analogy of those in 3-component mixture, and they were ensured to satisfy the equations approximately. The obtained approximations to the factors were the same as those to binary thermal diffusion factors. The same procedure led to approximate expressions to ordinary diffusion coefficients.

Velocity Correlation and the Spatial Diffusion Coefficients of Cosmic Rays: Compound Diffusion

We consider the transport of charged particles in a stochastic magnetic field using a method based on the velocity correlation function ⟨vi(0)vj(t)⟩ developed by R. Kubo. This can be used under very general conditions to evaluate the corresponding spatial diffusion coefficients, if the fluctuations are statistically homogeneous in space and time. Although Kubo's theory is quite general, it is not obvious how it can be applied to describe compound diffusion when particles are strictly tied to the magnetic field lines and perpendicular transport results solely from the random walk of the field lines. This motion is non-Markovian and leads to a slower ⟨Δx2⟩ ∝ t1/2 diffusion in contrast to the ⟨Δx2⟩ ∝ t dependence of the standard diffusion. We demonstrate how compound diffusion fits into Kubo's formalism. As intuitively as can be anticipated, the non-Markovian nature of the motion results in a long-term anticorrelation in ⟨vj(0)vi(t)⟩, which causes the ordinary spatial diffusion coefficient to vanish identically. The ⟨Δx2⟩ ∝ t1/2 dependence of the compound diffusion can also be recovered from the Laplace transform of the velocity correlation function. Some implications of the long-term anticorrelation are discussed.

Transport Coefficients of Hydrogen and Argon–Hydrogen Plasmas

Calculated values of the viscosity, thermal conductivity, and electrical conductivity of hydrogen and mixtures of argon and hydrogen at high temperatures are presented. Combined ordinary, pressure, temperature, and electric field diffusion coefficients are also given for the mixtures. The calculations, which assume local thermodynamic equilibrium, are performed for atmospheric pressure plasmas in the temperature range from 300 to 30,000 K. The results are compared with those of previously published studies. Generally, the agreement is reasonable; those discrepancies that exist are attributed to the improved values of some of the collision integrals used here in calculating the transport coefficients.

Thermal Field-Flow Fractionation Universal Calibration: Extension for Consideration of Variation of Cold Wall Temperature

The well-known size exclusion chromatography (SEC) universal calibration allows the characterization of a polymer sample using a set of polymer standards of a different polymer family. This is a polymer-transferable calibration method. A more “universal” calibration method has been proposed for thermal field-flow fractionation (ThFFF) where the calibration constants closely describe the ratio of ordinary (molecular) diffusion coefficient D to thermal diffusion coefficient (or, more correctly, thermophoretic mobility) DT. The universal calibration for ThFFF is therefore instrument or system transferable. Systematic experiments have previously been carried out to verify this calibration method for a wide range of conditions. Results showed that the method holds well provided experimental conditions such as sample size and cold wall temperature Tc are the same for each system. This paper quantifies the effect of cold wall temperature on polymer retention in ThFFF and on the universal calibration constants fo...