MATHEMATICAL MODELS OF NITROGEN CONCENTRATION PROFILE OF ION NITRIDED LAYERS AND COMPUTER SIMULATION

The mathematical models of the kinetics of the layer growth at different ion nitriding condi- tions of armco iron.steels 45,40Cr,42CrMo and 38CrMoAl have been established.Based on these models the expression of nitrogen concentration profile of ion nitrided layers have been deduced with profile simulating method.They are C_=C_(min)^+(P_4)/(ξ_1-x)+(P_5)/(ξ_(10)~2)(ξ_1-x)~2 C_(γ′)=C_(min)^(γ′)+(P_1)/(ξ_(21))(ξ_2-x)+(P_2)/(ξ_(21)~2)(ξ_2-x)~2 C_α=C_(min)~α+(C_(33))/(C_(33))/(ξ_(32))(ξ_3-x)~3 Using these models,the kinetics of layer growth and the nitrogen concentration profile of ion nitrided layers were sinulated on Apple-Ⅱ computer.Results show that the simulated curves coincide quite well with the experimental data.

Mathematical Models and Computer Simulation of Nitrogen Concentration Profiles in Pulse Ion Nitrided Layers

The nitrogen concentration profiles in surface layers and surface phase structures were accurately measured respectively using the glow discharge spectrometry and X-ray Diffractometer after the specimens had been pulse ion nitrided at 500℃ for 0.2-8h The results show that the compound layer growth, which is different from that of conventional DC nitriding, conforms to parabolic law At the same time the surface nitrogen concentration change little with increasing the nitriding time, at least it is so when the treating time is longer than 0.2h In addition, the mathematical models of nitrogen concentration profiles in ε -Fe2~3N,γ-Fe4N and α -Fe phases have been established. Using them the nitrogen concentration profiles in nitrided layers were simulated. Results show that the simulated curves coincide quite well with the experimental data.

Separating emitted dust from the total suspension in airflow based on the characteristics of PM10 vertical concentration profiles on a Gobi surface in northwestern China

During aeolian processes,the two most critical factors related to dust emissions are soil particle and aggregate saltation,which greatly affect the vertical profiles of near-surface dust concentrations.In this study,we measured PM10 concentrations at four different heights(0.10,0.50,1.00 and 2.00 m)with and without continuous and simultaneous aeolian saltation processes on a Gobi surface in northwestern China from 31 March to 10 April,2017.We found that the vertical concentration profiles of suspended PM10 matched the log-law model well when there was no aeolian saltation.For the erosion process with saltation,we divided the vertical concentration profiles of PM10 into the saltation-affected layer and the airflow-transport layer according to two different dust sources(i.e.,locally emitted PM10 and upwind transported PM10).The transition height between the saltation-affected layer and the airflow-transport layer was not fixed and varied with saltation intensity.From this new perspective,we calculated the airflow-transport layer and the dust emission rate at different times during a wind erosion event occurred on 5 April 2017.We found that dust emissions during wind erosion are primarily controlled by saltation intensity,contributing little to PM10 concentrations above the ground surface compared to PM10 concentrations transported from upwind directions.As erosion progresses,the surface supply of erodible grains is the most crucial factor for saltation intensity.When there was a sufficient amount of erodible grains,there was a significant correlation among the friction velocity,saltation intensity and dust emission rate.However,when supply is limited by factors such as surface renewal or an increase in soil moisture,the friction velocity will not necessarily correlate with the other two factors.Therefore,for the Gobi surface,compared to limiting dust emissions from upwind directions,restricting the transport of suspended dust in its path is by far a more efficient and realistic option for small areas that are often exposed to dust storms.This study provides some theoretical basis for correctly estimating PM10 concentrations in the Gobi areas.

Profile of Methane Concentrations in Soil and Atmosphere in Alpine Steppe Ecosystem on Tibetan Plateau

The methane concentration profile from -1.5m depth in soil to 32m height in air was measured in alpine steppe lo-cated in the permafrost area. Methane concentrations showed widely variations both in air and in soil during the study period. The mean concentrations in atmosphere were all higher than those in soil, and the highest methane concentration was found in air at the height of 16m with the lowest concentration occur-ring at the depth of 1.5m in soil. The variations of atmospheric methane concentrations did not show any clear pattern both temporally and spatially, although they exhibited a more steady-stable state than those in soil. During the seasonal variations, the methane concentrations at different depths in soil were sig-nificantly correlated (R2>0.6) with each other comparing to the weak correlations (R2<0.2) between the atmospheric concentra-tions at different heights. Mean methane concentrations in soil significantly decreased with depth. This was the compositive influence of the decreasing production rates and the increasing methane oxidation rates, which was caused by the descent soil moisture with depth. Although the methane concentrations at all depths varied widely during the growing season, they showed very distinct temporal variations in the non-growing season. It was indicated from the literatures that methane oxidation rates were positively correlated with soil temperature. The higher methane concentrations in soil during the winter were deter-mined by the lower methane oxidation rates with decreasing soil temperatures, whereas methane production rates had no reaction to the lower temperature. Relations between methane contribution and other environmental factors were not discussed in this paper for lacking of data, which impulse us to carry out further and more detailed studies in this unique area.

Possible emissions of N_2O from plants in coniferous-deciduous mixed forests

Aboveground vertical profiles of N2O concentrations were measured with in two natural coniferous-deciduous mixed forests of 1998 and 1999 in Changbai M ountain. Significant high N2O concentrations were found in six profiles out of t welve profiles. The results showed that high concentrations were 3.03% to 64.9% higher than the "normal concentrations" in these six profiles. Differences betwe en the high concentrations and the "normal concentrations" were statistically si gnificant. The simultaneous occurrence of high concentrations at/nearby the cano py height and normal concentrations at the trunk space height indicated an efflu x of N2O from foliage to atmosphere. This study afforded evidence supporting tha t plant per se, besides forest soil, was an important source of atmospheric N2O in a forest ecosystem.

Effect of Aluminum and Silicon on Transformation Induced Plasticity of the TRIP Steel

With the sublattice model, equilibrium compositions of ferrite (a) and austenite (7 ) phases, as well as the volume percent of austenite (7) at 780℃ in different TRIP steels were calculated. Concentration profiles of carbon, Mn, Al and Si in the steels were also estimated under the lattice fixed frame of reference so as to understand the complex mechanical behavior of TRIP steels after different isothermal bainitic transformation treatments. The effect of Si and Mn on transformation induced plasticity (TRIP) was discussed according to thermodynamic and kinetic analyses. It is recognized that Al also induces phase transformation in the steels but its TRIP effect is not as strong as that of Si.

CFD simulation with enhancement factor of sulfur dioxide absorption in the spray scrubber

A model describing the absorption process of SO2 into limestone slurry with a spray scrubber is presented. Both the physical performance of the spray liquid in the scrubber and the involved chemical reactions are analyzed in the model. A con- tinuous concentration change of H+ was solved by iterative coupling using Matlab, and it was found that there was a remarkable influence on the concentration of the other elements in the process of SO2 absorption. The calculations show that the enhancement factor exponentially grows with an increasing value of pH and logarithmically decays with an increasing value of the driving force. To verify the accuracy of the model, experiments were also carried out, and the results suggest that the model, after combining the physical performance of the spray and the enhancement factor, can more precisely describe SO2 absorption in a spray scrubber. Furthermore, a commercial computational fluid dynamics (CFD) tool is used to perform several simulations which describe and clarify the effects of variables on SO2 absorption. The results of numerical simulation can provide a basis for further design and optimization of the scrubber.

Computer-Aided Design of Some Advanced Steels and Cemented Carbides

Thermodynamic and kinetic study on TRIP （transformation induced plasticity） steels, cemented carbides and mold steel for plastics were carried out in order to design modern advanced materials. With the sublattice model, equilibrium compositions of ferrite and austenite phases in TRIP steels, as well as volume fraction of austenite at inter-critical temperatures for different time were calculated. Concentration profiles of carbon, manganese, aluminum and silicon in the steels were also estimated in the lattice fixed frame of reference. The effect of Si and Mn on TRIP was discussed according to thermodynamic and kinetic analyses. In order to understand and produce the graded nanophase structure of cemented carbides, miscellaneous phases in the M-Co-C （M= Ti, Ta, Nh） systems and Co-V-C system were modeled. Solution parameters and thermodynamic： properties were listed in detail. The improvement of machining behavior of prehardened mould steel for plastics was obtained by computer-aided composition design. The results showed that the matrix composition of large-section prehardened mould steel for plastic markedly influences the precipitation of non-metallic inclusion and the composition control by the aid of Thermo-Calc software package minimizes the amount of detrimental oxide inclusion. In addition, the modification of calcium was optimized in composition design.

Salt transport in polymeric pervaporation membrane

The salt transport in a PEBA membrane used in pervaporative desalination was studied.The concentration profile of salt in the membrane during pervaporation was investigated experimentally using a multilayer membrane.The salt was found to be sorbed in the membrane but was not removed during the pervaporative desalination process,and the salt concentration in the membrane varied linearly with position.High purity water was obtained as the permeate as long as the permeate side was kept dry under vacuum.The accumulated salt uptake in the membrane follows the order of MgCl2 N NaCl N Na2 SO4.The solubility of salt in the membrane follows the order of MgCl2 N NaCl N Na2 SO4.Both the permeability and diffusivity of salt in the membrane follow the order of NaCl N MgCl2 N Na2 SO4.The permeability of salt in the membrane is not influenced by the feed salt concentration.It is mainly determined by the diffusion coefficients.

A New Thiele＇s Modulus for the Monod Biofilm Model

A new Thiele＇s modulus, φF, was developed to provide a gradual transition between zero and the first order of kinetics, and to accurately calculate the mass transfer flux and the effectiveness factor for the Monod biofilm. Values of the effectiveness factor, calculated using the new Thiele＇s modulus, were compared with those obtained from numerical solutions and from other published moduli and empirical formulae. The comparison indi- cated that the new Thiele＇s modulus was the best modulus for the Monod biofilm model. In addition, another Thiele＇s modulus, φG, was developed for a Monod biofilm, covered with an external water layer. The overall effectiveness factor can also be calculated by using both moduli φF and φG. The criteria that were proposed for identifica- tion were based on the values of φF and φG, the limiting processes for biomass growth, and substrate conversion. Developed from φF, a new parameter ψ was related uniquely to such features as the depth and shallowness of the generalized substrate concentration profiles inside a Monod biofilm. Criteria were developed to identify the types of concentration distribution inside a Monod biofilm. These methods were used to estimate the substrate flux and the concentration distribution of the biofilms defined in the first benchmark problem （BM1）, by a task group of the International Water Association on Biofilm Modeling.

Generalized Van der Waals Equation for Liquid-Vapor Equilibria in a Stationary Gravitational Field

The behavior of liquids undergoing phase transition in the gravitational field is studied by considering the generalized Van der Waals equation. Considering the two simple models for liquid-vapor boundary of a pure classical fluid, the generalized Van der Waals equation shows how the three critical parameters (critical temperature, critical volume and critical pressure), suffice to describe the reduced state parameters (reduced temperature, reduced volume and reduced pressure), the concentration profile and the liquid-vapor boundary position, which can be used to observe transition phenomenon. This model shows how the form of the equation can influence the vertical phase separation induced by the stationary gravitational field, and on the gas condensation effects.

Application of Finite Fourier Transform and Similarity Approach in a Binary System of the Diffusion of Water in a Polymer

This paper describes the method of two important mathematical techniques used in chemical engineering applications. Solving a mass transfer problem, weather in finite or semi-infinite domain, may seem difficult without the practice of Finite Fourier Transform (FFT) and Similarity Transformation. Finite systems refer to any closed system that has a specific boundary that can be determined. For example, polymer sheets, membranes, storage tanks, oil reservoirs and a human stomach are determined to be finite systems where FFT is applicable to derive expressions for concentration profiles of the materials in the system. However, Similarity Transformation method is used to identify the concentration profile in semi-infinite systems that have no limits. It has been approved that we may also use the similarity procedure for finite systems since our results are almost the same. Methodologies of both techniques have been discussed thoroughly in order to apply them to a water-polymer diffusion system for the determination of the concentration of water in a polymer sheet of PET. Discussion and comparison between FFT and similarity is included to illustrate the power of each mathematical procedure in predicting and modeling mass concentrations.

A NEW MODIFIED LINEAR DRIVING FORCE(MLDF)MODEL

Linear driving force (LDF) model is widely used in a diffusion process. However thismodel has inherent weakness. When the dimensionless time is less than 0.1, its relativeerror is up to 95%. In this paper a new concentration profile is proposed, and then a newmodified LDF model (MLDF) is deduced. Compared with the exact solution ofintraparticle diffusion equation, the transient volume-average amount adsorbedcalculated from the MLDF is more accurate than that calculaled from the LDF modeL .Ifone takes ±10% relative error for the limit of validity of approximation, the new model isvalid when the dimensionless time is just larger than 0. 0002, while the LDF model is notvalid until the dimension time is large than 0.05. The new model is superior to the LDFmodel. The new concentration profiles corresponding to the MLDF model are much closeto the exact concentration profiles within a particle than the parabolic propescorresponding to the LDF model.

Possible emissions of N2O from plants in coniferous-deciduous mixed forests

Aboveground vertical profiles of N2O concentrations were measured with in two natural coniferous-deciduous mixed forests of 1998 and 1999 in Changbai M ountain. Significant high N2O concentrations were found in six profiles out of t welve profiles. The results showed that high concentrations were 3.03% to 64.9% higher than the 'normal concentrations' in these six profiles. Differences betwe en the high concentrations and the 'normal concentrations' were statistically si gnificant. The simultaneous occurrence of high concentrations at/nearby the cano py height and normal concentrations at the trunk space height indicated an efflu x of N2O from foliage to atmosphere. This study afforded evidence supporting tha t plant per se, besides forest soil, was an important source of atmospheric N2O in a forest ecosystem.

Effects of elevated atmospheric CO_2 concentration and temperature on the soil profile methane distribution and diffusion in rice–wheat rotation system

The aim of this experiment was to determine the impacts of climate change on soil profile concentrations and diffusion effluxes of methane in a rice-wheat annual rotation ecosystem in Southeastern China. We initiated a field experiment with four treatments：ambient conditions（CKs）, CO2 concentration elevated to - 500 μmol/mol（FACE）,temperature elevated by ca. 2°C（T） and combined elevation of CO2 concentration and temperature（FACE ＋ T）. A multilevel sampling probe was designed to collect the soil gas at four different depths, namely, 7 cm, 15 cm, 30 cm and 50 cm. Methane concentrations were higher during the rice season and decreased with depth, while lower during the wheat season and increased with depth. Compared to CK, mean methane concentration was increased by 42%, 57% and 71% under the FACE, FACE ＋ T and T treatments, respectively, at the 7 cm depth during the rice season（p 〈 0.05）. Mean methane diffusion effluxes to the 7 cm depth were positive in the rice season and negative in the wheat season, resulting in the paddy field being a source and weak sink, respectively. Moreover, mean methane diffusion effluxes in the rice season were 0.94, 1.19 and 1.42 mg C/（m^2·hr） in the FACE,FACE ＋ T and T treatments, respectively, being clearly higher than that in the CK. The results indicated that elevated atmospheric CO2 concentration and temperature could significantly increase soil profile methane concentrations and their effluxes from a rice-wheat field annual rotation ecosystem（p 〈 0.05）.

Two-dimensional Modeling of a Salt-gradient Solar Pond with Wall Shading Effect and Thermo-physical Properties Dependent on Temperature and Concentration

In this paper,the behavior of a salt-gradient solar pond with the square cross-section has been studied experimentally and numerically.A small-scale solar pond were designed and built to provide quantitative data.A two-dimensional,transient heat and mass transfer model has been solved numerically by using finite-control-volume method.In this study,all the thermo-physical properties are variable as the function of temperature and salt concentration.Numerical results as obtained for the experimental pond have been satisfactorily compared and validated against measured data.Furthermore,the wall shading effect has been elaborated to improve the agreement between two sets of results.The temperature of the storage zone is predicted well by the model.It also can be observed that the initial concentration profile is preserved with time.The stability of the pond in time has been investigated in order to distinguish the critical zones.Finally,the application of an energy analysis gives an efficiency of about 12%for the pond.

Existence and concentration behavior of sign-changing solutions for quasilinear Schr?dinger equations equations

We consider the quasilinear Schrdinger equations of the form-ε~2？u ＋ V（x）u- ε~2？（u2）u = g（u）, x ∈ R^N,where ε 〉 0 is a small parameter, the nonlinearity g（u） ∈ C^1（R） is an odd function with subcritical growth and V（x） is a positive Hlder continuous function which is bounded from below, away from zero, and infΛV（x） 0 such that for all ε∈（0, ε0],the above mentioned problem possesses a sign-changing solution uε which exhibits concentration profile around the local minimum point of V（x） as ε→ 0~＋.

Generation of Linear and Parabolic Concentration Gradients by Using a Christmas Tree-Shaped Microfluidic Network

This paper describes a simple method of generating concentration gradients with linear and parabolic profiles by using a Christmas tree-shaped microfluidic network.The microfluidic gradient generator consists of two parts：a Christmas tree-shaped network for gradient generation and a broad microchannel for detection.A two-dimensional model was built to analyze the flow field and the mass transfer in the microfluidic network.The simulating results show that a series of linear and parabolic gradient profiles were generated via adjusting relative flow rate ratios of the two source solutions（R_L^2≥0.995 and _PR^2≥0.999）,which could match well with the experimental results（R_L^2≥0.987 and _PR^2≥0.996）.The proposed method is promising for the generation of linear and parabolic concentration gradient profiles,with the potential in chemical and biological applications such as combinatorial chemistry synthesis,stem cell differentiation or cytotoxicity assays.

Vertical Distribution Characteristics of PM2.5 Observed by a Mobile Vehicle Lidar in Tianjin, China in 2016

We present mobile vehicle lidar observations in Tianjin, China during the spring, summer, and winter of 2016. Mobile observations were carried out along the city border road of Tianjin to obtain the vertical distribution characteristics of PM2.5. Hygroscopic growth was not considered since relative humidity was less than 60% during the observation experiments. PM2.5 profile was obtained with the linear regression equation between the particle extinction coefficient and PM2.5 mass concentration. In spring, the vertical distribution of PM2.5 exhibited a hierarchical structure. In addition to a layer of particles that gathered near the ground, a portion of particles floated at 0.6–2.5-km height. In summer and winter, the fine particles basically gathered below 1 km near the ground. In spring and summer, the concentration of fine particles in the south was higher than that in the north because of the influence of south wind. In winter, the distribution of fine particles was opposite to that measured during spring and summer. High concentrations of PM2.5 were observed in the rural areas of North Tianjin with a maximum of 350 μg m^–3 on 13 December2016. It is shown that industrial and ship emissions in spring and summer and coal combustion in winter were the major sources of fine particles that polluted Tianjin. The results provide insights into the mechanisms of haze formation and the effects of meteorological conditions during haze–fog pollution episodes in the Tianjin area.

Stochastic formulation of particle kinetics in wall-bounded two-phase flows

This paper presents a generalized framework of stochastic modeling for particle kinetics in wall-bounded flow.We modified a reflected Brownian motion process and straightforwardly obtained a Kramers equation for particle probability density function(PDF).After the wall effects were accounted for as a drift from zero in the mean displacement and suppression in the diffusivity of a particle,an analytical solution was worked out for PDF.Three distinguishable mechanisms were identified to affect the profile of particle probability distribution:external forces,turbophoresis effect,and wall-drift effect.The proposed formulation covers the Huang et al.(2009)model of a wall that produces electrostatic repulsion force and van der Waals force,as well as Monte-Carlo solutions for the Peter and Barenbrug(2002)model under a variety of relaxation times.Moreover,it successfully reproduces the two patterns of particle concentration profiles observed in experiments of sediment-laden open-channel flows.The strength of the wall-drift effect was found to be connected with the interaction frequency between particle and wall.Further exploration of the relationship among flow turbulence,particle inertia,and particle concentration is worthwhile.