Calculation of Thermodynamic Parameters for Freundlichand Temkin Isotherm Models

Derivation of the Freundlich and Temkin isotherm models from the kinetic adsorption/desorpt ion equations was carried out to calculate their thermodynamic equilibrium constants. The calculation formulae ofthree thermodynamic parameters, the standard molar Gibbs free energy change, the standard molar enthalpy change and the standard molar entropy change, of isothermal adsorption processes for Freundlich andTemkin isotherm models were deduced according to the relationship between the thermodynamic equilibriumconstats and the temperature.

A New Competitive Adsorption Isothermal Model of Heavy Metals in Soils

A new competitive adsorption isothermal model(CAIM)was developed for the coexistent and competitive binding of heavy metals to the soil surface.This model extended the earlier adsorption isothermal models by considering more than one kind of ion adsorption on the soil surface.It was compared with the Langmuir model using different conditions, and it was found that CAIM,which was suitable for competitive ion adsorption at the soil solid-liquid surface,had more advantages than the Langmuir model.The new competitive adsorption isothermal model was used to fit the data of heavy metal(Zn and Cd)competitive adsorption by a yellow soil at two temperatures.The results showed that CAIM was appropriate for the competitive adsorption of heavy metals on the soil surface at different temperatures.The fitted parameters of CAIM had explicit physical meaning.The model allowed for the calculation of the standard molar Gibbs free energy change,the standard molar enthalpy change,and the standard molar entropy change of the competitive adsorption of the heavy metals,Zn and Cd,by the yellow soil at two temperatures using the thermodynamic equilibrium constants.

MICRO-DESCRIPTION OF THE SOLUTE-FIELD AND THE PHASE-FIELD MODEL FOR ISOTHERMAL PHASE TRANSITION IN BINARY ALLOYS

A new phase field method for two-dimensional simulations of binary alloy solidification was studied. A model basing on solute conservative in every unit was developed for solving the solute diffusion equation during solidification. Two-dimensional computations were performed for ideal solutions and Ni-Cu dendritic growth into an isothermal and highly supersaturated liquid phase.

CO_2 isothermal adsorption models of coal in the Haishiwan Coalfield

Since the capacity of CO2 adsorption of coal is a key factor in coal and CO2 outbursts,an experimental study was carried out on CO2 isothermal adsorption with high-pressure volumetry with dry coal samples from the No.2 coal seam in the Haishiwan Coalfield.Four different equations(Langmuir,BET,D-R and D-A) were used to fit the experimental data.We discuss adsorption mechanisms.The results show that the amount of CO2 adsorption increases rapidly under low relative pressure,i.e.,the ratio of equilibrium pressure and saturated vapor pressure,which indicates that molecular layer adsorption or micropore filling may occur in coal.No clear equilibrium state was observed on the isothermal adsorption curves under relative pressure(P /P0 ) ranging from 0 to 0.8.The fitted results show that the accuracy of the D-A equation is highest with n=1.Micropores are more developed in coal by comparing the BET equation with a pressure mercury injection method on the surface area.The D-A equation(n=1) provides the best fit.By comparing the calculated specific surface area of the BET equation and the mercury intrusion method,it is found that micropore adsorption of CO2 occupies a dominant position.

Features of the Excess Adsorption Isotherms of High-Pressure Methane Adsorption on Coal and Simulation Model

Four coal samples of different ranks are selected to perform the adsorption measurement of high-pressure methane（CH4）.The highest equilibrium pressure of the measurement exceeds 20 MPa. Combined with the measuring results and theoretical analyses,the reasons for the peak or the maximum adsorption capacity appearing in the excess adsorption isotherms are explained.The rules of the peak occurrence are summarized.And then,based on the features of coal pore structure,the adsorption features of high-pressure gas,the microcosmic interaction relationship of coal surface and CH4 molecule,and the coalbed methane reservoir conditions,three theoretical assumptions on the coal adsorption high-pressure CH_4 are suggested.Thereafter,on the basis of these theoretical assumptions,the Ono-Kondo lattice model is processed for simplification and deformation. Subsequently,the equations modeling the excess adsorption isotherm of high-pressure CH_4 adsorption on coal are obtained.Through the verification on the measurement data,the fitting results indicate that it is feasible to use the Ono-Kondo lattice mode to model the excess adsorption isotherm of high-pressure CH_4 adsorption on coal.

Sorption Kinetics, Isotherm and Thermodynamic Modeling of Defluoridation of Ground Water Using Natural Adsorbents

The aim of study is to investigate the removal ability of some natural adsorbents for fluoride ion from aqueous solution. The batch dynamic adsorption method was carried out at neutral pH as the functions of contact time, adsorbent dose, adsorbate concentration, temperature and effect of co-anions, which are commonly present in water. The sorption kinetics and equilibrium adsorption isotherms of fluoride on natural adsorbing materials had been investigated at afore-mentioned optimized. Equilibrium adsorption isotherms, viz., Freundlich and Langmuir isotherms were investigated. Lagergren and Morris-Weber kinetic equations were employed to find the rate constants. The negative enthalpy ΔH = -46.54 KJ·mol-1 and Gibbs free energy calculated was ΔG288-333—(2.07785, 3.08966, 4.1064, 4.90716 and 5.38036 KJ·mol-1) respectively, envisage exothermic and spontaneous nature of sorption.

Comparative modeling of gas transport in isothermal chemical vapor infiltration process of C/SiC composites

Two comparative models taking into account of momentum, energy and mass transport coupled with chemical reaction kinetics were proposed to simulate gas transport in isothermal CVI reactor for fabrication of C/SiC composites. Convection in preform was neglected in one model where momentum transport in preform is neglected and mass transport in preform is dominated by diffusion. Whereas convection in preform was taken into account in the other model where momentum transport in preform is represented by BRINKMAN equations and mass transport in preform includes both diffusion and convection. The integrated models were solved by finite element method. The calculation results show that convection in preform have negligible effect on both velocity distribution and concentration distribution. The difference between MTS molarities in preform of the two models is less than 5×10-5, which indicates that ignorance of convection in preform is reasonable and acceptable for numerical simulation of ICVI process of C/SiC composites.

Stiffness Characteristics of a Basic Nonlinear Air Spring Model

This study predicts the characteristics of a compressible polytropic air spring model. A second-order nonlinear autonomous air spring model is presented. The proposed model is based on the assumption that polytropic processes occur. Isothermal and isentropic compression and expansion of the air within the spring chambers are the two scenarios that are taken into consideration. In these situations, the air inside the spring chambers compresses and expands, resulting in nonlinear spring restoring forces. The MATLAB/Simulink software environment is used to build a numerical simulation model for the dynamic behavior of the air spring. To quantify the values of the stiffnesses of the proposed models, a numerical solution is run over time for various values of the design parameters. The isentropic process case has a higher dynamic air spring stiffness than the isothermal process case, according to the results. The size of the air spring chamber and the area of the air spring piston influence the air spring stiffness in both situations. It is demonstrated that the stiffness of the air spring increases linearly with increasing piston area and decreases nonlinearly with increasing air chamber length. As long as the ratio of the vibration’s amplitude to the air spring’s chamber length is small, there is good agreement in both scenarios between the linearized model and the full nonlinear model. This implies that linear modeling is a reasonable approximation of the complete nonlinear model in this particular scenario.

Adsorption kinetics,isotherm,and thermodynamic studies of adsorption of pollutant from aqueous solutions onto humic acid

In the present study,humic acid was used as an adsorbent for the investigation of the adsorption kinetics,isotherms,and thermo-dynamic parameters of hexavalent chromium from aqueous solution at varying pH,temperatures,and concentrations.Adsorption isotherms and equilibrium adsorption capacities were determined by the fittings of the experimental data to three well-known iso-therm models:Langmuir,Freundlich,and Redlich-Peterson.The results showed that the Langmuir and Redlich-Peterson models appear to fit the adsorption better than did the Freundlich adsorption model for the adsorption of chromium onto humic acid.The equilibrium constants were used to calculate thermodynamic parameters such as the change of free energy,enthalpy,and entropy.The derived adsorption constants (logaL) and their temperature dependencies from Langmuir isotherm have been used to calculate the corresponding thermodynamic quantities such as the free energy of adsorption,heat,and entropy of adsorption.The thermo-dynamic data indicate that Cr (VI) adsorption onto humic acid is entropically driven and characterized by physical adsorption.

Date palm kernel-based GAC and its dynamic modeling of residual chlorine breakthrough curve in multimedia filter

First, the date palm kernel is used to produce granular activated carbon （GAC） by a physiochemical activation process. The process involves six steps： washing, drying, crushing, sieving, carbonization, and activation. Secondly, the ability of the produced GAC to remove pollutants is examined through batch experiments of residual chlorine adsorption whereas the equilibrium isotherm experimental data are tested for the Langmuir and Freundlich isotherms equations. Thirdly, the experimental and theoretical study of dynamic adsorption process and the effect of major operating parameters on dynamic adsorption are investigated. The results show that the Langmuir isotherm gives the best fitting to experimental data, which indicates that the residual chlorine adsorption can be characterized by mono layer adsorption behavior. The produced GAC has a great potential as an adsorbent for residual chlorine in water systems and it can compete favorably with the conventional adsorbents. The Thomas extended model with combined mass transfer resistances is used for verifying the experimental results and the results show that the proposed model coincides well with the experimental data of the dynamic adsorption process.

Adsorption isotherms and kinetic characteristics of methane on block anthracite over a wide pressure range

It is important to quantitatively understand the methane adsorption and transport mechanism in coal for an evaluation of the reserves and for its production forecast. In this work, a block coal sample was chosen to perform the CH_4 adsorption experiments using the gravimetric method at temperatures of 293.60 K, 311.26 K, 332.98 K and 352.55 K and pressures up to 19 MPa. The excess adsorption capacity of CH_4 in dry block anthracite increased, followed by a sequence decrease with the increasing pressure. High temperature restrained the growth of the excess adsorption due to that the adsorption is an intrinsically physical and exothermic process. The excess adsorption peak decreased slowly with the increase of temperature and intersected at a pressure of more than 18 MPa; meanwhile, the pressure at the excess adsorption peak increased. The existing correlations were exanfined in terms of density rather than pressure. The DR＋k correlation, with an average relative deviation of 4-0.51%, fitted our data better than the others, with an average relative deviation of up to 2.29%. The transportation characteristics of CH_4 adsorption was also investigated in this study, including the adsorption rate and diffusion in block coal. The kinetic data could be described by a modified unipore model. The adsorption rates were found to exhibit dependence on pressure and temperature at low pressures, while the calculated diffusivities exhibited little temperature dependence. In addition, the kinetic characteristics were compared between CH_4 and CO_2 adsorption on the block coal. The excess adsorption ratios of CO_2 to CH_4 obtained from the DR＋k model decreased with the increasing pressure.

Experimental Investigation and Numerical Simulation of the Grain Size Evolution during Isothermal Forging of a TC6 Alloy

Hot compression was conducted at a Thermecmaster-Z simulator, at deformation temperatures of 800-1040℃, with strain rates of 0.001-50 s-1 and height reduction of 50%. Grain size of the prior α phase was measured with a Leica LABOR-LUX12MFS/ST microscope to which QUANTIMET 500 software for image analysis for quantitative metallography was linked. According to the present experimental data, a constitutive relationship for a TC6 alloy and a model for grain size of the prior a phase were established based on the Arrhenius' equation and the Yada's equation, respectively. By finite element (FE) simulation, deformation distribution was determined for isothermal forging of a TC6 aerofoil blade at temperatures of 860-940℃ and hammer velocities of 9-3000.0 mm/min. Meanwhile, the grain size of the prior α phase is simulated during isothermal forging of the TC6 aerofoil blade, by combining FE outputs with the present grain size model. The present results illustrate the grain size and its distribution in the prior α phase during the isothermal forging of the TC6 aerofoil blade. The simulated results show that the height reduction, deformation temperature, and hammer velocity have significant effects on distribution of the equivalent strain and the grain size of the prior α phase.

Comparative Study on Constitutive Models to Predict Flow Stress of Fe-Cr-Ni Preform Reinforced Al-Si-Cu-Ni-Mg Composite

The isothermal compression tests were carried out on Gleeble-3500 thermal-mechanical simulation machine in a temperature range of 298-473 K and strain rate range of 0.001-10 s^-1. The experimental results show that the flow stress data are negatively correlated with temperature for temperature softening, and the strain rates sensitivity of this composite increases with elevating temperature. Based on the experimental data, Johnson-Cook, modified Johnson-Cook and Arrhenius constitutive models were established. The accuracy of these three constitutive models was analyzed and compared. The results show that the values predicted by Johnson-Cook model could not agree well with the experimental values. The prediction accuracy of Arrhenius model is higher than that of Johnson-Cook model but lower than that of the Modified Johnson-Cook model.

Adsorption of Naphthol Green B on unburned carbon：2-and3-parameter linear and non-linear equilibrium modelling

The study deals with adsorption of Naphthol Green B on two unburned carbons and the parent coal,from which the UCs have been created in a fluidised-bed power station.Particular attention has been paid to the adsorption equilibrium modelling:experimental data has been analysed using 2-parameter(Langmuir,Freundlich) and3-parameter(Redlich-Peterson) isotherms — both linear and non-linear regressions have been used for the estimation of the isotherm parameters.In the case of both UCs,the Langmuir isotherm model provides the worst fit,whereas 2-parameter Freundlich and 3-parameter Redlich-Peterson models are both good,from which 3-parameter Redlich-Peterson isotherm provides slightly better results(despite the penalty used for the higher number of parameters).In the case of both UCs,the linear regression of Freundlich and Redlich-Peterson models provides good results(comparable with non-linear regressions).Unlike both UCs,the best fit of the experimental data from the adsorption on the coal has been achieved by the Langmuir isotherm model.The results based on the Freundlich or Redlich-Peterson model were(in this case) somewhat worse.

Experimental determination and modeling of equilibrium moisture content from the sapwood of Mexican pine (Pinus pseudostrobus Lindl.)

A desorption isotherm is a very important basis in the understanding of drying process. In this study, the desorption isotherms from the sapwood of Mexican pine （Pinus pseudostrobus Lindl.） were determined by the gravimetric method （discontinuous control of sample weight） at 30℃ and 50℃. The salt method was used in the range of water activities from 0.11 to 0.89. The results show that the desorption ability of Mexican pine sapwood increased with temperature at a given relative humidity. The experimental data was further simulated with the models, i.e., BET, GAB, Oswin and Henderson models. The GAB, Oswin and Henderson models allow the representation of the entire desorption isotherms. The BET model showed a better fit for water activity lower than 0.35, with a mean relative deviation of 0.0286 at 30℃ and 0.0167 at 50℃. Simultaneously, the BET model gave a better representation of moisture content in the monolayer saturation region. Overall, the GAB model ensured the best simulation of the entire isotherm, while the Henderson model displayed the worst simulation.

Modeling of Adsorption of Bi(III) from Nitrate Medium by Impregnated Resin D2EHPA/XAD-1180

Di(2-ethylhexyl)phosphoric acid (D2EHPA) in acetone was supported on the Amberlite XAD-1180 polystyrene divinylbenzene copolymer resin. The use of XAD-1180 impregnated with D2EHPA for the extraction of bismuth(III) from nitrate medium was carried out using batch technique. Various parameters affecting the uptake of this metal ion were described in the previous paper (Belkhouche and Didi, 2010) and the capacity of the impregnated resin for bismuth(III) was found to be 490.7 mg/g of resin. Effect of temperature on the values of distribution equilibrium was studied to evaluate the changes in standard thermodynamic quantities. A comparison of Langmuir forms I, II and Freundlich sorption isotherms was realized and the kinetic models applied to the adsorption rate data were evaluated for Lagergren first order, the pseudo second order and Morris–Weber models. From the results, the adsorption of Bi(III) onto D2EHPA/XAD-1180 resin shown the exothermic character and followed the Langmuir form II isotherm. Thus, the capacity of monolayer adsorption of Bi(III) was equal to 769.23 mg/g of resin. Both the Lagergren pseudo first order and film-diffusion models were found to best describe the experimental rate data.

Phase field modeling of dendrite growth

Single dendrite and multi-dendrite growth for Al-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking phenomenon can be observed. For multi-dendrite growth, there exists the competitive growth among the dendrites during solidification. As solidification proceeds, growing and coarsening of the primary arms occurs, together with the branching and coarsening of the secondary arms. When the diffusion fields of dendrite tips come into contact with those of the branches growing from the neighboring dendrites, the dendrites stop growing and being to ripen and thicken.

Adsorption of 5.5’-Disulfonicindigotin(5.5’-DI)onto Green Coconut Fiber(Cocos nucifera L.):Kinetic and Isotherms

Green coconut fiber (Cocos nucifera L.) has been largely used in solid-phase extraction. The effect of the initial dye concentration (1.91, 3.02 and 4.02) × 10-5 mol&#183L-1 and solid phase contact (SPE) time were evaluated at different temperatures (283, 298 and 313) K at pH 2. Kinetic experimental data were applied to three simplified kinetic models: pseudo-first order, pseudo-second order, and intraparticle diffusion. The adsorption of 5.5’-DI onto the solid phase showed excellent fit to the pseudo-second order model. At 283, 298 and 313 K the maximum sorption, qmax,exp, for the lowest initial concentration (Co = 1.91 × 10-5 mol&#183L-1) of 5.5’-DI were (5.01, 5.24 and 6.14) × 10-4 g&#183g-1;for Co = 3.02 × 10-5 mol&#183L-1 (0.93, 1.01 and 1.03) × 10-3

Isothermal precision forging of Ti-6.5Al-3.5Mo-1.5Zr-0.3Si alloy impeller with twisted blades

Ti-6.5Al-3.5Mo-1.5Zr-0.3Si (TC11) alloy impeller is an important part in the airspace engine that serves under severe working conditions, and it requires excellent mechanical properties and high dimensional precision. However, the integral titanium alloy impeller is difficult to precisely forge because of its complex shape and poor formability. In order to develop optimum forging process of this kind of complex parts, the deformation characteristics of TC11 alloy under isothermal compressing conditions were studied. Furthermore, an alternative material, namely pure lead, was selected to model the forming process of the impeller and investigate metal flow during forging. Based on the research, local loading method was determined to forge the TC11 alloy impeller precisely under isothermal condition. The dimensional accuracy, mechanical properties and microscopic structure of the forged product satisfy operating requirements.