Particle residence time distribution and axial dispersion coefficient in a pressurized circulating fluidized bed by using multiphase particle-in-cell simulation

The particle residence time distribution(RTD)and axial dispersion coefficient are key parameters for the design and operation of a pressurized circulating fluidized bed(PCFB).In this study,the effects of pressure(0.1-0.6 MPa),fluidizing gas velocity(2-7 m·s^(-1)),and solid circulation rate(10-90 kg·m^(-2)·s^(-1))on particle RTD and axial dispersion coefficient in a PCFB are numerically investigated based on the multiphase particle-in-cell(MP-PIC)method.The details of the gas-solid flow behaviors of PCFB are revealed.Based on the gas-solid flow pattern,the particles tend to move more orderly under elevated pressures.With an increase in either fluidizing gas velocity or solid circulation rate,the mean residence time of particles decreases while the axial dispersion coefficient increases.With an increase in pressure,the core-annulus flow is strengthened,which leads to a wider shape of the particle RTD curve and a larger mean particle residence time.The back-mixing of particles increases with increasing pressure,resulting in an increase in the axial dispersion coefficient.

Molecular Dynamics, Diffusion Coefficients and Activation Energy of the Electrolyte (Anode) in Lithium (Li and Li+), Sodium (Na and Na+) and Potassium (K and K+)

This work is a simulation modelling with the LAMMPS calculation code of an electrode based on alkali metals (lithium, sodium and potassium) using the MEAM potential. For different multiplicities, two models were studied;with and without gap. In this work, we present the structural, physical and chemical properties of the lithium, sodium and potassium electrodes. For the structural properties, the cohesive energy and the mesh parameters were calculated, revealing that, whatever the chemical element selected, the compact hexagonal hcp structure is the most stable, followed by the face-centred cubic CFC structure, and finally the BCC structure. The most stable structure is lithium, with a cohesion energy of -6570 eV, and the lowest bcc-hcp transition energy of -0.553 eV/atom, followed by sodium. For physical properties, kinetic and potential energies were calculated for each of the sectioned chemical elements, with lithium achieving the highest value. Finally, for the chemical properties, we studied the diffusion coefficient and the activation energy. Only potassium followed an opposite order to the other two, with the quantities with lacunae being greater than those without lacunae, whatever the multiplicity. The order of magnitude of the diffusion coefficients is given by the relationship DLi > DNa > Dk for the multiplicity 6*6*6, while for the activation energy the order is reversed.

Molecular Dynamics, Physical Properties, Diffusion Coefficients and Activation Energy of the Lithium Oxide (Li-O) and Sodium Oxide (Na-O) Electrolyte (Cathode)

This work is a simulation model with the LAMMPS calculation code of an electrode based on alkali metal oxides (lithium, sodium and potassium) using the Lennard Jones potential. For a multiplicity of 8*8*8, we studied a gap-free model using molecular dynamics. Physical quantities such as volume and pressure of the Na-O and Li-O systems exhibit similar behaviors around the thermodynamic ensembles NPT and NVE. However, for the Na2O system, at a minimum temperature value, we observe a range of total energy values;in contrast, for the Li2O system, a minimum energy corresponds to a range of temperatures. Finally, for physicochemical properties, we studied the diffusion coefficient and activation energy of lithium and potassium oxides around their melting temperatures. The order of magnitude of the diffusion coefficients is given by the relation Dli-O >DNa-O for the multiplicity 8*8*8, while for the activation energy, the order is well reversed EaNa-O > EaLi-O.

Identification of the Diffusion Coefficients of Pollutants ( N O 3 - and Mn2+) through the Walls of Concrete Tank and Vulnerability of the Stored Water Quality

The populations of urban centers in Congo-Brazzaville have decided to develop various methods of water storage (concrete or masonry underground tanks) for domestic use, due to shortages in the distribution of water through the public network. However, questions remain as to the physico-chemical quality of the water stored in these tanks, when these structures are built in wet and relatively polluted areas. This paper presents a model of pollutant diffusion through the cementitious matrix (concrete) of tank walls simulated at a buried reservoir. The results of the experimental and numerical simulations show that certain concrete parameters, such as porosity, permeability and diffusivity, have a significant influence on the transfer of pollutants through the concrete walls, thus altering the physico-chemical quality of the stored water. The numerical models (1D) used to predict pollutant transfer and the quality of the stored water are consistent with those of the optimal control for identifying the diffusion coefficient. Major ion concentrations appear to be correlated with system porosity and diffusion coefficient. Nevertheless, the identification of the diffusion coefficient from the optimal control method, based on an explicit numerical resolution of a finite volume PDE for the approximation of the experiment, is not consistent with that of the optimal control method.

Effect of Size and Initial Water Content on the Effective Diffusion Coefficient during Convective Drying of Sweet Potato Cut into Cubic and Cylindrical Shapes

In this article, we investigated the influence of size and initial water content on the effective diffusion coefficient of sweet potatoes samples cut into cubic and cylindrical shapes. The sizes of the cubic samples are 0.5, 1, 1.5, 1.75, 2, 2.5 and 3 cm edge with a respective initial water content of 2.7, 3.76, 3.48, 2.68, 3.28, 2.17 and 2.29 kg/kgms. For cylindrical samples, the radius is set at 0.5 cm and sample heights are 1, 1.5, 2, 2.5, 3, 3.5 and 4 cm with respective water contents of 2.2, 3.19, 2.85, 2.1, 2.17, 2.39 and 2.03 kg/kgms. The effective diffusion coefficients of cubic samples are of the order of 10−10 and 10−9 m2∙s−1 grew with sample edge. As for the cylindrical samples, the effective diffusion coefficients were of the order of 10−9 m2∙s−1 and there was no linear correlation between cylinder height and their effective diffusion coefficient. As for the examination of the initial water content on the effective diffusion coefficient, it turned out that the initial water content had no influence on the effective diffusion coefficient of the sweet potato samples.

Determination of Natural Logarithm of Diffusion Coefficient and Activation Energy of Thin Layer Drying Process of Ginger Rhizome Slices

This study is an extension of the previous work done with ARS-680 Environmental Chamber. Drying is a complex operation that demands much energy and time. Drying is essentially important for preservation of ginger rhizome. Drying of ginger was modeled, and then the effective diffusion coefficient and activation energy were determined. For this purpose, the experiments were done at six levels of varied temperatures: 10°C, 20°C, 30°C, 40°C, 50°C and 60°C. The values of effective diffusion coefficients obtained in this work for the variously treated ginger rhizomes closely agreed with the average effective diffusion coefficients of other notable authors who determined the drying kinetics and convective heat transfer coefficients of ginger slices.

Vertical Diffusion Coefficient with Stratification Effect for Silty Sediment Suspension Under Waves

To analyze previous experimental data of suspended sediment concentration for silty sediment with different sediment particle sizes due to waves, a new stratification correction coefficient is presented. The suspended sediment concentration gradient and sediment particle diameter are selected as parameters. Furthermore, a diffusion coefficient model with a stratification effect over the whole water depth for silty sediment suspension under waves is developed. The comparison between the suspended sediment concentration calculated by the presented model and several groups of experimental data shows that the model can reasonably reflect the vertical distribution of silty sediment suspension.The stratification effect calculated by the present model decreases with an increase in the sediment particle diameter,which indicates that the model can be extended to describe the suspended sediment concentration of fine to medium sand when the near-bottom sediment concentration is not very high. Although the original model needs to be iteratively solved, the approximate method without iteration is recommended for applications when the near bottom sediment concentration is between 10 and 20 kg/m~3 due to the small difference between the non-iterative and iterative solution for near bed layer suspended sediment concentration, which plays a major role in sediment transport.

ANALYSIS AND DISCRETIZATION FOR AN OPTIMAL CONTROL PROBLEM OF A VARIABLE-COEFFICIENT RIESZ-FRACTIONAL DIFFUSION EQUATION WITH POINTWISE CONTROL CONSTRAINTS

We present a mathematical and numerical study for a pointwise optimal control problem governed by a variable-coefficient Riesz-fractional diffusion equation.Due to the impact of the variable diffusivity coefficient,existing regularity results for their constantcoefficient counterparts do not apply,while the bilinear forms of the state(adjoint)equation may lose the coercivity that is critical in error estimates of the finite element method.We reformulate the state equation as an equivalent constant-coefficient fractional diffusion equation with the addition of a variable-coefficient low-order fractional advection term.First order optimality conditions are accordingly derived and the smoothing properties of the solutions are analyzed by,e.g.,interpolation estimates.The weak coercivity of the resulting bilinear forms are proven via the Garding inequality,based on which we prove the optimal-order convergence estimates of the finite element method for the(adjoint)state variable and the control variable.Numerical experiments substantiate the theoretical predictions.

Overview of computation strategies on the dispersion analysis for explicit finite difference solution of acoustic wave equation

Finite-difference(FD)method is the most extensively employed numerical modeling technique.Nevertheless,when using the FD method to simulate the seismic wave propagation,the large spatial or temporal sampling interval can lead to dispersion errors and numerical instability.In the FD scheme,the key factor in determining both dispersion errors and stability is the selection of the FD weights.Thus,How to obtain appropriate FD weights to guarantee a stable numerical modeling process with minimum dispersion error is critical.The FD weights computation strategies can be classified into three types based on different computational ideologies,window function strategy,optimization strategy,and Taylor expansion strategy.In this paper,we provide a comprehensive overview of these three strategies by presenting their fundamental theories.We conduct a set of comparative analyses of their strengths and weaknesses through various analysis tests and numerical modelings.According to these comparisons,we provide two potential research directions of this field:Firstly,the development of a computational strategy for FD weights that enhances stability;Secondly,obtaining FD weights that exhibit a wide bandwidth while minimizing dispersion errors.

Unveiling the Re,Cr,and I diffusion in saturated compacted bentonite using machine-learning methods

The safety assessment of high-level radioactive waste repositories requires a high predictive accuracy for radionuclide diffusion and a comprehensive understanding of the diffusion mechanism.In this study,a through-diffusion method and six machine-learning methods were employed to investigate the diffusion of ReO_(4)^(−),HCrO_(4)^(−),and I−in saturated compacted bentonite under different salinities and compacted dry densities.The machine-learning models were trained using two datasets.One dataset contained six input features and 293 instances obtained from the diffusion database system of the Japan Atomic Energy Agency(JAEA-DDB)and 15 publications.The other dataset,comprising 15,000 pseudo-instances,was produced using a multi-porosity model and contained eight input features.The results indicate that the former dataset yielded a higher predictive accuracy than the latter.Light gradient-boosting exhibited a higher prediction accuracy(R2=0.92)and lower error(MSE=0.01)than the other machine-learning algorithms.In addition,Shapley Additive Explanations,Feature Importance,and Partial Dependence Plot analysis results indicate that the rock capacity factor and compacted dry density had the two most significant effects on predicting the effective diffusion coefficient,thereby offering valuable insights.

Calculation of ion diffusion coefficient related to concrete deterioration based on Debye-Hückel-Onsager theory

This paper applies the Debye-Hückel-Onsager electrolyte solution theory to investigate the diffusivity of ions in concrete pore solutions.First,a model of the diffusion coefficient associated with the ionic species,solution concentration and ambient temperature is proposed in the saturated concrete.Secondly,as an example,the effects of sodium chloride solution concentration,which are associated with influencing factors such as the ionic cloud radius,electrophoresis and relaxation,on the chloride diffusion coefficient are analyzed.It is found that the diffusion coefficient decreases with the increase in solution concentration,and the electrophoresis and ionic cloud radius are two important factors influencing the ionic diffusivity.Finally,the experiments,in which the chloride diffusion coefficients in specimens under different water-cement ratios are measured by the rapid chloride migration（RCM）method,are carried out to validate the effectiveness of the proposed model,and the results indicate that there is a generally reasonable agreement between the experimental and the proposed model results.

Diffusion Equations of the Electric Charges and Magnetic Flux

Innovative definitions of the electric and magnetic diffusivities through conducting mediums and innovative diffusion equations of the electric charges and magnetic flux are verified in this article. Such innovations depend on the analogy of the governing laws of diffusion of the thermal, electrical, and magnetic energies and newly defined natures of the electric charges and magnetic flux as energy, or as electromagnetic waves, that have electric and magnetic potentials. The introduced diffusion equations of the electric charges and magnetic flux involve Laplacian operator and the introduced diffusivities. Both equations are applied to determine the electric and magnetic fields in conductors as the heat diffusion equation which is applied to determine the thermal field in steady and unsteady heat diffusion conditions. The use of electric networks for experimental modeling of thermal networks represents sufficient proof of similarity of the diffusion equations of both fields. By analysis of the diffusion phenomena of the three considered modes of energy transfer;the rates of flow of these energies are found to be directly proportional to the gradient of their volumetric concentration, or density, and the proportionality constants in such relations are the diffusivity of each energy. Such analysis leads also to find proportionality relations between the potentials of such energies and their volumetric concentrations. Validity of the introduced diffusion equations is verified by correspondence their solutions to the measurement results of the electric and magnetic fields in microwave ovens.

Transient elastography and diffusion-weighted magnetic resonance imaging for assessment of liver fibrosis in children with chronic hepatitis C

BACKGROUND Chronic hepatitis C(CHC)is a health burden with consequent morbidity and mortality.Liver biopsy is the gold standard for evaluating fibrosis and assessing disease severity and prognostic purposes post-treatment.Noninvasive altern-atives for liver biopsy such as transient elastography(TE)and diffusion-weighted magnetic resonance imaging(DW-MRI)are critical needs.AIM To evaluate TE and DW-MRI as noninvasive tools for predicting liver fibrosis in children with CHC.METHODS This prospective cross-sectional study initially recruited 100 children with CHC virus infection.Sixty-four children completed the full set of investigations including liver stiffness measurement(LSM)using TE and measurement of apparent diffusion coefficient(ADC)of the liver and spleen using DW-MRI.Liver biopsies were evaluated for fibrosis using Ishak scoring system.LSM and liver and spleen ADC were compared in different fibrosis stages and correlation analysis was performed with histopathological findings and other laboratory parameters.RESULTS Most patients had moderate fibrosis(73.5%)while 26.5%had mild fibrosis.None had severe fibrosis or cirrhosis.The majority(68.8%)had mild activity,while only 7.8%had moderate activity.Ishak scores had a significant direct correlation with LSM(P=0.008)and were negatively correlated with both liver and spleen ADC but with no statistical significance(P=0.086 and P=0.145,respectively).Similarly,histopatho-logical activity correlated significantly with LSM(P=0.002)but not with liver or spleen ADC(P=0.84 and 0.98 respectively).LSM and liver ADC were able to significantly discriminate F3 from lower fibrosis stages(area under the curve=0.700 and 0.747,respectively)with a better performance of liver ADC.CONCLUSION TE and liver ADC were helpful in predicting significant fibrosis in children with chronic hepatitis C virus infection with a better performance of liver ADC.

Selective Impact of Dispersion and Nonlinearity on Waves and Solitary Wave in a Strongly Nonlinear and Flattened Waveguide

The waveguide which is at the center of our concerns in this work is a strongly flattened waveguide, that is to say characterized by a strong dispersion and in addition is strongly nonlinear. As this type of waveguide contains multiple dispersion coefficients according to the degrees of spatial variation within it, our work in this article is to see how these dispersions and nonlinearities each influence the wave or the signal that can propagate in the waveguide. Since the partial differential equation which governs the dynamics of propagation in such transmission medium presents several dispersion and nonlinear coefficients, we check how they contribute to the choices of the solutions that we want them to verify this nonlinear partial differential equation. This effectively requires an adequate choice of the form of solution to be constructed. Thus, this article is based on three main pillars, namely: first of all, making a good choice of the solution function to be constructed, secondly, determining the exact solutions and, if necessary, remodeling the main equation such that it is possible;then check the impact of the dispersion and nonlinear coefficients on the solutions. Finally, the reliability of the solutions obtained is tested by a study of the propagation. Another very important aspect is the use of notions of probability to select the predominant solutions.

Effect of liquid diffusion coefficients on microstructure evolution during solidification of Al356.1 alloy

（The effect of liquid diffusion coefficients on the microstructure evolution during solidification of primary （Al） phase in Al356.1 alloy was investigated by means of the phase-field simulation using two sets of diffusion coefficients in liquid phase, while fixing other thermophysical and numerical parameters. The first set is only with impurity coefficients of liquid phase in Arrhenius formula representing only the temperature dependence. While the second set is with the well-established atomic mobility database representing both temperature and concentration dependence. For the second set of liquid diffusion coefficients, the effect of non-diagonal diffusion coefficients on the microstructure evolution in Al356.1 alloy during solidification was also analyzed. The differences were observed in the morphology, tip velocity and composition profile ahead of the tip of the dendrite due to the three cases of liquid diffusivities. The simulation results indicate that accurate databases of mobilities in the liquid phase are highly needed for the quantitative simulation of microstructural evolution during solidification.

Hydrogen diffusion coefficient in liquid metals evaluated by solid-gas eutectic unidirectional solidification

Based on the solid-gas eutectic unidirectional solidification technique and the principle of unidirectional solidification of single-phase alloy, a new method for evaluating the diffusion coefficient of hydrogen in liquid metals was proposed. Taking Cu-H2 system for example, the influences of argon partial pressure and superheat degree of melt on the diffusion coefficient of hydrogen in liquid metal were studied and the predicted values were similar to each other. The obtained temperature-dependent equation for diffusion coefficient of hydrogen in liquid copper is comparable with experimental data in literature, which validates the effectiveness of this method. The temperature-dependent equations for diffusion coefficient of hydrogen in liquid Mg, Si and Cu-34.6%Mn alloy were also evaluated by this method, along with the values at the melting point of each metal and alloy.

Effect of Rare Earths on Diffusion Coefficient and Transfer Coefficient of Carbon during Carburizing

The diffusion coefficient of carbon in surface layer of steel-20 rare earth carburixed at 880 degreesC and 900 degreesC for 8 h was calculated by substituting the measured layer depths into the diffusion equation. The mathematical model of the transfer coefficient of carbon was deduced based on the kinetics of weight gain during gas carburizing. The calculated results show that the main reason why the gas carburizing process is accelerated is due to the obvious increase in the diffusion coefficient and transfer coefficient of carbon resulted from the addition of RE.

Apparent diffusion coefficient by diffusion-weighted magnetic resonance imaging as a sole biomarker for staging and prognosis of gastric cancer

Objective： To investigate the role of apparent diffusion coefficient （ADC） from diffusion-weighted magnetic resonance imaging （DW-MRI） when applied to the 7th TNM classification in the staging and prognosis of gastric cancer （GC）. Methods： Between October 2009 and May 2014, a total of 89 patients with non-metastatic, biopsy proven GC underwent 1.5T DW-MRI, and then treated with radical surgery. Tumor ADC was measured retrospectively and compared with final histology following the 7th TNM staging （local invasion, nodal involvement and according to the different groups -- stage Ⅰ, Ⅱ and Ⅲ）. Kaplan-Meier curves were also generated. The follow-up period is updated to May 2016. Results： Median follow-up period was 33 months and 45/89 （51%） deaths from GC were observed. ADC was significantly different both for local invasion and nodal involvement （P〈0.001）. Considering final histology as the reference standard, a preoperative ADC cut-offof 1.80×10-3 mm^2/s could distinguish between stages I and Ⅱ and an ADC value of ≤1.36-10-3 mm^2/s was associated with stage Ⅲ（P〈0.001）. Kaplan-Meier curves demonstrated that the survival rates for the three prognostic groups were significantly different according to final histology and ADC cut-offs （P〈0.001）. Conclusions： ADC is different according to local invasion, nodal involvement and the 7th TNM stage groups for GC, representing a potential, additional prognostic biomarker. The addition of DW-MRI could aid in the staging and risk stratification of GC.

Influence of Binder Composition and Concrete Pore Structure on Chloride Diffusion Coefficient in Concrete

The influence of binder composition and pore structure of concrete on chloride diffusion coefficient in concrete were investigated by the natural immersion test, MIP test, SEM and EDS test, respectively. The experimental results showed that the effect of binder composition on chloride diffusion coefficient was the comprehensive result of concrete pore structure and binder hydration products, and the porosity and pore size distribution were the main factors that influence the changes of diffusion coefficient. The chloride diffusion coefficient decreased with increasing the curing temperature and the relative humidity. The hydration degree were promoted by improving curing temperatures, and then the porosity of concrete decreased and the proportion of gel pore and transitional pore increased, respectively. But the water evaporation decreased with increasing the relative humidity and then decreased porosity and increased the proportion of gel pore and transitional pore. Additionally, The chloride diffusion coefficient of concrete got the lower value when the appropriate replacement of fly ash in the ranges of 10%-20%, when the double-adding fly ash and slag content was 50%. The porosity increased and the ratio of C/S in C-S-H decreased with further increasing the fly ash content, which led to increase the chloride diffusion coefficient in concrete.