Wetting front migration model of ion-adsorption rare earth during the multi-hole unsaturated liquid injection

In the process of ion-adsorption rare earth ore leaching,the migration characteristics of the wetting front in multi-hole injection holes and the influence of wetting front intersection effect on the migration distance of wetting fronts are still unclear.Besides,wetting front migration distance and leaching time are usually required to optimize the leaching process.In this study,wetting front migration tests of ionadsorption rare earth ores during the multi-hole fluid injection(the spacing between injection holes was 10 cm,12 cm and 14 cm)and single-hole fluid injection were completed under the constant water head height.At the pre-intersection stage,the wetting front migration laws of ion-adsorption rare earth ores during the multi-hole fluid injection and single-hole fluid injection were identical.At the postintersection stage,the intersection accelerated the wetting front migration.By using the Darcy’s law,the intersection effect of wetting fronts during the multi-hole liquid injection was transformed into the water head height directly above the intersection.Finally,based on the Green-Ampt model,a wetting front migration model of ion-adsorption rare earth ores during the multi-hole unsaturated liquid injection was established.Error analysis results showed that the proposed model can accurately simulate the infiltration process under experimental conditions.The research results enrich the infiltration law and theory of ion-adsorption rare earth ores during the multi-hole liquid injection,and this study provides a scientific basis for optimizing the liquid injection well pattern parameters of ion-adsorption rare earth in situ leaching in the future.

Full Dynamic Model for Liquid Sloshing Simulation in Cylindrical Tank Shape

This study presents a comprehensive full dynamic model designed for simulating liquid sloshing behavior within cylindrical tank structures. The model employs a discretization approach, representing the liquid as a network of interconnected spring-damper-mass systems. Key aspects include the adaptation of liquid discretization techniques to cylindrical lateral cross-sections and the calculation of stiffness and damping coefficients. External forces, simulating various vehicle maneuvers, are also integrated into the model. The resulting system of equations is solved using Maple Software with the Runge-Kutta-Fehlberg method. This model enables accurate prediction of liquid displacement and pressure forces, offering valuable insights for tank design and fluid dynamics applications. Ongoing refinement aims to broaden its applicability across different liquid types and tank geometries.

Numerical simulation of gas–liquid flow in the bubble column using Wray–Agarwal turbulence model coupled with population balance model

In this paper,an improved computational fluid dynamic(CFD)model for gas-liquid flow in bubble column was developed using the one-equation Wary-Agarwal(WA)turbulence model coupled with the population balance model(PBM).Through 18 orthogonal test cases,the optimal combination of interfacial force models,including drag force,lift force,turbulent dispersion force.The modified wall lubrication force model was proposed to improve the predictive ability for hydrodynamic behavior near the wall of the bubble column.The values simulated by optimized CFD model were in agreement with experimental data,and the errors were within±20%.In addition,the axial velocity,turbulent kinetic energy,bubble size distribution,and the dynamic characteristic of bubble plume were analyzed at different superficial gas velocities.This research work could provide a theoretical basis for the extension of the CFD-PBM coupled model to other multiphase reactors..

Modeling of liquid film thickness around Taylor bubbles rising in vertical stagnant and co-current slug flowing liquids

The hydrodynamic study of the liquid film around Taylor bubbles in slug flow has great significance for understanding parallel flow and interaction between Taylor bubbles.The prediction models for liquid film thickness mainly focus on stagnant flow,and some of them remain inaccurate performance.However,in the industrial process,the slug flow essentially is co-current flow.Therefore,in this paper,the liquid film thickness is studied by theoretical analysis and experimental methods under two conditions of stagnant and co-current flow.Firstly,under the condition of stagnant flow,the present work is based on Batchelor's theory,and modifies Batchelor's liquid film thickness model,which effectively improves its prediction accuracy.Under the condition of co-current flow,the prediction model of average liquid film thickness in slug flow is established by force and motion analysis.Taylor bubble length is introduced into the model as an important parameter.Dynamic experiments were carried out in the pipe with an inner diameter of 20 mm.The liquid film thickness,Taylor bubble velocity and length were measured by distributed ultrasonic sensor and intrusive cross-correlation conductivity sensor.Comparing the predicted value of the model with the measured results,the relative error is controlled within 10%.

Measurement and model of density,viscosity,and hydrogen sulfide solubility in ferric chloride/trioctylmethylammonium chloride ionic liquid

The density and viscosity of ferric chloride/trioctylmethylammonium chloride ionic liquid(rFeCl_(3)/[A336]Cl)with different molar ratios(r=0.1-0.8)of FeCl_(3) to[A336]Cl were measured at temperatures from 313.15 to 358.15 K and atmospheric pressure.The density and viscosity data were fitted by the relevant temperature variation equations,respectively.The variation of density and viscosity with temperature and r was obtained.The solubility of rFeCl_(3)/[A336]Cl to H_2S was measured at temperatures from 318.15 to 348.15 K and pressures from 0 to 150 kPa.The effects of temperature,pressure,and r on the solubility of H_(2)S were discussed.The reaction equilibrium thermodynamic model(RETM)was used to fit the H_(2)S solubility data,and the average relative error was less than 1.3%,indicating that the model can relate the solubility data well.And Henry's constant and chemical reaction equilibrium constant were obtained by the RETM fitting.The relationships of Henry's constant and chemical reaction equilibrium constant with temperature and r were analyzed.

Absorption characteristics,model,and molecular mechanism of hydrogen sulfide in morpholine acetate aqueous solution

The solubility of H_(2)S was measured in solutions of N-butyl-N-methylmorpholine acetate([Bmmorp][Ac])containing 20%-40%(mass)water at experimental temperatures ranged from 298.15 to 328.15 K and pressures up to 320 k Pa.The total solubility of H_(2)S increased with higher temperatures,lower pressures,and reduced water content.The reaction equilibrium thermodynamic model was used to correlate the solubility data.The results indicate that the chemical reaction equilibrium constant decrease with increasing water content and temperature,whereas Henry constant increase with increasing water content and temperature.Compared with other ionic liquids,H_(2)S exhibits a higher physical absorption enthalpy and a lower chemical absorption enthalpy in[Bmmorp][Ac]aqueous solution.This suggests that[Bmmorp][Ac]has a strong physical affinity for H_(2)S and low energy requirement for desorption.Quantum chemical methods were used to investigate the molecular mechanism of H_(2)S absorption in ionic liquids.The interaction energy analysis revealed that the binding of H_(2)S with the ionic liquid in a1:2 ratio is more stable.Detailed analyses by the methods of the interaction region indicator and the atoms in molecules were conducted to the interactions between H_(2)S and the ionic liquid.

Parameterization of COSMO-RS model for ionic liquids

The adjustable parameters in the popular conductor-like screening model for real solvents(COSMO-RS)within the Amsterdam density functional(ADF)framework have been re-optimized to fit for the systems containing ionic liquids(ILs).To get the optimal values of misfit energy constant a^0,hydrogen bond coefficient c_(hb)and effective contact surface area of a segment a_(eff),2283 activity coefficient data points at infinite dilution and 1433 CO_2 solubility data points exhaustively collected from references were used as training set.The average relative deviations(ARDs)of activity coefficients at infinite dilution and CO_2 solubility between experimental data and predicted values are 32.22%and17.61%,respectively,both of which are significantly lower than the original COSMO-RS versions.Predictions for other activity coefficients of solutes in ILs,solubility data of CO_2 in pure ILs and the binary mixtures of ILs at either high or low temperatures,and vapor–liquid equilibrium(VLE)for binary systems involving ILs have also been performed to demonstrate the validity of the parameterization of COSMO-RS model for ILs.The results showed that the predicted results by COSMO-RS model with the new optimized parameters are in much better agreement with experimental data than those by the original versions over a wide temperature and pressure range.The COSMO-RS model for ILs presented in this work improves the prediction accuracy of thermodynamic properties for the systems containing ILs,which is always highly desirable for general chemical engineers.

Mechanical model study of relationship of molecular configuration and multiphase in liquid crystal materials

A mechanical model of liquid crystals （LCs） is applied to study the polymorphism of homologous series of terphenyl compounds. With a senti-experimental molecular orbit method, we calculate the moment of inertia which represents the rotation state to describe the phase transition temperature obtained from experimental data. We propose a novel explanation of the phase sequence or polymorphism of LC materials using the two key parameters, the moment of inertia and critical rotational velocity. The effect of molecular polarity on the appearance of liquid crystalline is also discussed.

Modelling of a tubular membrane contactor for pre-combustion CO_2 capture using ionic liquids:Influence of the membrane configuration, absorbent properties and operation parameters

A membrane contactor using ionic liquids(ILs) as solvent for pre-combustion capture CO_2 at elevated temperature(303-393 K) and pressure(20 bar) has been studied using mathematic model in the present work. A comprehensive two-dimensional(2 D) mass-transfer model was developed based on finite element method. The effects of liquid properties, membrane configurations, as well as operation parameters on the CO_2 removal efficiency were systematically studied. The simulation results show that CO_2 can be effectively removed in this process. In addition, it is found that the liquid phase mass transfer dominated the overall mass transfer. Membranes with high porosity and small thickness could apparently reduce the membrane resistance and thus increase the separation efficiency. On the other hand, the membrane diameter and membrane length have a relatively small influence on separation performance within the operation range.

PREDICTION OF THE MIXING ENTHALPIES OF BINARY LIQUID ALLOYS BY MOLECULAR INTERACTION VOLUME MODEL

The mixing enthalpies of 23 binary liquid alloys are calculated by molecular interaction volume model （MIVM）, which is a two-parameter model with the partial molar infinite dilute mixing enthalpies. The predicted values are in agreement with the experimental data and then indicate that the model is reliable and convenient.

Modeling Non-aqueous Phase Liquid Displacement Process

A pore-network model physically based on pore level multiphase flow was used to study the water-non-aqueous phase liquid （NAPL） displacement process, especially the effects of wettability, water-NAPL interracial tension, the fraction of NAPL-wet pores, and initial water saturation on the displacement. The computed data show that with the wettability of the mineral surfaces changing from strongly water-wet to NAPL-wet, capillary pressure and the NAPL relative permeability gradually decrease, while water-NAPL interfacial tension has little effect on water relative permeability, but initial water saturation has a strong effect on water and NAPL relative permeabilities. The analytical results may help to understand the micro-structure displacement process of non-aqueous phase liquid and to provide the theoretical basis for controlling NAPL migration.

Vapor-Liquid Equilibrium Prediction of Ammonia-Ionic Liquid Working Pairs of Absorption Cycle Using UNIFAC Model

On the basis of reported experimental vapor-liquid equilibrium （VLE） data of NH3-1-ethyl-3-methylimidazolium acetate （NH3-[Emim]Ac）, NH3-1-butyl-3-methylimidazolium tetrafluoroborate （NH3-[Bmim][BF4]）, NH3-1,3-dimethylimidazolium dimethyl phosphate （NH3-[Mmim]DMP） and NH3-1-ethyl-3-methylimidazolium ethylsulfate （NH3-[Emim]EtOSO3） binary systems, the interaction parameters of 14 new groups have been regressed by means of the UNIFAC model. To validate the reliability of the method, these parameters have been used to calculate the VLE data with the average relative deviation of pressures of less than 9.35%. The infinite dilution activity coefficient （ γ1∞ ） and the absorption potential （ φ1 ） are important evaluation criterions of the affinity between working pair species of the absorption cycle. The UNIFAC model is implemented to predict the values of and φ1 of t6 sets of NH3-ionic liquid （1L） systems. The work found that the φ1 gradually increases following the impact order： φ1（[Cnmim][BF4]）〈φ1（[Cnmim]EtOSO3）〈φ1（[Cnmim]DMP）〈φ1（[Cnmim]Ac） （n= 1, 2, 3, … ） at a given cation of IL species and constant temperature, and φ1（[Mmim]X）〈φ1（[Emim]X）〈φ1（[Pmim]X）〈 φ1（[Bmim]X）（X= Ac, [BF4], DMP or EtOSO3） at a given anion of IL species and constant temperature. Furthermore, the φ1 gradually increases with increasing temperature. Then, it could be concluded that the working pair NH3-[BmimlAc has the best potential research value relatively.

A Theoretical Model for the Size Prediction of Single Bubbles Formed under Liquid Cross-flow

The size of initial bubbles is an important factor to the developed bubble size distribution in a gas-liquid contactor. A liquid cross-flow over a sparger can produce smaller bubbles, and hereby enhance the performance of contactor. A one stage model by balancing the forces acting on a growing bubble was developed to describe the formation of the bubble from an orifice exposed to liquid cross-flow. The prediction with this model agrees with the experimental data available in the literatures, and show that orifice size strongly affects the bubble size. It is showed that the shear-lift force, inertia force, surface tension force and buoyancy force are major forces, and a simplified mathematical model was developed, and the detachment bubble diameter can be predicted with accuracy of <±21%.

Cast-rolling force model in solid-liquid cast-rolling bonding(SLCRB) process for fabricating bimetal clad strips

Based on twin-roll casting, a cast-rolling force model was proposed to predict the rolling force in the bimetal solid-liquid cast-rolling bonding(SLCRB) process. The solid-liquid bonding zone was assumed to be below the kiss point(KP). The deformation resistance of the liquid zone was ignored. Then, the calculation model was derived. A 2D thermal-flow coupled simulation was established to provide a basis for the parameters in the model, and then the rolling forces of the Cu/Al clad strip at different rolling speeds were calculated. Meanwhile, through measurement experiments, the accuracy of the model was verified. The influence of the rolling speed, the substrate strip thickness, and the material on the rolling force was obtained. The results indicate that the rolling force decreases with the increase of the rolling speed and increases with the increase of the thickness and thermal conductivity of the substrate strip. The rolling force is closely related to the KP height. Therefore, the formulation of reasonable process parameters to control the KP height is of great significance to the stability of cast-rolling forming.

Numerical Prediction for Subcooled Boiling Flow of Liquid Nitrogen in a Vertical Tube with MUSIG Model

Multiple size group （MUSIG） model combined with a threedimensional twofluid model were em ployed to predict subcooled boiling flow of liquid nitrogen in a vertical upward tube. Based on the mechanism of boiling heat transfer, some important bubble model parameters were amended to be applicable to the modeling of liquid nitrogen. The distribution of different discrete bubble classes was demonstrated numerically and the distribu tion patterns of void fraction in the wallheated tube were analyzed. It was found that the average void fraction in creases nonlinearly along the axial direction with wall heat flux and it decreases with inlet mass flow rate and sub cooled temperature. The local void fraction exhibited a Ushape distribution in the radial direction. The partition of the wall heat flux along the tube was obtained. The results showed that heat flux consumed on evaporation is the leading part of surface heat transfer at the rear region of subcooled boiling. The turning point in the pressure drop curve reflects the instability of bubbly flow. Good agreement was achieved on the local heat transfer coefficient aalnst experimental measurements, which demonstrated the accuracy of the numerical model.

Effects of fufang yimucao oral liquid on acute ache model mice

BACKGROUND： Fufang yimucao oral liquid has markedly effects on ameliorating circulation, restraining uterine constriction induced by oxytocin, alleviating dysmenorrhea, as a traditional medicine on promoting blood circulation by removing blood stasis, yimucao could ameliorate abnormal hemorrheological when hemorrhagic shock happens, enhance the hemoperfusion of organs and actively react on the result of hemorrhagic shock. OBJECTIVE： To investigate the abirritation offufang yimucao oral liquid on pain model mice induced by hot board method and acetic acid twist body method and dysmenorrhea model mice induced by estradiol. DESIGN： Entirely randomly grouping and control experiment. SETTING： Pharmacological Laboratory, Henan College of Traditional Chinese Medicine. MATERIALS： A total of 200 female Kunming genus mice of grade 2 and weighing 18- 21 g were collected. Fufang yimucao oral liquid, mainly consist ofyimucao, danggui, chuanxiong, muxiang, and so on, was produced by Henan Joyline ＆ Joysun Pharmaceutical Stock Co., Ltd. （batch number： 050701）; yimucao oral liquid was produced by Shangqiu Lvyuan Pharmaceutical Co., Ltd. （batch number： 050108）; estradiol slice by Shanghai Xinyi Kangjie Pharmaceutical Co., Ltd. （batch number： 050301）; YSL-6A intelligence hot plate instrument by Shandong Equipments Station of the Medical Science. METHODS： The experiment was carried out in the Animal Experiment Center of the Henan College of Traditional Chinese Medicine from August to November 2005. The high-, middle- and low-dosage fufang yimucao oral liquid in the experiment was 1, 0.5 and 0.25 in volume fraction, respectively, andyimucao oral liquid was 0.5. ① Among 80 mice, 60 mice were eligible in pain threshold tested by hot plate, and randomly dividing into 5 groups with 12 in each group. Mice in the high-, middle- and low-dose fufang yimucao oral liquid groups were perfused with 1 mL, 0.5 mL and 0.25 mL/mLfufang yimucao, and mice in the yimucao group and saline group were perfused with the same volume yimucao oral liquid and saline, respectively, once a day for 3 successive days. Half an hour and one hour after administration for the last time, the range of pain was tested in hot plate and the increasing numerical value was counted. ② Another 60 mice were randomly divided into 5 groups. The grouping ways, numbers of animal and administration were as the same as those mentioned above. Forty minutes after administration for the last time, mice were given the celiac injecting with the fresh acetic acid, then observed and registered the delitescence of turned body and the times of turning in 10 minutes. ③ The rest of 60 mice were randomly divided into 6 groups with 10 in each group. The five groups were divided as the same as mentioned above, and the last group was the blank control group. Mice in the 5 former groups were given synestrin tablets CMC suspension with the dose of 2 mg/kg, 0.1 g/L and 0.2 mL/10 g once a day for 12 successive days. Ten days later, mice were administrated as the same ways and dosage mentioned above. Mice in blank control group were perfused with the same volume of saline. Two days after modeling and 40 minutes after administration, mice were injected with oxytocin to observe the latent period and the frequency of twisting reaction in 10 minutes. MAIN OUTCOME MEASURES： Effect offufangyimucao oral liquid on mice pain model induced by hot board method, twisting body response induced by acetic acid and mice dysmenorrhea model. RESULTS： ① Effect offufang yimucao oral liquid on mice pain model induced by hot board： Thirty minutes after administration, the pain threshold ofyimucao oral liquid group and high-, middle- and low-dose fufang yimucao oral liquid groups were respectively （25.42 ± 2.10）, （22.40 ± 3.42）, （25.24± 2.51 ） and （ 19.80 ±2.00） s, which were markedly higher than saline group [（17.98± 1.68） s, P 〈 0.05 - 0.01]. Sixty minutes after administration, the pain threshold ofyimucao oral liquid group and high-, middle- and low-dosefufang yimucao oral liquid groups were respectively （27.42 ± 2.17）, （23.83 ± 2.66）, （27.64 ± 2.64） and （21.51 ± 2.41 ） s, which were markedly higher than saline group [（17.8± 1.75） s, P 〈 0.01]. ② Effect offufangyimucao oral liquid on twisting body response induced by celiac injecting acetic acid： The twisting body latent period of yimucao oral liquid group and high-, middle- and low-dose fufang yimucao oral liquid groups were respectively （2.43±0.19）, （2.09±0.20）, （2.60±0.14） and （1.85±0.35） s, which were markedly higher than saline group [（1.45±0.22） s, P 〈 0.01]. The twisting body times in 10 minutes ofyimucao oral liquid group and high-, middle- and low-dose fufang yimucao oral liquid groups were respectively （14.8 ±4.0）, （15.8 ± 3.5）, （12.2±3.7） and （18.7±3.3） times, which were markedly lower than saline group [（25.0±5.0） times, P 〈 0.01]. ③ Effect offufangyimucao oral liquid on mice dysmenorrhea model： After injecting estradiol, the twisting body latent period ofyimucao oral liquid group and high-, middle- and Iow-dosefufangyimucao oral liquid groups were respectively （61.8±20.8）, （105.8±29.8）, （78.9± 14.0） and （71.9±20.0） s, which were higher than the saline group [（31.6± 14.71） s, P 〈 0.01]. The twisting body times in 10 minutes of yimucao oral liquid group and high-, middle- and low-dose fufang yimucao oral liquid groups were respectively （18.1± 4.2）, （9.5 ±2.8）, （16.2 ± 3.5） and （19.9 ±4.6） times, which were lower than the saline group [（28.5 ±4.7） times, P 〈 0.01]. CONCLUSION： Fufang yimucao oral liquid has a good effect on abirritation, condignly as yimucao oral liquid, besides it does not have obvious dependent effect.

Methyl chloride dehydration with ionic liquid based on COSMO-RS model

A suitable ionic liquid for methyl chloride drying experiment was screened out from 210 ionic liquids by COSMO-RS model.Moreover,the experimental mechanism of ionic liquids drying is further explained by the COSMO-RS model,and it is further confirmed by analyzing the binding energy.The solubility of methyl chloride in[EMIM][BF4]and TEG and[EMIM][BF4]+H2O was completed,and the experimental results well proved the reliability of the UNIFAC-Lei model.The unknown interaction parameters were obtained through the solubility data of this work and the experimental data in the literatures.The methyl chloride drying experiment was completed in the laboratory,and the water content of the methyl chloride can be reduced to below 200 ppm.The simulation of the methyl chloride drying process using[EMIM][BF4]or TEG as absorbents was carried out by ASPEN software on an industrial scale.The final simulation results show that the[EMIM][BF4]drying process has lower energy consumption and better drying effect.

Germanium transport across supported liquid membrane with Cyanex 923: Mathematical modeling

A mathematical model was developed to monitor the facilitated transport of germanium(IV) from oxalic acid solutions through a flat sheet supported liquid membrane(FSSLM) containing four trialkylphosphine oxides(Cyanex 923). The FSSLM modeling was based on the extraction constant(Kext) calculated from the liquid-liquid extraction(LLX) modeling. The LLX model presented a reliable calculation of the extraction constant(Kex= 2.057×103 L/mol4). The FSSLM model was solved using Matlab■ software according to extraction constant, Fick’s law, and diffusional principles. The model predicts the overall mass transfer coefficient(Korg) to be 3.84 cm/s. Using this value, diffusion coefficients(Dm) for various Cyanex 923 concentrations of 0.126, 0.252, 0.378, 0.505, 0.631 and 0.757 mol/L are found to be 8.50×10^-4, 4.30×10^-4, 1.87×10^-4, 5.87×10^-5, 2.57×10^-5, 2.09×10^-5 cm2/s, respectively. The results show that the diffusion rate of the current study is approximately more than that of similar FSSLM systems containing Cyanex 923 used to transport various metals. The modeling values are in good agreement with the experimental data, showing the good reliability of the mathematical model.

Modification to solution-diffusion model for performance prediction of nanofiltration of long-alkyl-chain ionic liquids aqueous solutions based on ion cluster

Mathematical modeling for nanofiltration of ionic liquids(ILs) solutions could assist to understand transfer mechanism and predict experimental values. In this work, modeling by solution-diffusion model for nanofiltration of long-alkyl-chain ILs aqueous solutions was proposed. Molecular simulations were performed to validate the existence of ion cluster in long-alkyl-chain ILs aqueous solution. Based on the results of simulations, parameters used in the solution-diffusion model were modified, such as concentration of ILs and diameter of ion cluster.The modeling process was developed for three long-alkyl-chain ILs aqueous solutions with different concentrations(1-alkyl-3-methylimidazolium chloride: [C6 mim]Cl, [C8 mim]Cl, [C10 mim]Cl). The calculated values obtained from modified solution-diffusion model could well match the experimental values.

A Surface Tension Model for Liquid Mixtures Based on NRTL Equation

A new equation for predicting surface tension is proposed based on the thermodynamic definition of surface tension and the expression of the Gibbs free energy of the system. Using the NRTL equation to represent the excess Gibbs free energy, a two-parameter surface tension equation is derived. The feasibility of the new equation has been tested in terms of 124 binary and 16 multicomponent systems(13-ternary and 3-quaternary) with absolute relative deviations of 0.59% and 1.55% respectively. This model is also predictive for the temperature dependence of surface tension of liquid mixtures. It is shown that, with good accuracy, this equation is simple and reliable for practical use.