A one-dimensional transport model for multi-component solute in saturated soil

A modified multi-component solute diffusion equation described with diffusion flux was derived in detail based on the classical MaxwellStefan diffusion theory. The friction between the solute species and the soil skeleton wall, which is proportional to the relative velocity between the solute species and the soil skeleton, is introduced. The chemical potential gradient is considered the driving force. A one-dimensional model for transport of multi-component solute in saturated soil was developed based on the modified diffusion equation and the modified competitive Langmuir adsorption equation. Numerical calculation of a case of two heavy metal ion species, which was chosen as an example, was carried out using the finite element software COMSOL Multiphysics. A comparative analysis was performed between the multi-component solute transport model developed in this study and the convection-diffusion transport model of single-component solute based on Fick's law. Simulation results show that the transport behavior of each species in a multi-component solute system is different from that in a single-component system, and the friction characteristics considered in the developed model contribute to obstructing the movement of each solute component. At the same time,the influence of modified competitive Langmuir adsorption on solute transport was investigated. These research results can provide strong theoretical support for the design of antifouling barriers in landfills and the maintenance of operation stability.

Research on shell-side heat and mass transfer with multi-component in LNG spiral-wound heat exchanger under sloshing conditions

The spiral-wound heat exchanger(SWHE) is the primary low-temperature heat exchanger for large-scale LNG plants due to its high-pressure resistance, compact structure, and high heat exchange efficiency. This paper studied the shell-side heat and mass transfer characteristics of vapor-liquid two-phase mixed refrigerants in an SWHE by combining a multi-component model in FLUENT software with a customized multicomponent mass transfer model. Besides, the mathematical model under the sloshing condition was obtained through mathematical derivation, and the corresponding UDF code was loaded into FLUENT as the momentum source term. The results under the sloshing conditions were compared with the relevant parameters under the steady-state condition. The shell-side heat and mass transfer characteristics of the SWHE were investigated by adjusting the component ratio and other working conditions. It was found that the sloshing conditions enhance the heat transfer performance and sometimes have insignificant effects. The sloshing condition is beneficial to reduce the flow resistance. The comprehensive performance of multi-component refrigerants has been improved and the improvement is more significant under sloshing conditions, considering both the heat transfer and pressure drop.These results will provide theoretical support for the research and design of multi-component heat and mass transfer enhancement of LNG SWHE under ocean sloshing conditions.

Solute transport and geochemical modeling of the coastal quaternary aquifer, Delta Dahab Basin, South Sinai, Egypt

The wadi dahab delta is in a dry, arid coastal zone within Egypt’s south Sinai Peninsula’s eastern portion. The primary water source is the Quaternary coastal alluvial aquifer. The groundwater salinity varies from 890to 8213 mg/L, with a mean value of 3417 mg/L. The dissolved major ions have been used to calculate the seawater mixing index(SWMI) using a linear equation that discriminates the groundwater mostly affected by water–rock interaction(SWMI 1>) and other samples mixed with Seawater(SWMI < 1). The isotopic composition of groundwater for specifically chosen groundwater samples ranges from-0.645‰ to +5.212‰ for δ^(18)O and from-9.582‰ to + 22.778‰ for δ^(2)H, where the seawater represented by a Red Sea water sample(δ^(18)O + 1.64‰-δ^(2)H + 9.80‰) and reject brine water are considerably enriched the isotopic groundwater values. The geochemical NETPATH model constrained by the dissolved significant ions, isotopes, and the rock aquifer forming minerals as phases indicate the mixing percent with the seawater ranges from 9% to 97% of seawater from 91% to 3% of original recharge water. According to the SEAWAT 3-D flow models, seawater has penetrated the Northeastern Dahab delta aquifer, with the intrusion zone extending1500 m inland. The salt dissolution, upwelling of saline water, recharge from the upstream mountain block, and seawater encroachment are the primary aspects contributing to the deterioration of groundwater quality. These findings may have significance for effective groundwater withdrawal management in arid locations worldwide with similar hydrogeological systems.

Numerical Modelling of Dissolving and Driving Exploitation of Potash Salt in the Qarhan Playa——A Coupled Model of Reactive Solute Transport and Chemical Equilibrium in a Multi-component Underground Brine System

Firstly, the macroscopic chemical equilibrium state of a series of chemical reactions between intercrystal brine and its media salt layer （salt deposit） in Qarhan Salt Lake was studied by using the Pitzer theory. The concept of macroscopic solubility product and its relation with accumulated ore dissolving ratio were presented, which are used in the numerical model of dissolving and driving exploitation of potassium salt in Qarhan Salt Lake. And secondly, with a model forming idea of transport model for reacting solutes in the multi-component fresh groundwater system in porous media being a reference, a two-dimensional transport model coupled with a series of chemical reactions in a multi-component brine porous system （salt deposits） was developed by using the Pitzer theory. Meanwhile, the model was applied to model potassium/magnesium transport in Qarhan Salt Lake in order to study the transfer law of solid and liquid phases in the dissolving and driving process and to design the optimal injection/abstraction strategy for dissolving and capturing maximum Potassium/ Magnesium in the mining of salt deposits in Qarhan Salt Lake.

A Solute Pinning Approach to Solute Drag in Multi-Component Solid Solution Alloys

The Cahn, Lücke and Stüwe theory remains the backbone of more complex analysis dealing with solute drag, however, the mathematical treatment is rather involved. A new approach based on solute pinning the boundary has therefore recently been suggested, which has the main advantage of a simpler mathematical treatment. In the present paper this approach has been generalized to take into account the influence of different types of solute atoms in the high solute content/low driving force regime.

Modeling impact of culture facilities on hydrodynamics and solute transport in marine aquaculture waters of North Yellow Sea

An increasing number of marine aquaculture facilities have been placed in shallow bays and open sea,which might significantly affect hydrodynamic and solute transport processes in marine aquaculture waters.In this study,a coupled hydrodynamic and solute transport model was developed with high-resolution schemes in marine aquaculture waters based on depth-averaged shallow water equations.A new expression of drag force was incorporated into the momentum equations to express the resistance of suspended culture cages.The coupled model was used to simulate the effect of suspended structures on tidal currents and the movement of a contaminant cloud in the marine aquaculture of the North Yellow Sea,China.The simulation results showed a low-velocity area appearing inside the aquaculture cage area,with a maximum reduction rate of velocity close to 45%under high-density culture.The results also showed that tidal currents were sensitive to the density of suspended cages,the length of cages,and the drag coefficients of cages.The transport processes of pollutants inside aquaculture facilities were inhibited away from the vicinity of the culture cage area because of the diminished tidal currents.Therefore,the suspended cages significantly affected the transport processes of pollutants in the coastal aquaculture waters.Furthermore,the reduced horizontal velocity significantly decreased the food supply for the aquaculture areas from the surrounding sea.

2D Q-compensated multi-component elastic Gaussian beam migration

Elastic waves are affected by viscoelasticity during the propagation through the Earth,resulting in energy attenuation and phase distortion,in turn resulting in low seismic imaging accuracy.Therefore,viscoelasticity should be considered in seismic migration imaging.We propose a Q compensated multicomponent elastic Gaussian beam migration(Q-EGBM)method to(1)separate the elastic-wave data into longitudinal(P)and transverse(S)waves to perform PP-wave and PS-wave imaging;(2)recover the amplitude loss caused by attenuation;(3)correct phase distortions caused by dispersion;(4)improve the resolution of migration imaging.In this paper,to accomplish(2),(3),and(4),we derive complex-valued traveltimes in viscoelastic media.The results of numerical experiments using a simple five-layer model and a sophisticated BP gas model show that the method presented here has significant advantages in recovering energy decay and correcting phase distortion,as well as significantly improving imaging resolution.

Modeling of thermodynamic properties of multi-component electrolyte solutions

An empiric equation, G ex H 2O /(1- x (H 2O)) 2= α+β·x (H 2O)/ln( x (H 2O)), representing the relation between the excess free energy G ex H 2O and mole fraction of water x (H 2O) in binary electrolyte solution, was developed and the parameters α and β in the equation were determined by fitting the experimental data for some binary aqueous systems of electrolytes such as CuCl 2, NiCl 2, HCl, NaCl, KCl, CaCl 2 and BaCl 2. The activities of water in such ternary and multi component systems composed of 7 binaries as HClH 2OCuCl 2, HClH 2ONiCl 2, HClH 2ONaCl, NaClH 2OKCl, NaCl H 2OCaCl 2, KClH 2OCaCl 2, NaClH 2OBaCl 2, KClH 2OCaCl 2 and NaClH 2OKClBaCl 2 were predicted by a simplified sub regular solution model developed by authors from the corresponding binary systems. The predicted results are in good agreement with the measured ones. [

Analysis on the formation principle and present situation of nano phase state of multi-component self-assembly of traditional Chinese compound medicine decoction

Traditional Chinese medicine decoction is a complex polydispersed phase system containing real solution,colloid solution,emulsion and suspension.The compound decoction of traditional Chinese medicine has complex components,including saponins,alkaloids,polysaccharides,flavonoids,amino acids and so on,which can be self-assembled to form gels,fibers,micelles,vesicles and so on.The self-assembled nano-phase not only neutralizes the single drug and reduces the toxicity and side effects,but also has its own pharmacological effects,which complement each other to achieve synergistic effect,so as to achieve the role of drug supplement,which is of research significance.The formation principle,solubilization and synergism principle and characterization method of multi-component self-assembly of traditional Chinese medicine compound decoction are discussed in this paper.

Effects of CH_(4)/CO_(2) multi-component gas on components and properties of tight oil during CO_(2) utilization and storage: Physical experiment and composition numerical simulation

An essential technology of carbon capture, utilization and storage-enhanced oil recovery (CCUS-EOR) for tight oil reservoirs is CO_(2) huff-puff followed by associated produced gas reinjection. In this paper, the effects of multi-component gas on the properties and components of tight oil are studied. First, the core displacement experiments using the CH_(4)/CO_(2) multi-component gas are conducted to determine the oil displacement efficiency under different CO_(2) and CH_(4) ratios. Then, a viscometer and a liquid density balance are used to investigate the change characteristics of oil viscosity and density after multi-component gas displacement with different CO_(2) and CH_(4) ratios. In addition, a laboratory scale numerical model is established to validate the experimental results. Finally, a composition model of multi-stage fractured horizontal well in tight oil reservoir considering nano-confinement effects is established to investigate the effects of multi-component gas on the components of produced dead oil and formation crude oil. The experimental results show that the oil displacement efficiency of multi-component gas displacement is greater than that of single-component gas displacement. The CH_(4) decreases the viscosity and density of light oil, while CO_(2) decreases the viscosity but increases the density. And the numerical simulation results show that CO_(2) extracts more heavy components from the liquid phase into the vapor phase, while CH_(4) extracts more light components from the liquid phase into the vapor phase during cyclic gas injection. The multi-component gas can extract both the light components and the heavy components from oil, and the balanced production of each component can be achieved by using multi-component gas huff-puff.

Optimization of extended warranty cost for multi-component systems with economic dependence based on group maintenance

During extended warranty(EW)period,maintenance events play a key role in controlling the product systems within normal operations.However,the modelling of failure process and maintenance optimization is complicated owing to the complex features of the product system,namely,components of the multi-component system are interdependent with each other in some form.For the purpose of optimizing the EW pricing decision of the multi-component system scientifically and rationally,taking the series multi-component system with economic dependence sold with EW policy as a research object,this paper optimizes the imperfect preventive maintenance(PM)strategy from the standpoint of EW cost.Taking into consideration adjusting the PM moments of the components in the system,a group maintenance model is developed,in which the system is repaired preventively in accordance with a specified PM base interval.In order to compare with the system EW cost before group maintenance,the system EW cost model before group maintenance is developed.Numerical example demonstrates that offering group maintenance programs can reduce EW cost of the system to a great extent,thereby reducing the EW price,which proves to be a win-win strategy to manufacturers and users.

GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.

Solute carrier-related signature for assessing prognosis and immunity in patients with clear-cell renal cell carcinoma

Background:Clear-cell renal cell carcinoma(ccRCC)is the most common malignant kidney cancer.However,the tumor microenvironment and crosstalk involved in metabolic reprogramming in ccRCC are not well-understood.Methods:We used The Cancer Genome Atlas to obtain ccRCC transcriptome data and clinical information.The EMTAB-1980 cohort was used for external validation.The GENECARDS database contains the first 100 solute carrier(SLC)-related genes.The predictive value of SLC-related genes for ccRCC prognosis and treatment was assessed using univariate Cox regression analysis.An SLC-related predictive signature was developed through Lasso regression analysis and used to determine the risk profiles of patients with ccRCC.Patients in each cohort were separated into high-and low-risk groups based on their risk scores.The clinical importance of the signature was assessed through survival,immune microenvironment,drug sensitivity,and nomogram analyses using R software.Results:SLC25A23,SLC25A42,SLC5A1,SLC3A1,SLC25A37,SLC5A6,SLCO5A1,and SCP2 comprised the signatures of the eight SLCrelated genes.Patients with ccRCC were separated into high-and low-risk groups based on the risk value in the training and validation cohorts;the high-risk group had a significantly worse prognosis(p<0.001).The risk score was an independent predictive indicator of ccRCC in the two cohorts according to univariate and multivariate Cox regression(p<0.05).Analysis of the immune microenvironment showed that immune cell infiltration and immune checkpoint gene expression differed between the two groups(p<0.05).Drug sensitivity analysis showed that compared to the low-risk group,the high-risk group was more sensitive to sunitinib,nilotinib,JNK-inhibitor-VIII,dasatinib,bosutinib,and bortezomib(p<0.001).Survival analysis and receiver operating characteristic curves were validated using the E-MTAB-1980 cohort.Conclusions:SLC-related genes have predictive relevance in ccRCC and play roles in the immunological milieu.Our results provide insight into metabolic reprogramming in ccRCC and identify promising treatment targets for ccRCC.

Solute drag-controlled grain growth in magnesium investigated by quasi in-situ orientation mapping and level-set simulations

Critical properties of metallic materials,such as the yield stress,corrosion resistance and ductility depend on the microstructure and its grain size and size distribution.Solute atoms that favorably segregate to grain boundaries produce a pinning atmosphere that exerts a drag pressure on the boundary motion,which strongly affects the grain growth behavior during annealing.In the current work,the characteristics of grain growth in an annealed Mg-1 wt.%Mn-1 wt.%Nd magnesium alloy were investigated by advanced experimental and modeling techniques.Systematic quasi in-situ orientation mappings with a scanning electron microscope were performed to track the evolution of local and global microstructural characteristics as a function of annealing time.Solute segregation at targeted grain boundaries was measured using three-dimensional atom probe tomography.Level-set computer simulations were carried with different setups of driving forces to explore their contribution to the microstructure development with and without solute drag.The results showed that the favorable growth advantage for some grains leading to a transient stage of abnormal grain growth is controlled by several drivers with varying importance at different stages of annealing.For longer annealing times,residual dislocation density gradients between large and smaller grains are no longer important,which leads to microstructure stability due to predominant solute drag.Local fluctuations in residual dislocation energy and solute concentration near grain boundaries cause different boundary segments to migrate at different rates,which affects the average growth rate of large grains and their evolved shape.

New Exact Solutions of Multi-component mKdV Equation

In this paper, new Jacobi elliptic function solutions of multi-component mKdV equation are obtained directly in a unified way. When the modulus m → 1, those periodic solutions degenerate as the corresponding hyperbolic function solutions. Then, to the three-component mKdV equation, five types of effective solution are presented in detail.

Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation

This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.

Exact Periodic and Solitary-Wave Solutions of Multi-component Modified Korteweg-de Vries Equations

The present work extends the search of Jacobi elliptic function solutions for the multi-component modified Korteweg-de Vries equations. When the modulum m →1, those periodic solutions degenerate as the corresponding solitary wave and shock wave ones. Especially, exact solutions for the three-component system are presented in detail and graphically.

PDE Standardization Analysis and Solution of TypicalMechanics Problems

A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach through the standard forms of the PDE module in COMSOL.Two typical mechanics problems are exemplified:The deflection of a thin plate,which can be addressed with the dedicated finite element module,and the stress of a pure bending beamthat cannot be tackled.The procedure for the two problems regarding the three standard forms required by the PDE module is detailed.The results were in good agreement with the literature,indicating that the PDE module provides a promising means to solve complex PDEs,especially for those a dedicated finite element module has yet to be developed.

THE LIMITING PROFILE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS WITH A SHRINKING SELF-FOCUSING CORE

In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are bounded given functions whose self-focusing cores{x∈R^(N)|Q_(n)(x)>0} shrink to a set with finitely many points as n→∞.Motivated by the work of Fang and Wang[13],we use variational methods to study the limiting profile of ground state solutions which are concentrated at one point of the set with finitely many points,and we build the localized concentrated bound state solutions for the above equation systems.

Solution approximations for a mathematical model of relativistic electrons with beta derivative

The main aim of this paper is to obtain the exact and semi-analytical solutions of the nonlinear Klein-Fock-Gordon(KFG)equation which is a model of relativistic electrons arising in the laser thermonuclear fusion with beta derivative.For this purpose,both the modified extended tanh-function(mETF)method and the homotopy analysis method(HAM)are used.While applying the mETF the chain rule for beta derivative and complex wave transform are used for obtaining the exact solution.The advantage of this procedure is that discretization or normalization is not required.By applying the mETF,the exact solutions are obtained.Also,by applying the HAM semi-analytical results for the considered equation are acquired.In HAM?curve gives us a chance to find the suitable value of the for the convergence of the solution series.Also,comparative graphical representations are given to show the effectiveness,reliability of the methods.The results show that the m ETF and HAM are reliable and applicable tools for obtaining the solutions of non-linear fractional partial differential equations that involve beta derivative.This study can bring a new perspective for studies on fractional differential equations.On the other hand,it can be said that scientists can apply the considered methods for different mathematical models arising in physics,chemistry,engineering,social sciences and etc.which involves fractional differentiation.Briefly the results may cause a new insight who studies on relativistic electron modelling.