• 제목/요약/키워드: Equilibrium profile

검색결과 103건 처리시간 0.027초

Equilibrium and kinetic studies on the adsorption of copper onto carica papaya leaf powder

  • Varma V., Geetha;Misra, Anil Kumar
    • Membrane and Water Treatment
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    • 제7권5호
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    • pp.403-416
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    • 2016
  • The possibility of using carica papaya leaf powder for removal of copper from wastewater as a low cost adsorbent was explored. Different parameters that affect the adsorption process like initial concentration of metal ion, time of contact, adsorbent quantity and pH were evaluated and the outcome of the study was tested using adsorption isotherm models. A maximum of 90%-94.1% copper removal was possible from wastewater having low concentration of the metal using papaya leaf powder under optimum conditions by conducting experimental studies. The biosorption of copper ion was influenced by pH and outcome of experimental results indicate the optimum pH as 7.0 for maximum copper removal. Copper distribution between the solid and liquid phases in batch studies was described by isotherms like Langmuir adsorption and Freundlich models. The adsorption process was better represented by the Freundlich isotherm model. The maximum adsorption capacity of copper was measured to be 24.51 mg/g through the Langmuir model. Pseudo-second order rate equation was better suited for the adsorption process. A dynamic mode study was also conducted to analyse the ability of papaya leaf powder to remove copper (II) ions from aqueous solution and the breakthrough curve was described by an S profile. Present study revealed that papaya leaf powder can be used for the removal of copper from the wastewater and low cost water treatment techniques can be developed using this adsorbent.

Gibbs 함수의 포텐샬로 해석한 토양 흡착수 (Adsorbed Water in Soil a Interpreted by Its Potentials Based on Gibbs Function)

  • 오영택;신제성
    • 한국광물학회지
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    • 제9권1호
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    • pp.17-25
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    • 1996
  • Usual experimental adsorption isotherms as a function of relative humidity were constructed from adsorbed water contents in soils, which were kept more than 2 days in vacuum desiccators with constant humidities controlled by sulfuric acids of various concentrations. From the experimental data, the adsorption surface areas were calculated on the basis of the existing adsorption theory, such as Langmuir, BET, and Aranovich. Based on the Gibbs function describing chemical potential of perfect gas, the relative humidities in the desiccators were transformed into their chemical potentials, which were assumed to be the same as the potentials of equilibratedly adsorbed water in soils. Moreover, the water potentials were again transformed into the equivalent capillary pressures, heads of capillary rise, and equivalent radius of capillary pores, on the basis of Laplace equation for surface tension pressure of spherical bubbles in water. Adsorption quantity distributions were calculated on the profile of chemical potentials of the adsorbed water, equivalent adsorption and/or capillary pressures, and equivalent capillary radius. The suggested theories were proved through its application for the prediction of temperature rise of sulfuric acid due to hydration heat. Adsorption heat calculated on the basis of the potential difference was dependant on various factors, such as surface area, equilibrium constants in Langumuir, BET, etc.

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Buckling analysis of noncontinuous linear and quadratic axially graded Euler beam subjected to axial span-load in the presence of shear layer

  • Heydari, Abbas
    • Advances in Computational Design
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    • 제5권4호
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    • pp.397-416
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    • 2020
  • Functionally graded material (FGM) illustrates a novel class of composites that consists of a graded pattern of material composition. FGM is engineered to have a continuously varying spatial composition profile. Current work focused on buckling analysis of beam made of stepwise linear and quadratic graded material in axial direction subjected to axial span-load with piecewise function and rested on shear layer based on classical beam theory. The various boundary and natural conditions including simply supported (S-S), pinned - clamped (P-C), axial hinge - pinned (AH-P), axial hinge - clamped (AH-C), pinned - shear hinge (P-SHH), pinned - shear force released (P-SHR), axial hinge - shear force released (AH-SHR) and axial hinge - shear hinge (AH-SHH) are considered. To the best of the author's knowledge, buckling behavior of this kind of Euler-Bernoulli beams has not been studied yet. The equilibrium differential equation is derived by minimizing total potential energy via variational calculus and solved analytically. The boundary conditions, natural conditions and deformation continuity at concentrated load insertion point are expressed in matrix form and nontrivial solution is employed to calculate first buckling loads and corresponding mode shapes. By increasing truncation order, the relative error reduction and convergence of solution are observed. Fast convergence and good compatibility with various conditions are advantages of the proposed method. A MATLAB code is provided in appendix to employ the numerical procedure based on proposed method.

열전도에 의해 지배되는 이성분혼합물의 응고문제에 대한 해석해 (Analytical solution to the conduction-dominated solidification of a binary mixture)

  • 정재동;유호선;노승탁;이준식
    • 대한기계학회논문집B
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    • 제20권11호
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    • pp.3655-3665
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    • 1996
  • An analytical solution is presented for the conduction-dominated solidification of a binary mixture in a semi-infinite medium. The present approach differs from that of other solution by these four characteristics. (1) Solid fraction is determined from the phase diagram, (2) thermophysical properties in mushy zone are weighted according to the local solid fraction, (3) non-equilibrium solidification can be simulated and (4) the cooling condition of under-eutectic temperature can be simulated. Up to now, almost all analyses are based on the assumption of constant properties in mushy zone and solid fraction linearly with temperature or length. The validation for these assumptions, however, shows that serious error is found except some special cases. The influence of microscopic model on the macroscopic temperature profile is very small and can be ignored. But the solid fraction and average solid concentration which directly influence the quality of materials are drastically changed by the microscopic models. An approximate solution using the method of weighted residuals is also introduced and shows good agreement with the analytical solution. All calculations are performed for NH$_{4}$Cl-H$_{2}$O and Al-Cu system.

수지상가지의 조대화를 고려한 이원합금의 응고과정동안 용질 재분배 해석 (Analysis on the solute redistribution in coarsening dendrite arms during solidification of binary metal alloys)

  • 유호선
    • 대한기계학회논문집B
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    • 제20권4호
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    • pp.1437-1448
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    • 1996
  • This paper presents a simplified model for approximate analysis of the solute redistribution in coarsening dendrite arms during solidification of binary metal alloys. By introducing a quadratic concentration profile with a time-dependent coefficient, the integral equation for diffusion in the solid phase is reduced to a simple differential relation between the coefficient and the solid-liquid interface position. The solid fraction corresponding to the system temperature is readily determined from the relation, phase equilibrium and the overall solute balance in which the liquid phase is assumed to be completely mixed. In order to validate the developed model, calculations are performed for the directional solidification of Al-4.9 mass Cu alloy. The predicted eutectic fractions for a wide range of the cooling rate reasonably agree with data from the well-known experiment as well as sophisticated numerical analyses. Also, the results for the back diffusion limits are consistent with available references. Additional calculations show that the characteristic parameters such as the coarsening, density variation and nonlinarity in the phase diagram significantly affect the microsegregation. Owing to the simplicity, efficiency and compatibility, the present model may be suitable for the micro-macroscopic solidification model as a microscopic component.

비평형 2.5 난류모델을 이용한 라그란지안 입자 확산모델 개발 (Development of Lagrangian Particle Dispersion Model Based on a Non-equilibrium 2.5 Level Closure Turbulence Model)

  • 구윤서
    • 한국대기환경학회지
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    • 제15권5호
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    • pp.613-623
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    • 1999
  • A Lagrangian particle dispersion mode l(LPDM) coupled with the prognostic flow model based on nonequilibrium level 2.5 turbulence closure has been dcveloped to simulate the dispersion from an elevated emission source. The proposed model did not require any empirical formula or data for the turbulent statistics such as velocity variances and Lagrangian time scales since the turbulence properties for LPDM were calculated from results of the flow model. The LPDM was validated by comparing the model results against the wind tunnel tracer experiment and ISCST3 model. The calculated wind profile and turbulent velocity variances were in good agreement with those measured in the wind tunnel. The ground level concentrations along the plume centerline as well as the dispersion codfficients also showed good agreement in comparison with the wind tunnel tracer experiment. There were some discrepancies on the horizontal spread of the plume in comparison with the ISCST3 but the maximum ground level concentrations were in a good confidence range. The results of comparisons suggested that the proposed LPDM with the flow model was an effective tool to simulate the dispersion in the flow situation where the turbulent characteristics were not available in advance.

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A piecewise linear transverse shear transfer model for bolted side-plated beams

  • Li, Ling-Zhi;Jiang, Chang-Jiu;Su, Ray Kai-Leung;Lo, Sai-Huen
    • Structural Engineering and Mechanics
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    • 제62권4호
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    • pp.443-453
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    • 2017
  • The performance of bolted side-plated (BSP) beams is affected by the degree of transverse partial interaction, which is a result of the interfacial slip caused by transverse shear transfer between the bolted steel plates and the reinforced concrete beams. However, explicit formulae for the transverse shear transfer profile have yet to be derived. In this paper, a simplified piecewise linear shear transfer model was proposed based on force superposition principle and simplification of shear transfer profiles derived from a previous numerical study. The magnitude of shear transfer was determined by force equilibrium and displacement compatibility condition. A set of design formulae for BSP beams under several basic load cases was also derived. Then the model was verified by test results. A worked example was also provided to illustrate the application of the proposed design formulae. This paper sheds some light on the shear force transfer mechanism of anchor bolts in BSP beams, and offers a practical method to evaluate the influence of transverse partial interaction in strengthening design.

2차원 양자 역학적 해석에 의한 고속 통신용 $Al_{x}Gal{-x}As/Ga_{x}In1$_{-x}$As/GaAs HEMT 소자의 전자 농도 및 전위분포 계산 (Calculation of Electron concentration and Electrostatic potential profile for $Al_{x}Gal{-x}As/Ga_{x}In1$_{-x}$As/GaAs HEMT device by 2-Dimensional Quantum Mechanical analysis))

  • 송영진;황호정
    • 전자공학회논문지A
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    • 제30A권3호
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    • pp.76-87
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    • 1993
  • We present a self-consistent, 2-dimensional solution of the Poisson and Sch rodinger equation based on the finite difference method with a nonuniform mesh size for a AlGaAs/GaInAs/GaAs HEMT devide. During the interative self-consistent calculation, however, we calculate Schrodinger equation only a some region of device, not a fully region in order to save the moemory and the speed-up of computation, and then use the approximated data for the other region using by a interpolation method with a given values. Also we adopt the proper matrix transformation method that allows preservation of the symmetric, form of the discretized Schrodinger equation, even with the use of a nonumiform mesh size, therefor, can reduce the computation time. We calculate the wavefunction, eigenstates and the electron concentration uat channel layer nder the thermal equilibrium and the biased conditions, respectively. Also,these parameters are used to solve 2-dimensional tdistribution of potential in he entire region of device. It is proved that the method is very efficient in finding eigenstages extending over relatively large spatial area without loss of accuracy. So, it can be used rather easily in any sarbitrary modulation doped utucture.

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A Numerical Solution of Transport of Mono- and Tri-valent Cations during Steady Water Flow in a Binary Exchange System

  • Ro, Hee-Myong;Yoo, Sun-Ho
    • Journal of Applied Biological Chemistry
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    • 제43권1호
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    • pp.18-24
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    • 2000
  • A one-dimensional transport of displacing monovalent ion, $A^+$, and a trivalent ion being displaced, $B^{3+}^ in a porous exchange system such as soil was approximated using the Crank-Nicolson implicit finite difference technique and the Thomas algorithm in tandem. The variations in the concentration profile were investigated by varying the ion-exchange equilibrium constant (k) of ion-exchange reactions, the influent concentrations, and the cation exchange capacity (CEC) of the exchanger, under constant flux condition of pore water and dispersion coefficient. A higher value of k resulted in a greater removal of the native ion, behind the sharper advancing front of displacing ion, while the magnitude of the penetration distance of $A^+$ was not great. As the CEC increased, the equivalent fraction of $B^{3+}^ initially in the soil was greater, thus indicating that a higher CEC adsorbed trivalent cations preferentially over monovalent ions. Mass balance error from simulation results was less than 1%, indicating this model accounted for instantaneous charge balance fairly well.

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하안단구와 수비분지의 지형발달 (River Terraces and Geomorphic Development of Subi Basin, Yeongyang)

  • 손명원
    • 한국지형학회지
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    • 제24권2호
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    • pp.15-25
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    • 2017
  • Subi basin is located at the crestline of Taebaek mountains. This paper aims to elucidate the geomorphic development of Subi basin through the analysis of river terraces built in Wangpi-cheon and Banbyeon-cheon. Wangpi-cheon flows northeastward from Subi basin, and Banbyeon-cheon flows southward at the west of Subi basin. Absolute age of terrace is measured by means of OSL methodology, long profile of Wangpi-cheon is made up with 10m interval contour line, and the elevation above river bed of high terraces is measured at the end part of terrace. The results are as follow: Firstly, high river terraces of Subi basin, Wangpi-cheon and Banbyeon-cheon are formed about 40 kyr(MIS 3) being interstadial stage of last glacial period. Secondly, the elevation above river bed of high terraces of Wangpi-cheon and Banbyeon-cheon tends to increase toward upstream. It means that the uplift of Taebaek Mountains influences considerably the formation of their terraces. Thirdly, the elevation above river bed of high terraces at the reach from Seomchon to Suha-ri of Wangpi-cheon tends to decrease toward upstream. This section is captured from Banbyeon-cheon flowing in the opposite direction. River piracy has occurred from the time of formation of Suha-ri high terrace to the time of formation of Hantee wind gap. Finally, for fluvial system of Wangpi-cheon to establish dynamic equilibrium, topographic axis will move toward Banbyeon-cheon.