• Title/Summary/Keyword: ion transport equation

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Continuous ion-exchange membrane electrodialysis of mother liquid discharged from a salt-manufacturing plant and transport of Cl- ions and SO42- ions

  • Tanaka, Yoshinobu;Uchino, Hazime;Murakami, Masayoshi
    • Membrane and Water Treatment
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    • v.3 no.1
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    • pp.63-76
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    • 2012
  • Mother liquid discharged from a salt-manufacturing plant was electrodialyzed at 25 and $40^{\circ}C$ in a continuous process integrated with $SO_4{^{2-}}$ ion low-permeable anion-exchange membranes to remove $Na_2SO_4$ and recover NaCl in the mother liquid. Performance of electrodialysis was evaluated by measuring ion concentration in a concentrated solution, permselectivity coefficient of $SO_4{^{2-}}$ ions against $Cl^-$ ions, current efficiency, cell voltage, energy consumption to obtain one ton of NaCl and membrane pair characteristics. The permselectivity coefficient of $SO_4{^{2-}}$ ions against $Cl^-$ ions was low enough particularly at $40^{\circ}C$ and $SO_4{^{2-}}$ transport across anion-exchange membranes was prevented successfully. Applying the overall mass transport equation, $Cl^-$ ion and $SO_4{^{2-}}$ ion transport across anion-exchange membranes is evaluated. $SO_4{^{2-}}$ ion transport number is decreased due to the decrease of electro-migration of $SO_4{^{2-}}$ ions across the anion-exchange membranes. $SO_4{^{2-}}$ ion concentration in desalting cells becomes higher than that in concentration cells and $SO_4{^{2-}}$ ion diffusion is accelerated across the anion-exchange membranes from desalting cells toward concentrating cells.

Separation of Chromium(VI) Ion in Industrial Waste Water throunh Liquid Surfactant Membrane (산업폐수중 유화액막에 의한 크롬(VI)의 분리)

  • 초민승;강안수;우인성;이영순
    • Journal of the Korean Society of Safety
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    • v.4 no.1
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    • pp.15-24
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    • 1989
  • The transport of Chromium(Vl) ion from waste water throughl the liquid surfactant membrane containing tri-n-octylamine as a carrier, was analyzed by a slab model and was investigated through experiments. For the experiment of membrane stability, concentrations of surfactant and liquid parafnn oil were analyzed. Extraction euperiments were carried out to observe the effect of system variables, such as stirring speed, concentration of carrier, and NaOH in internal aqueous phase, and concentrations of H$_2$SO$_4$and initial chromium(VI) ion in external aqueous phase at $25^{\circ}C$. It is concluded that the most stable formation of liquid membrane emulsion was obtained when surfactant concentration is above 3 wt. % and liquid parafnn oil concentration is 50 vol. %. The transport of chromium(VI) ion in bacth extractor increased with increasing carrier concentration, the volume ratio of emulsion to external aqueous phases, and initial concentration of chromium(VI) ion under the optimum stirring speed of chromium(VI) ion below 2 ppm. The theoretical equation on the transport of chromium(Vl) ion agreed well with the experimental results.

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Numerical analysis of particle transport in low-pressure, low-temperature plasma environment

  • Kim, Heon Chang
    • Particle and aerosol research
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    • v.5 no.3
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    • pp.123-131
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    • 2009
  • This paper presents simulation results of particle transport in low-pressure, low-temperature plasma environment. The size dependent transport of particles in the plasma is investigated with a two-dimensional simulation tool developed in-house for plasma chamber analysis and design. The plasma model consists of the first two and three moments of the Boltzmann equation for ion and electron fluids respectively, coupled to Poisson's equation for the self-consistent electric field. The particle transport model takes into account all important factors, such as gravitational, electrostatic, ion drag, neutral drag and Brownian forces, affecting the motion of particles in the plasma environment. The particle transport model coupled with both neutral fluid and plasma models is simulated through a Lagrangian approach tracking the individual trajectory of each particle by taking a force balance on the particle. The size dependant trap locations of particles ranging from a few nm to a few ${\mu}m$ are identified in both electropositive and electronegative plasmas. The simulation results show that particles are trapped at locations where the forces acting on them balance. While fine particles tend to be trapped in the bulk, large particles accumulate near bottom sheath boundaries and around material interfaces, such as wafer and electrode edges where a sudden change in electric field occurs. Overall, small particles form a "dome" shape around the center of the plasma reactor and are also trapped in a "ring" near the radial sheath boundaries, while larger particles accumulate only in the "ring". These simulation results are qualitatively in good agreement with experimental observation.

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Coupled diffusion of multi-component chemicals in non-saturated concrete

  • Damrongwiriyanupap, Nattapong;Li, Linyuan;Xi, Yunping
    • Computers and Concrete
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    • v.11 no.3
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    • pp.201-222
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    • 2013
  • A comprehensive simulation model for the transport process of fully coupled moisture and multi-species in non-saturated concrete structures is proposed. The governing equations of moisture and ion diffusion are formulated based on Fick's law and the Nernst-Planck equation, respectively. The governing equations are modified by explicitly including the coupling terms corresponding to the coupled mechanisms. The ionic interaction-induced electrostatic potential is described by electroneutrality condition. The model takes into account the two-way coupled effect of moisture diffusion and ion transport in concrete. The coupling parameters are evaluated based on the available experimental data and incorporated in the governing equations. Differing from previous researches, the material parameters related to moisture diffusion and ion transport in concrete are considered not to be constant numbers and characterized by the material models that account for the concrete mix design parameters and age of concrete. Then, the material models are included in the numerical analysis and the governing equations are solved by using finite element method. The numerical results obtained from the present model agree very well with available test data. Thus, the model can predict satisfactorily the ingress of deicing salts into non-saturated concrete.

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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    • v.43 no.1
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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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The Ion Transport Phenomena through the Liquid Membrane with Macrocylic Compound (II). Transport of $H^+$Ion through Organic Liquid Membranes Containing Dibenzo-18-crown-6 and Dicyclohexyl-18-crown-6 as Carrier (마크로고리 화합물을 운반체로 하는 액체막을 통한 이온의 운반에 관한 연구 (제2보). 유기액체막 운반체를 통한 수소이온의 운반)

  • Yoon, Chang-Ju;Lee, Shim-Sung;Kim, Young-Hee;Kim, Si-Joong
    • Journal of the Korean Chemical Society
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    • v.28 no.3
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    • pp.170-175
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    • 1984
  • The transport rates of $H^+$ ion by DBC and DCC as carrier molecules through organic liquid membranes were determined at 25$^{\circ}$C. The transport rates depend highly on the dielectric constants of membrane solvents and these results were discussed in terms of Born's potential energy barrier methods. The sizes of anions also affect the transport rates and these results were well explained theoreticlly by extended Born's equation.

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Electrical Quadruple Layer under the AC Electric Field

  • Suh, Yong-Kweon
    • 한국전산유체공학회:학술대회논문집
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    • 2006.10a
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    • pp.167-176
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    • 2006
  • In this paper we show that solutions of the nonlinear Nernst-Planck equation possesses the quadruple-layer structure near the interface when the electrolyte receives a high frequency forcing such as a high-frequency alternating current. Very near to the interface wall, the well-known, classical Stern layer exists. Near to the Stern layer we have the secondly thin layer (to be called inner layer in this paper) where the ion concentrations behave under the same frequency as the external forcing. However, in this layer, the positive and negative ion concentrations develop with the time phase 180-degree different from each other. Next to this second layer, we have the third layer (called middle layer) in which two ion concentrations change with the time period double the forcing, and both concentrations behave in the same time phase. In the outermost layer, i.e. the forth layer, (called outer layer) the ion concentrations show the same-phase development as the third one but decaying very slowly in time. Our assertion is mostly based on the 1-D numerical simulation for the Nernst-Planck equation under a high frequency AC field assuming that the quadruple layer is very thin compared with the length scale representative of the bulk region.

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1-Dimensional Simulation of the Corona Discharge using Fluid Method (유체법을 이용한 코로나 방전의 1차원 수치해석)

  • 이용신;심재학;고광철;강형부
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 1997.04a
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    • pp.172-176
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    • 1997
  • It is likely that the corona discharge appears due to the motion and the multiplication of electron and ion under the nonuniform electric field. Because the motion and the multiplication of electron and ion are the function of electric field, for the simulation of the corona discharge, we have to calculate the electric field, before the calculation of the motion and the multiplication of electron and ion. In this paper, the electric field is calculated on the assumption that the gap between a hyperboloidal needle and a plane is 1-dimension, and the motion and the multiplication of electron and ion are determined by Flux-Corrected Transport method. For this purpose, we solve the electron and ion continuity equation together with Poisson equation. We calculated the current density and the electron and ion density distributions between electrodes as well as electric field distortion due to the space charge assuming that the discharge channel radius is 100${\mu}{\textrm}{m}$. In this simulation, it is found that the current density has one peak as observed by experiment, and electric field distortion is important to the formation and the stability of the corona discharge.

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Tansport Rate of Chromium ion from Waste Water through the Liquid Surfactant Membrane Containing Carrier (운반체 함침 유화액막에 의한 폐수중 크롬(VI)의 이동속도)

  • Woo, In-Sung;Kim, Kyoung-Ho;Lee, Sang-Jin;Kang, An-Soo;Choi, Sei-Young
    • Elastomers and Composites
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    • v.23 no.1
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    • pp.11-17
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    • 1988
  • The transport of chromium(VI) ion from waste water through the liquid surfactant membrane containing tri-n-octylamine as a carrier, was analyzed by a slab model and was investigated through experiments. For the experiment of membrane stability, concentrations of surfactant and liquid paraffin oil were analyzed. Extraction experiments were carried out to observe the effect of system variables, such as concentrations of carrier, and initial chromium(VI) ion in external aqueous phase at $25^{\circ}C$. It is concluded that the most stable formation of liquid membrane emulsion was obtained when surfactant concentration is above 3 wt.% and liquid paraffin oil concentration is 50 vol.%. The theoretical equation on the transport of chromium(VI) ion agreed well with the experimental results.

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Transport of Water through Polymer Membrane in Proton Exchange Membrane Fuel Cells (고분자전해질 연료전지에서 고분자막을 통한 물의 이동)

  • Lee, Daewoong;Hwang, Byungchan;Lim, Daehyun;Chung, Hoi-Bum;You, Seung-Eul;Ku, Young-Mo;Park, Kwonpil
    • Korean Chemical Engineering Research
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    • v.57 no.3
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    • pp.338-343
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    • 2019
  • The water transport and water content of the electrolyte membrane greatly affect the performance of the membrane in PEMFC(Proton Exchange Membrane Fuel Cell). In this study, the parameters (electroosmotic coefficient, water diffusion coefficient) of polymer membranes for water transport were measured by a simple method, and water flux and ion conductivity were simulated by using a model equation. One dimensional steady state model equation was constructed by using only the electro-osmosis and diffusion as the driving force of water transport. The governing equations were simulated with MATLAB. The electro-osmotic coefficient of $144{\mu}m$ thick polymer membranes was measured in hydrogen pumping cell, the value was 1.11. The water diffusion coefficient was expressed as a function of relative humidity and the activation energy for water diffusion was $2,889kJ/mol{\cdot}K$. The water flux and ion conductivity results simulated by applying these coefficients showed good agreement with the experimental data.