• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2006년도 추계 학술대회논문집
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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.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2004년도 추계 학술대회논문집
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• pp.161-164
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• 2004

A finite volume numerical model is developed for simulating non-equilibrium electroosmotic flow in micro- and nanochannels. The Guoy-Chapman model is adopted to compute the flow and electric potential. The Nernst-Planck equation is employed to trace unsteady transports of ionic species, i.e., time-dependent net charge density. A new set of boundary conditions based on surface charge density are designed rather than using the conventionally-employed zeta potential. A few issues for an efficient computation of electroosmotic flows are discussed. Representative computational examples are given to illustrate the robustness of the numerical model.

• Computers and Concrete
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• 제13권2호
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• pp.149-171
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• 2014

This study presents the mathematical model for predicting chloride penetration into saturated concrete under non-isothermal condition. The model considers not only diffusion mechanism but also migration process of chloride ions and other chemical species in concrete pore solution such as sodium, potassium, and hydroxyl ions. The coupled multi-ionic transport in concrete is described by the Nernst-Planck equation associated with electro-neutrality condition. The coupling parameter taken into account the effect of temperature on ion diffusion obtained from available test data is proposed and explicitly incorporated in the governing equations. The coupled transport equations are solved using the finite element method. The numerical results are validated with available experimental data and the comparison shows a good agreement.

• Membrane and Water Treatment
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• 제12권2호
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• pp.59-64
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• 2021

The rejection of sodium chloride (NaCl) and calcium chloride (CaCl2) single salt solutions were carried out for commercial nanofiltration NFDK membrane. Results showed that the NFDK membrane had a negative surface charge and had a higher observed rejection of 93.65% for calcium (Ca2+) ion and 78.27% for sodium (Na+) ions. Prediction of rejection for aqueous solutions of both salts was made using Donnan Steric Pore Model based on Extended Nernst-Planck Equation in addition to concentration polarization film theory. A MATLAB program was developed to execute the model calculations. Absolute Average Relative Error (% AARE) was found below 5% for real rejection of the NFDK membrane. This research could be used successfully to assess the membrane characterization parameter using a proposed procedure which can reduce the number of experiments.

• Journal of Electrical Engineering and Technology
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• 제10권2호
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• pp.647-652
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• 2015

A fully coupled finite element analysis (FEA) technique was developed for analyzing the discharge phenomena and dielectric liquid flow while considering surface charge density effects in dielectric flow guidance. In addition, the simulated speed of surface charge propagation was compared and verified with the experimental results shown in the literature. Recently, electrohydrodynamics (EHD) techniques have been widely applied to enhance the cooling performance of electromagnetic systems by utilizing gaseous or liquid media. The main advantage of EHD techniques is the non-contact and low-noise nature of smart control using an electric field. In some cases, flow can be achieved using only a main electric field source. The driving sources in EHD flow are ionization in the breakdown region and ionic dissociation in the sub-breakdown region. Dielectric guidance can be used to enhance the speed of discharge propagation and fluidic flow along the direction of the electric field. To analyze this EHD phenomenon, in this study, the fully coupled FEA was composed of Poisson's equation for an electric field, charge continuity equations in the form of the Nernst-Planck equation for ions, and the Navier-Stokes equation for an incompressible fluidic flow. To develop a generalized numerical technique for various EHD phenomena that considers fluidic flow effects including dielectric flow guidance, we examined the surface charge accumulation on a dielectric surface and ionization, dissociation, and recombination effects.

• Computers and Concrete
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• 제11권3호
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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.

• 전기화학회지
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• 제14권4호
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• pp.231-238
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• 2011

수치해석을 이용하여 아연공기전지의 전기화학적 성능을 예측하였다. KOH 수계전해질 내부의 이동현상을 예측하기 위하여 Nernst-Planck식을 사용하였고, 전극 표면의 활성화손실을 모사하기 위해 아연극(음극)에는 Butler-Volmer식을, 공기극(양극)에는 Tafel식을 적용하였다. 정상상태해석을 통하여 아연/공기전지의 I-V곡선을 도출하였으며, 실험결과와의 I-V곡선 비교/분석을 통하여 수치 해석 모델의 타당성을 검증하였다. 전지반응 진행에 따른 전해질 내부의 이온 이동 및 분포 특성을 조사하기 위해 과도상태해석을 수행하였으며, 전극주변에서의 ${Zn(OH)_4}^{-2}$, $OH^-$, $K^+$ 이온들의 농도변화를 확인할 수 있었다. 또한, 다양한 전지전압조건 하에서 반응시간에 따라 아연극 표면에서의 ${ZnOH_4}^{2-}$의 농도 변화를 해석한 결과, 반응진행시 아연극 표면에서 ${ZnOH_4}^{2-}$의 농도가 최고성능을 나타내는 운전전압 0.63 V에서 약 1초 만에 포화농도에 도달하였으며, 일반적인 운전조건인 1.04 V에서는 약 13초 만에 포화농도에 접근하는 것으로 나타났다.

• Membrane and Water Treatment
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• 제2권3호
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• pp.187-205
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• 2011

The electric transport of the mixture of hydrochloric and phosphoric acids through strong base (Neosepta ACM) and weak base (Selemion AAV) anion-exchange membranes was investigated. The instantaneous efficiency of HCl removal from the cathode solution, $CE_{Cl}$, with and without $H_3PO_4$ was determined. It was found that $CE_{Cl}$ was 0.8-0.9 if the number of moles of elementary charge passed through the system, $n_F$, did not exceed ca. 80% of the initial number of HCl moles in the cathode solution, $n_{Cl,ca,0}$. The retention efficiency of $H_3PO_4$ in that range was close to one. The transport of acid mixtures was satisfactorily described by a model based on the extended Nernst-Planck and Donnan equations for $n_F$ not exceeding $n_{Cl,ca,0}$. Among the tested model parameters, most important were: concentration of fixed charges, the porosity-tortuosity coefficient, and the partition coefficient of an undissociated form of $H_3PO_4$. For the both membranes, the obtained optimal values of fixed charge concentration, $\bar{c}_m$, were up to 40% lower than the literature values of $\bar{c}_m$ obtained from the equilibrium measurements. Regarding the $H_3PO_4$ equilibria, it was sufficient to consider $H_3PO_4$ as a monoprotic acid.

• Nuclear Engineering and Technology
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• 제47권7호
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• pp.859-866
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• 2015

The aim of this work is to investigate the transport mechanism of radioactive nuclides through the reverse osmosis (RO) membrane and to estimate its effectiveness for nuclide separation from radioactive liquid waste. An analytical model is developed to simulate the RO separation, and a series of experiments are set up to confirm its estimated separation behavior. The model is based on the extended Nernst-Plank equation, which handles the convective flux, diffusive flux, and electromigration flux under electroneutrality and zero electric current conditions. The distribution coefficient which arises due to ion interactions with the membrane material and the electric potential jump at the membrane interface are included as boundary conditions in solving the equation. A high Peclet approximation is adopted to simplify the calculation, but the effect of concentration polarization is included for a more accurate prediction of separation. Cobalt and cesium are specifically selected for the experiments in order to check the separation mechanism from liquid waste composed of various radioactive nuclides and nonradioactive substances, and the results are compared with the estimated cobalt and cesium rejections of the RO membrane using the model. Experimental and calculated results are shown to be in excellent agreement. The proposed model will be very useful for the prediction of separation behavior of various radioactive nuclides by the RO membrane.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 추계학술대회
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• pp.1528-1533
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• 2004

A numerical investigation is made of transient evolutionary prcocess of electroosmotic flow in a two-dimensional microchannel connected to a reservoir. The channel height is very small so that two electric double layers forming on the charged surfaces are overlapped. Transient transports of ions in the electrolyte solution are computed by integrating the Nernst-Planck equation together with the Poisson equation for electric potential. The numerical results illustrate that there are two distinct transient phases. The physical mechanisms and relevant time scales for the transient evolution are described.