• 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.

• 한국전산유체공학회:학술대회논문집
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• 2004.10a
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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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• v.13 no.2
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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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• v.12 no.2
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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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• v.10 no.2
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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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• 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.

• Journal of the Korean Electrochemical Society
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• v.14 no.4
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• pp.231-238
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• 2011

In this work, the numerical analysis for the zincate behavior at a zinc electrode with an electrolyte flow was carried out for a ZAFC. The Nernst-Planck equation with a boundary condition of Butler-Volmer type was adopted to describe electrochemical effects of mass transfer, migration, kinetics of electrode. The Navier-Stokes equation, coupling to the Nernst-Planck equation, is also applied to describe the internal electrolyte flow fields. The validity of the numerical model is proved through the comparative analysis between numerical and experimental results. The concentration of zincate and the current density were also investigated at a zinc anode according to various electrolyte velocities. We have found the concentration of zincate decreased and the current density increased with an increase in the electrolyte velocity.

• Membrane and Water Treatment
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• v.2 no.3
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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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• v.47 no.7
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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.

• Proceedings of the KSME Conference
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• 2004.11a
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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.