• Title/Summary/Keyword: reaction-diffusion equations

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A Study on the Hydriding Reaction Characteristics and the Change of the Hydriding Reaction Rates of MmNi4.5Al0.5 during Temperature-Induced Cycling (MmNi4.5Al0.5의 수소화 반응특성 및 Temperature-Induced Cycling에 따른 수소화 반응속도의 변화에 관한 연구)

  • Kim, Soo-Ryoung;Lee, Jai-Young
    • Transactions of the Korean hydrogen and new energy society
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    • v.1 no.1
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    • pp.1-8
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    • 1989
  • The hydriding kinetic mechanism and the change of the hydriding reaction rate of $MmNi_{4.5}Al_{0.5}$ during the thermally induced hydrogen absorption-desorption cycling are investigated. Comparison of the reaction rate data which are obtained by the pressure sweep method with the theoretical rate equations suggests that the hydriding rate controlling step has changed from the dissociative chemisorption of hydrogen molecules at the surface to the hydrogen diffusion through the hydride phase with the increase of the hydriding fraction. These hydriding kinetic mechanism is not changed during the cycling. However, the intrinsic hydriding reaction rate of $MmNi_{4.5}Al_{0.5}$ after 5500 cycles increases significantly comparing with the activated one. It is suggested that the change of the hydriding kinetic behavior due to intrinsic degradation of $MmNi_{4.5}Al_{0.5}$ can be interpreted as follows ; the formation of nickel cluster at the surface of the sample and the host metal atom exchange in bulk by thermal cycling.

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An Introduction to Kinetic Monte Carlo Methods for Nano-scale Diffusion Process Modeling (나노 스케일 확산 공정 모사를 위한 동력학적 몬테칼로 소개)

  • Hwang, Chi-Ok;Seo, Ji-Hyun;Kwon, Oh-Seob;Kim, Ki-Dong;Won, Tae-Young
    • Journal of the Institute of Electronics Engineers of Korea SD
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    • v.41 no.6
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    • pp.25-31
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    • 2004
  • In this paper, we introduce kinetic Monte Carlo (kMC) methods for simulating diffusion process in nano-scale device fabrication. At first, we review kMC theory and backgrounds and give a simple point defect diffusion process modeling in thermal annealing after ion (electron) implantation into Si crystalline substrate to help understand kinetic Monte Carlo methods. kMC is a kind of Monte Carlo but can simulate time evolution of diffusion process through Poisson probabilistic process. In kMC diffusion process, instead of. solving differential reaction-diffusion equations via conventional finite difference or element methods, it is based on a series of chemical reaction (between atoms and/or defects) or diffusion events according to event rates of all possible events. Every event has its own event rate and time evolution of semiconductor diffusion process is directly simulated. Those event rates can be derived either directly from molecular dynamics (MD) or first-principles (ab-initio) calculations, or from experimental data.

A Study on the Hydriding and Dehydriding Kinetics of a Mechanically-Alloyed Mg-25wt.%Ni Mixture (기계적 합금처리된 Mg-25wt.%Ni 혼합물의 수소화물 형성 및 분해에 대한 반응속도론적 연구)

  • Song, Myoung Youp
    • Transactions of the Korean hydrogen and new energy society
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    • v.10 no.1
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    • pp.9-17
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    • 1999
  • The hydriding and dehydriding kinetics were studied for a Mg-25wt.%Ni mixture which has the most excellent hydrogen-storage characteristics among many mechanically-alloyed mixtures. The hydriding and dehydriding rates were measured and the rate-controlling steps were determined by comparing the hydriding and dehydriding rates with the theoretical rate equations. The rate-controlling step in the hydriding reaction is the Knudsen flow and the ordinary gaseous diffusion of hydrogen molecules through interparticle channels, cracks, etc. in the various ranges of weight percentage of absorbed hydrogen $H_a$ below $H_a$=4.0. In the $H_a$ range 4.0 < $H_a{\leq}4.25$, the diffusion of hydrogen atoms through the growing hydride layer is considered the rate-controlling step. The rate-controlling step in the dehydriding reaction is the Knudsen flow and the ordinary gaseous diffusion of hydrogen molecules for all the ranges of weight percentage of desorbed hydrogen $H_d$.

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Mathematical Model for the Removal of SO2 by the γ-Alumina Impregnated with CuO (γ-Alumina에 담지된 산화구리에 의한 SO2의 제거에 관한 수치모사)

  • Jeon, Bup Ju;Hong, In Kwon;Park, Kyung Ai;Jung, Il Hyun
    • Applied Chemistry for Engineering
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    • v.5 no.3
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    • pp.385-394
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    • 1994
  • Numerical solutions were obtained to the model equations for various of the parameters characterizing the pore structure, effective internal diffusion, and the chemical reaction constant. The conversion was decreased with the cause of pore closure at the surface of reacting particles, reduction of porosity, surface area of reaction and effective diffusion coefficient in the solid with the progress of reaction. Total conversion was strongly dependent on the local conversion at surface. According to the decreasing of impregnated concentration of the copper oxide and the increase of the flue gases concentration, total conversion was increased. The conversion was affected by gas flow rate and pore size distribution in the reacting solid.

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Cure Characteristics of Naphthalene Type Epoxy Resins for SEMC (Sheet Epoxy Molding Compound) for WLP (Wafer Level Package) Application (WLP(Wafer Level Package)적용을 위한 SEMC(Sheet Epoxy Molding Compounds)용 Naphthalene Type Epoxy 수지의 경화특성연구)

  • Kim, Whan Gun
    • Journal of the Semiconductor & Display Technology
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    • v.19 no.1
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    • pp.29-35
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    • 2020
  • The cure characteristics of three kinds of naphthalene type epoxy resins(NET-OH, NET-MA, NET-Epoxy) with a 2-methyl imidazole(2MI) catalyst were investigated for preparing sheet epoxy molding compound(SEMC) for wafer level package(WLP) applications, comparing with diglycidyl ether of bisphenol-A(DGEBA) and 1,6-naphthalenediol diglycidyl ether(NE-16) epoxy resin. The cure kinetics of these systems were analyzed by differential scanning calorimetry with an isothermal approach, and the kinetic parameters of all systems were reported in generalized kinetic equations with diffusion effects. The NET-OH epoxy resin represented an n-th order cure mechanism as like NE-16 and DGEBA epoxy resins, however, the NET-MA and NET-Epoxy resins showed an autocatalytic cure mechanism. The NET-OH and NET-Epoxy resins showed higher cure conversion rates than DGEBA and NE-16 epoxy resins, however, the lowest cure conversion rates can be seen in the NET-MA epoxy resin. Although the NETEpoxy and NET-MA epoxy resins represented higher cure reaction conversions comparing with DGEBA and NE-16 resins, the NET-OH showed the lowest cure reaction conversions. It can be figured out by kinetic parameter analysis that the lowest cure conversion rates of the NET-MA epoxy resin are caused by lower collision frequency factor, and the lowest cure reaction conversions of the NET-OH are due to the earlier network structures formation according to lowest critical cure conversion.

Predictions on the Flame Structure and Soot Distribution in the Coflowing Laminar Diffusion Flames (동층류 축대칭 확산화염내의 화염구조 및 매연입자 분포의 예측)

  • 이정기;김상수
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.8
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    • pp.1583-1594
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    • 1992
  • A numerical calculation on the flame structure and soot particle distribution in a coannular laminar diffusion flame was performed. Flame analysis model utilized basically flame sheet concepts, Shvab-Zel'dovich assumption, and one step overall irreversible reaction. It was also considered the variation of thermodynamics and transport properties, and the stagnation enthalpy was used for solving temperature field. Radiation was taken into account, since it has been found to be important in determining the flame temperature in sooty flames. For soot particle analysis, we adopted the coagulation, suface condensation, and the oxidation model in addition to tesner's two-step formation model. Equations for primary soot particle excluding the agglomeration process were solved. Based on the results, the regions of soot generation, growth, and oxidation in the flame have been observed and radiation strongly influenced flame temperature and soot distribution.

Study of Kinetics for Removal H2S by Natural Manganese ore Sorbent (황화수소 제거를 위한 천연망간광석 탈황제의 반응 속도 연구)

  • Yoon, Yeo Il;Kim, Myung Wook;Kim, Sung Hyun
    • Clean Technology
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    • v.7 no.3
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    • pp.187-194
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    • 2001
  • The desulfurization process which belongs to the gas refining part is the unit process that eliminates $H_2S$ and COS in the coal gas formed by the coal gasification part in the integrated gasification combined cycle(IGCC). In this study, natural manganese ores were selected as the raw material of the desulfurization sorbent due to economical efficiency. Initial rates for the reactions between $H_2S$ and desulfurization sorbent using natural manganese ores were determined in a temperature range of $400{\sim}800^{\circ}C$ using a thermobalance reactor. All reactions were first order with respect to $H_2S$ and were in accord with the Arrhenius equations. When sulfidation reaction was controlled by diffusion, the temperature dependence of the effective diffusivity was given by the Arrhenius equation. Activation energies and frequency factors were obtained from the product layer diffusion coefficient of various sorbents by plotting as Arrhenius equation form.

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Cure Kinetics of Self-Extinguishing Epoxy Resin Systems with Charge Transfer Complex Type Latent Catalyst for Semiconductor Encapsulation (전하전이착체형 잠재성 촉매를 사용한 반도체 성형용 자소성 에폭시 수지 시스템의 경화 반응속도 연구)

  • Kim, Whan Gun
    • Journal of the Semiconductor & Display Technology
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    • v.13 no.4
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    • pp.27-32
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    • 2014
  • The cure properties of self-extinguishing epoxy resin systems with different charge transfer type latent catalysts were investigated, which are composed of YX4000H as a biphenyl epoxy resin, MEH-7800SS as a hardener, and charge transfer type latent catalysts. We designed and used five kinds of charge transfer type latent catalyst and compared to epoxy resin systems with Triphenylphosphine-Benzoquinone(TPP-BQ) as reference system. The cure kinetics of these systems were analyzed by differential scanning calorimetry with an isothermal approach, the kinetic parameters of all systems were reported in generalized kinetic equations with diffusion effects. The epoxy resin systems with Triphenylphosphine-Quinhydrone(TPP-QH), Triphenylphosphine-Benzanthrone(TPP-BT) and Triphenylphosphine-Anthrone(TPP-AT) as a charge transfer type latent catalyst showed a cure conversion rate of equal or higher rate than those with TPP-BQ. These systems with TPP-QH and Triphenylphosphine-Tetracyanoethylene(TPP-TCE) showed a critical cure reaction conversion of equal or higher conversion than those with TPP-BQ. The increases of cure conversion rates could be explained by the decrease of the activation energy of these epoxy resin systems. It can be considered that the increases of critical cure reaction conversion would be dependent on the crystallinity of the biphenyl epoxy resin systems.

Numerical Simulation of Laminar Reacting Flows Using Unstructured Finite Volume Method With Adaptive Refinement

  • Kang, Sung-Mo;Kim, Hoo-Joong;Kim, Yong-Mo
    • Journal of the Korean Society of Combustion
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    • v.6 no.2
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    • pp.15-22
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    • 2001
  • A pressure-based, unstructured finite volume method has been applied to couple the chemical kinetics and fluid dynamics and to capture effectively and accurately the steep gradient flame field. The pressure-velocity coupling is handled by two methodologies including the pressure-correction algorithm and the projection scheme. A stiff, operator-split projection scheme for the detailed nonequilibrium chemistry has been employed to treat the stiff reaction source terms. The conservative form of the governing equations are integrated over a cell-centered control volume with collocated storage for all transport variables. Computations using detailed chemistry and variable transport properties were performed for two laminar reacting flows: a counterflow hydrogen-air diffusion flame and a lifted methane-air triple flame. Numerical results favorably agree with measurements in terms of the detailed flame structure.

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A SUFFICIENT CONDITION FOR THE UNIQUENESS OF POSITIVE STEADY STATE TO A REACTION DIFFUSION SYSTEM

  • Kang, Joon-Hyuk;Oh, Yun-Myung
    • Journal of the Korean Mathematical Society
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    • v.39 no.3
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    • pp.377-385
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    • 2002
  • In this paper, we concentrate on the uniquencess of the positive solution for the general elliptic system $\Delta$u+u($g_1$(u)-$g_2$(v))=0 $\Delta$u+u($h_1$(u)-$h_2$(v))=0 in$R_{+}$ $\times$ $\Omega$, $u\mid\partial\Omega = u\mid\partial\Omega = 0$. This system is the general model for the steady state of a competitive interacting system. The techniques used in this paper are upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.