• Computers and Concrete
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• v.10 no.1
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• pp.79-93
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• 2012

This paper estimates theoretically the diffusion-reaction behaviour of sulfate ion in concrete caused by environmental sulfate attack. Based on Fick's second law and chemical reaction kinetics, a nonlinear and nonsteady diffusion-reaction equation of sulfate ion in concrete, in which the variable diffusion coefficient and the chemical reactions depleting sulfate ion concentration in concrete are considered, is proposed. The finite difference method is utilized to solve the diffusion-reaction equation of sulfate ion in concrete, and then it is used to simulate the diffusion-reaction process and the concentration distribution of sulfate ion in concrete. Afterwards, the experiments for measuring the sulfate ion concentration in concrete are carried out by using EDTA method to verify the proposal model, and results show that the proposed model is basically in agreement with the experimental results. Finally, Numerical example has been completed to investigate the diffusion-reaction behavior of sulfate ion in the concrete plate specimen immersed into sulfate solution.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.249-281
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• 2020

A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.

• The Korean Journal of Ceramics
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• v.4 no.3
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• pp.235-239
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• 1998

Ultrafine $SnO_2$ powder was prepared by the diffusion mixing gas-phase reaction of $SnCl_4$(g) and water vapor. The effects of reaction variables, such as the chloride partial pressure, the reaction temperature, and the residence time is the reactor, on the powder size were examined systematically. Calculated concentration and distribution of chemical species, using the Burke-Schumann diffusion mixing model, were compared with the experimetal results. The effects of the reaction variables on the powder size were also discussed qualitatively.

• Bulletin of the Korean Chemical Society
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• v.21 no.12
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• pp.1213-1216
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• 2000

Localized structures with fronts connecting a Turing patterns and Hopf oscillations are found in discrete reaction-diffusion system. The Chorite-Iodide-Malonic Acid (CIMA) reaction model is used for a reaction scheme. Localized structures in discrete reaction-diffusion system have more diverse and interesting features than ones in continuous system. Various localized structures can be obtained when a single perturbation is applied with variation of coupling strength of two intermediates. Roles of perturbations are not so simple that perturbations are sources of both Turing patterns and Hopf oscillating domains, and spatial distribution of them is determined by strength of a perturbation applied initially.

• Nuclear Engineering and Technology
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• v.53 no.3
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• pp.833-841
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• 2021

During the postulated severe accident of nuclear reactor, eutectic reaction leads to low-temperature melting of fuel cladding and early failure of core structure. In order to model eutectic melting with the moving particle semi-implicit (MPS) method, the eutectic reaction model is developed to simulate the eutectic reaction phenomenon. The coupling of mass diffusion and phase diagram is applied to calculate the eutectic reaction with the uniform temperature. A heat transfer formula is proposed based on the phase diagram to handle the heat release or absorption during the process of eutectic reaction, and it can combine with mass diffusion and phase diagram to describe the eutectic reaction with temperature variation. The heat transfer formula is verified by the one-dimensional melting simulations and the predicted interface position agrees well with the theoretical solution. In order to verify the eutectic reaction models, the eutectic reaction of uranium and iron in two semi-infinite domains is simulated, and the profile of solid thickness decrease over time follows the parabolic law. The modified MPS method is applied to calculate Transient Reactor Test Facility (TREAT) experiment, the penetration rate in the simulations are agreeable with the experiment results. In addition, a hypothetical case based on the TREAT experiment is also conducted to validate the eutectic reaction with temperature variation, the results present continuity with the simulations of TREAT experiment. Thus the improved method is proved to be capable of simulating the eutectic reaction in the severe accident.

• International Journal of Concrete Structures and Materials
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• v.6 no.3
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• pp.155-163
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• 2012

In order to predict the neutralization of concrete which is the reaction of carbonation dioxide from the outside and cement hydration product, such as calcium hydroxide and C-S-H, it was studied the numerical analysis method considering change of the pore structure and relative humidity during the neutralization reaction. Diffusion-reaction neutralization model was developed to predict the neutralization depth of concrete with coating finishing material. In order to build numerical analysis models considering outdoor environment and finishing materials, the adaption of proposed model was shown the results of existing outdoor exposure test results and accelerated carbonation test.

• Computers and Concrete
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• v.15 no.5
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• pp.847-864
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• 2015

In this paper, a reaction-diffusion model of carbonation process in self-compacting concrete (SCC) was realized with a consideration of multi-field couplings. Various effects from environmental conditions, e.g. ambient temperature, relative humidity, carbonation reaction, were incorporated into a numerical simulation proposed by ANSYS. In addition, the carbonation process of SCC was experimentally investigated and compared with a conventionally vibrated concrete (CVC). It is found that SCC has a higher carbonation resistance than CVC with a comparable compressive strength. The numerical solution analysis agrees well with the test results, indicating that the proposed model is appropriate to calculate and predict the carbonation process in SCC. The parameters sensitivity analysis also shows that the carbon dioxide diffusion coefficient and moisture field are essentially crucial to the carbonation process in SCC.

• Journal of the Korean Society of Safety
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• v.25 no.3
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• pp.22-27
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• 2010

A prediction performance of Fire Dynamics Simulator(FDS) developed by NIST for the diffusion flame structure was validated with experimental results of a laminar slot jet diffusion flame. Two mixture fraction combustion models and two finite chemistry combustion models were used in the FDS simulation for the validation of the jet diffusion flame structure. In order to enhance the prediction performance of flame structure, DNS and radiation model was applied to the simulation. The reaction rates of the finite chemistry combustion models were appropriately adjusted to the diffusion flame. The mixture fraction combustion model predicted the diffusion flame structure reasonably. A 1-step finite chemistry combustion model cannot predict the flame structure well, but the simulation results of a 2-step model were in good agreement with those of experiment except $CO_2$ concentration. It was identified that the 2-step model can be used in the investigation of flame suppression limit with further adjustment of reaction rates

• Nuclear Engineering and Technology
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• v.49 no.5
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• pp.1019-1030
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• 2017

Diffusion is a crucial mechanism that regulates the migration of radioactive nuclides. In this study, an innovative numerical method was developed to simultaneously calculate the diffusion coefficient of both parent and, afterward, series daughter nuclides in a sequentially reactive through-diffusion model. Two constructed scenarios, a serial reaction (RN_1 ${\rightarrow}$ RN_2 ${\rightarrow}$ RN_3) and a parallel reaction (RN_1 ${\rightarrow}$ RN_2A + RN_2B), were proposed and calculated for verification. First, the accuracy of the proposed three-member reaction equations was validated using several default numerical experiments. Second, by applying the validated numerical experimental concentration variation data, the as-determined diffusion coefficient of the product nuclide was observed to be identical to the default data. The results demonstrate the validity of the proposed method. The significance of the proposed numerical method will be particularly powerful in determining the diffusion coefficients of systems with extremely thin specimens, long periods of diffusion time, and parent nuclides with fast decay constants.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.389-399
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• 1995

We consider the reaction-diffusion system of two-component model in one-dimensional space described by $$ (1) u_s = d_1 u_{xx} + f(u, \upsilon) \upsilon_t = d_2\upsilon_{xx} + \gammag(u, \upsilon) $$ where $d_1$ and $d_2$ are the diffusion rates of u and $\upsilon$, and $\gamma$ is the ration of reaction rates. It is interesting the case of that there are differences in the diffusion and reaction rates of u and $\upsilon$.