• The Journal of Engineering Research
• /
• v.3 no.1
• /
• pp.223-233
• /
• 1998

The kinetic and mechanism of the hydrothermal reaction between lime and quartz used solid state reaction equations have been investigated. Hydrothermal reaction on the starting materials was carried out in an autoclave that quartz mixed with calcium hydroxide in CaO/$SiO_2$ ratio of 0.8-1.0 for 0.5-8 hour at saturated steam pressure of $180-200^{\circ}C$. The rate of reaction was given from the ratio of uncombined lime and quartz content to the total lime and quartz content. The rate of reaction was obtained the results by the Jander's equation $[1-(1-\alpha)^{1/3}]^N=Kt$. The reaction of lime is controlled mainly by the dissolution such as N=1, and the reaction of quartz is controlled mostly by the diffusion such as $N\risingdotseq2$. The rate of hydrothermal reaction in the calcium silicate hydrates system is suggested to be determined generally by the mass transfer through the product laver formed around the reactant particles. The rate equation for whole hydrothermal reaction is shown that it is converted into the rate determining step by the diffusion from the boundary reaction such as approximately $N=1-2$.

• Korean Journal of Food Science and Technology
• /
• v.27 no.3
• /
• pp.387-393
• /
• 1995

Diffusion coefficients of moisture and solid, reaction rate constants of carotene destruction, and the fitness of drying models for moisture transfer were determined to study the characteristics of mass transfer during osmotic dehydration. Moisture loss and solid gain were increased with increase of temperature and concentration; temperature had higher osmotic effect than concentration. Diffusion coefficient showed similar trend with osmotic effect. Diffusion coefficients of solids were larger than those of moisture because the movement of solid was faster than that of moisture at the high temperature. Reaction rate constants were affected to the greater extent by concentration changes than by temperature changes. Arrhenius equation was applied to determine the effect of temperature on diffusion coefficients and reaction rate constants. Moisture diffusion required high activation energy in $20^{\circ}Brix$, while relatively low in $60^{\circ}Brix$. To predict the diffusion coefficients and reaction rate constants, a model was established by using the optimum functions of temperature and concentration. The model had high $R^2$ value when applied to diffusion coefficients, but low when applied to reaction rate constants. Quadratic drying model was most fittable to express moisture transfer during drying. In conclusion, moisture content of carrots could be predictable during the osmotic dehydration process, and thereby mass transfer characteristics could be determined by predicted moisture content and diffusion coefficient.

• Journal of the Korean Chemical Society
• /
• v.52 no.3
• /
• pp.217-222
• /
• 2008

We investigate the kinetics of diffusion-influenced catalytic reactions occurring in small reaction volume. From a simple exact model study, we find that the reaction rate coefficient decreases with the size of reaction volume. The explicit expression for the average reaction rate constant is presented, which can be regarded as a generalization of well-known Collins-Kimball rate constant into the reactions occurring in a small reaction volume. It turns out that the traditional diffusion influenced reaction dynamics is followed by a single exponential relaxation phase with a rate constant dependent on the reaction volume for the catalytic reactions occurring in small reaction volumes.

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

• Journal of the Korean Electrochemical Society
• /
• v.5 no.1
• /
• pp.7-12
• /
• 2002

The gas diffusion electrodes as oxygen cathodes f3r the brine electrolysis process were investigated. The gas diffusion electrode consists of a reaction layer, a gas diffusion layer, and a current distributor. The reaction layer was made from hydrophilic carbon black, hydrophobic carbon black, PTFE(polyterafluoroethylene), and Ag catalyst loaded by the silver mirror reaction or impregnation method. The gas diffusion layer was made from hydrophobic carbon black and PTFE, and Ni mesh was used as the current distributor in the reaction layer. The result that the gas diffusion electrode $(10wt\%\;Ag\;catalyst\;and\;20wt\%\;binder)$ manufactured by applying impregnation method to the carbon black f3r reaction layer showed the better performance was obtained from experiments. From the half-cell test, the measured overpotential of this oxygen cathode was about 700mV, And through the electrolysis experiment under the condition of $80^{\circ}C,\;32wt\%$ NaOH, and $300mA/cm^2$, the electrolysis voltage of this electrode was about 2.2 V, The gas diffusion electrodes manufactured in the present research were capable of continuous operations for three months.

• Journal of applied mathematics & informatics
• /
• v.34 no.5_6
• /
• pp.495-508
• /
• 2016

A singularly perturbed reaction-diffusion fourth-order ordinary differential equation(ODE) with discontinuous source term is considered. Due to the discontinuity, interior layers also exist. The considered problem is converted into a system of weakly coupled system of two second-order ODEs, one without parameter and another with parameter ε multiplying highest derivatives and suitable boundary conditions. In this paper a computational method for solving this system is presented. A zero-order asymptotic approximation expansion is applied in the second equation. Then, the resulting equation is solved by the numerical method which is constructed. This involves non-overlapping Schwarz method using Shishkin mesh. The computation shows quick convergence and results presented numerically support the theoretical results.

• Journal of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1317-1328
• /
• 2010

In this paper, we study the properties of positive solutions for the reaction-diffusion equation $u_t$ = $\Delta_u+{\int}_\Omega u^pdx-ku^q$ in $\Omega\times(0,T)$ with nonlocal nonlinear boundary condition u (x, t) = ${\int}_{\Omega}f(x,y)u^l(y,t)dy$ $\partial\Omega\times(0,T)$ and nonnegative initial data $u_0$ (x), where p, q, k, l > 0. Some conditions for the existence and nonexistence of global positive solutions are given.

• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.1-28
• /
• 2004

We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by an $H^1$-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index one. A priori error estimates for semidiscrete scheme are derived for both differ-ential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.17 no.4
• /
• pp.221-237
• /
• 2013

In this paper an asymptotic numerical method named as Initial Value Method (IVM) is suggested to solve the singularly perturbed weakly coupled system of reaction-diffusion type second order ordinary differential equations with negative shift (delay) terms. In this method, the original problem of solving the second order system of equations is reduced to solving eight first order singularly perturbed differential equations without delay and one system of difference equations. These singularly perturbed problems are solved by the second order hybrid finite difference scheme. An error estimate for this method is derived by using supremum norm and it is of almost second order. Numerical results are provided to illustrate the theoretical results.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.3
• /
• pp.677-690
• /
• 2020

In this article, we study a reaction-diffusion system with homogeneous Dirichlet boundary conditions, which describing a three-species food chain model. Under some conditions, the predator-prey subsystem (u₁ ≡ 0) has a unique positive solution (${\bar{u_2}}$, ${\bar{u_3}}$). By using the birth rate of the prey r1 as a bifurcation parameter, a connected set of positive solutions of our system bifurcating from semi-trivial solution set (r₁, (0, ${\bar{u_2}}$, ${\bar{u_3}}$)) is obtained. Results are obtained by the use of degree theory in cones and sub and super solution techniques.