• 제목/요약/키워드: kinetic equation

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Protein Adsorption on Ion Exchange Resin: Estimation of Equilibrium Isotherm Parameters from Batch Kinetic Data

  • Chu K.H.;Hashim M.A.
    • Biotechnology and Bioprocess Engineering:BBE
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    • 제11권1호
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    • pp.61-66
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    • 2006
  • The simple Langmuir isotherm is frequently employed to describe the equilibrium behavior of protein adsorption on a wide variety of adsorbents. The two adjustable parameters of the Langmuir isotherm - the saturation capacity, or $q_m$, and the dissociation constant, $K_d$ - are usually estimated by fitting the isotherm equation to the equilibrium data acquired from batch equilibration experiments. In this study, we have evaluated the possibility of estimating $q_m$ and $K_d$ for the adsorption of bovine serum albumin to a cation exchanger using batch kinetic data. A rate model predicated on the kinetic form of the Langmuir isotherm, with three adjustable parameters ($q_m,\;K_d$, and a rate constant), was fitted to a single kinetic profile. The value of $q_m$ determined as the result of this approach was quantitatively consistent with the $q_m$ value derived from the traditional batch equilibrium data. However, the $K_d$ value could not be retrieved from the kinetic profile, as the model fit proved insensitive to this parameter. Sensitivity analysis provided significant insight into the identifiability of the three model parameters.

키토산비드를 이용한 양이온/음이온의 흡착모델 적용 (Applicability of adsorption kinetic model for cation/anion for chitosan hydrogel bead)

  • 안병렬
    • 상하수도학회지
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    • 제33권3호
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    • pp.205-213
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    • 2019
  • Batch adsorption tests were performed to evaluate the applicability of adsorption kinetic model by using hydrogel chitosan bead crosslinked with glutaraldehyde (HCB-G) for Cu(II) as cation and/or phosphate as anion. Pseudo first and second order model were applied to determine the sorption kinetic property and intraparticle and Boyd equation were used to predict the diffusion of Cu(II) and phosphate at pore and boundary-layer, respectively. According to the value of theoretical and experimental uptake of Cu(II) and phosphate, pseudo second order is more suitable. On comparison with the value of adsorption rate constant (k), phosphate kinetic was 2-4 times faster than that of Cu(II) at any experimental condition indicating the electrostatic interaction between ${NH_3}^+$ and phosphate is dominated at the presence of single component. However, when Cu(II) and phosphate simultaneously exist, the value of k for phosphate was sharply decreased and then the difference was not significant. Both diffusion models confirmed that the sorption rate was controlled by film mass transfer at the beginning time (t < 3 hr) and pore diffusion at next time section (t > 6 hr).

Correlation of the Rates on Solvolysis of 2,2,2-Trichloroethyl Chloroformate Using the Extended Grunwald-Winstein Equation

  • Koh, Han-Joong;Kang, Suk-Jin
    • Bulletin of the Korean Chemical Society
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    • 제33권5호
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    • pp.1729-1733
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    • 2012
  • The solvolysis rate constants of 2,2,2-trichloroethyl chloroformate ($Cl_3CCH_2OCOCl$, $\mathbf{3}$) in 30 different solvents are well correlated with the extended Grunwald-Winstein equation, using the $N_T$ solvent nucleophilicity scale and the $Y_{Cl}$ solvent ionizing scale, with sensitivity values of $1.28{\pm}0.06$ and $0.46{\pm}0.03$ for $l$ and $m$, respectively. The activation enthalpies (${\Delta}H^{\neq}$) are 10.1 to 12.8 $kcal{\cdot}mol^{-1}$ and the activation entropies (${\Delta}S^{\neq}$) are -27.8 to -36.8 $cal{\cdot}mol^{-1}{\cdot}K^{-1}$, which is consistent with the proposed bimolecular reaction mechanism. The kinetic solvent isotope effect ($k_{MeOH}/k_{MeOD}$) of 2.39 is also in accord with $S_N2$ mechanism probably assisted by general-base catalysis.

Correlation of the Rates of Solvolysis of Electron-Rich Benzoyl Chloride Using the Extended Grunwald-Wistein Equation

  • Oh, Hyunjung;Choi, Hojune;Park, Jong Keun;Yang, Kiyull;Koo, In Sun
    • Bulletin of the Korean Chemical Society
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    • 제34권9호
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    • pp.2697-2701
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    • 2013
  • The solvolysis rate constants of piperonyloyl chloride (1) in 27 different solvents are well correlated with the extended Grunwald-Winstein equation, using the $N_T$ solvent nucleophilicity scale, $Y_{Cl}$ solvent ionizing scale, and I aromatic ring parameter with sensitivity values of $0.30{\pm}0.05$, $0.71{\pm}0.02$, and $0.60{\pm}0.04$ for l, m, and h, respectively. The solvent kinetic isotope effect values (SKIE, $k_{MeOH}/k_{MeOD}$ and $k_{50%MeOD-50%D2O}$) of 1.16 and 1.12 were also in accord with the values for the $S_N1$ mechanism and/or the dissociative $S_N2$ mechanism. The product selectivity values (S) for solvolysis of 1 in alcohol/water mixtures were in the range of 0.5 to 1.9, which is also consistent with the proposed unimolecular ionization mechanism.

Reaction Rates for the Oxidation of Pitch based Carbon Fibers in Air and Carbon Dioxide Gas

  • Roh, Jae-Seung
    • Carbon letters
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    • 제4권4호
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    • pp.185-191
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    • 2003
  • Two types of carbon fiber based high modulus- and isotropic-pitch were exposed to isothermal oxidation in air and $CO_2$ gas and the weight change was measured by TGA apparatus. The kinetic equation was introduced $f=1-{\exp}(-at^b)$ and the constant b was obtained in the range of 1.02~1.68 for the isotropic fiber and obtained 0.91~1.93 for the high modulus fiber respectively. In considering the effect of the atmosphere for isothermal oxidation, the value of the constant b obtained in the carbon dioxide was higher than that obtained in the air. Therefore, it was found that the pitch based carbon fiber shows sigmoidal characteristic when it is oxidized in the carbon dioxide. In addition, it was also found that $k_f = 0.5$, which was reaction constant at f = 0.5, was a very useful parameter for evaluation of the oxidation reactivity of pitch based carbon fibers. According to the consideration, it is suggested that the conversion-time curves of the pitch based carbon fibers are correlated by normalized equation $f=1-{\exp}(-A{\tau}^B)$, where ${\tau}=t/t_f= 0.5$.

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Application of the Extended Grunwald-Winstein Equation to the Solvolyses of 4-(Chlorosulfonyl)biphenyl

  • Kang, Suk Jin;Koh, Han Joong
    • 대한화학회지
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    • 제61권1호
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    • pp.25-28
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    • 2017
  • Solvolyses with the reaction center being the sulfur of 4-(chlorosulfonyl)biphenyl ($C_6H_5C_6H_4SO_2Cl$, 1) was studied under solvolytic conditions and the extended Grunwald-Winstein equation was applied. The thirty five kinds of solvents gave a reasonable extended Grunwald-Winstein plot with a correlation coefficient (R) of 0.940. The sensitivity values (l = 0.60 and m = 0.47) of 1 were smaller than those obtained for benzenesulfonyl chloride ($C_6H_5SO_2Cl$, 2; l = 1.10 and m = 0.61) proposed to undergo dissociative $S_N2$ mechanism. These l and m values for the solvolyses of 1 can be considered to support a $S_N2$ pathway with some ionization reaction. The activation parameters, ${\Delta}H^{\neq}$ and ${\Delta}S^{\neq}$, were determined and they are also in line with values expected for a bimolecular reaction. The kinetic solvent isotope effect (KSIE) of 1.26 is also in accord with a bimolecular mechanism, probably assisted by general-base catalysis.

CHARACTERISTlCS OF PLANE JETS IN THE TRANSITION REGION

  • Seo, Il-Won;Ahn, Jung-Kyu;Kwon, Seok-Jae
    • Water Engineering Research
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    • 제3권3호
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    • pp.163-176
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    • 2002
  • In this study, laboratory experiments have been performed to investigate characteristics of the velocity fields and turbulence for non-buoyant plane jet in the vicinity of the jet nozzle using PIV system. The experimental results show that, in the transition region, the lateral velocity profile is in good agreement with Gaussian distribution. However, the coefficient of Gaussian distribution, $\K_{u,}$, decreases with longitudinal distance in the transition region. The existing theoretical equation for the centerline velocity tends to overestimate the measured data in the transition region. A new equation for the centerline velocity derived by incorporating varying $k_{u}$ gives better agreement with the measured data than the previous equation. The results of the turbulence characteristics show peak values are concentrated on the shear layers. The Reynolds shear stress profile shows the positive peak in the upper layer and negative peak in the lower layer. The turbulent kinetic energy also provides double peaks at the shear layers. The peak of the Reynolds shear stress and the turbulent kinetic energy increases until x/B=8, and then it decreases afterwards.s.

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낙하 충격에 의한 풍화토의 비산먼지 발생 특성 분석 (Analysis of dust emission characteristic by drop impact on decomposed granite soil)

  • 민슬기;손영환;박재성;노수각;봉태호
    • 한국농공학회논문집
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    • 제56권3호
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    • pp.39-45
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    • 2014
  • Dust is mostly caused by human activity. The effect of natural factors on dust emission were studied in many research, but the little effort in researching artificial factors of dust emission. The object of study is to analysis dust emission characteristic by drop impact. Particle matter $10{\mu}m$ ($PM_{10}$) was measured by drop impact on paved soil with changing drop height, weight and drop size. Increasing drop height cause more $PM_{10}$ emission. Increasing drop weight cause more $PM_{10}$ emission but had limit weight for increasing dust emission. Because the exceed kinetic energy of drop weight penetrate the soil surface. The limit perimeter was exist that separating $PM_{10}$ emission aspect. Under limit perimeter, $PM_{10}$ emission was increasing while perimeter was increasing, but over limit perimeter showed the opposite aspect. Regression equations for estimating $PM_{10}$ with kinetic energy and perimeter were made under limit perimeter and over limit perimeter. The $R^2$ of those equations were 0.784, 0.743. The error has occurred between measured $PM_{10}$ and calculated $PM_{10}$ in the equation under limit perimeter. But using equation of case for over limit perimeter, PM10 can be estimated with kinetic energy and drop perimeter.

저레이놀즈수 k-$\varepsilon$난류모형 개선에 관한 연구 (A Study on the Development of Low Reynolds Number k-$\varepsilon$ Turbulence Model)

  • 김명호;신종근;최영돈
    • 대한기계학회논문집
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    • 제16권10호
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    • pp.1940-1954
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    • 1992
  • 본 연구에서는 가공기 자체의 파라메터와 성능에 관한 연구로서 출력 에너지 가 서로 다른 가공기를 사용하여 SUS 304 스테인리스 시험편을 관통, 절단하면서 출력 에너지와 최대 출력을 비교하여 보고, 시험편 관통시 주파수와 출력 에너지와의 관계, 시험편 관통시 응융 금속 제거량에 의한 절단 속도의 예측, 서로 다른 출력의 가공에 있어서 슬릿 절단 폭, 커프 폭, 드로스 길이, 절단면의 표면 거칠기 등을 비교하여 출 력차에 따른 가공 특성을 고찰하였다.