• Biotechnology and Bioprocess Engineering:BBE
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• v.11 no.1
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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.

• Clean Technology
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• v.9 no.2
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• pp.81-85
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• 2003

A simple method of isotherm determination for HPLC is discussed. The equilibrium-dispersive model describing the behavior of elution peaks in HPLC for single component is solved numerically by using PDE solver Macsyma$^{(R)}$(Macsyma Inc., Arlington, MA, USA.) and compared to the experimental data obtained in overloaded isocratic chromatography with caffeine as model species. The effect of sample concentration and flow velocity on the band profiles of elution peaks are described.

• Journal of Environmental Science International
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• v.13 no.7
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• pp.689-695
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• 2004

The properties of biosorption of dye(Rhodmine B) was investigated to figure out the effects of temperature as a function of dye concentration and sludge concentration by the Langmuir and Lagergen adsorption model. It was found that the uptake capacity of biosorption was increased at low temperature. The Langmuir adsorption model was found suitable for describing the biosorption of the dye. The experimental results indicated that the dye uptake process followed the pseudo-first-order kinetics.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.44.2-44.2
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• 2016

The solar wind electrons are made of three or four distinct components, which are core Maxwellian background, isotropic halo, and super-halo (and sometimes, highly field-aligned strahl component which can be considered as a fourth element). We put forth a steady-state model for the solar wind electrons by considering both the steady-state particle and wave kinetic equations. Since the steady-state solar wind electron VDFs and the steady-state wave fluctuation spectrum are related to each other, we also investigate the complete fluctuation spectra in the whistler and Langmuir frequency ranges by considering halo- and superhalo-like model electron VDFs. It is found that the energetic electrons make important contributions to the total emission spectrum. Based on this, we complete the steady-state model by considering both the whistler and Langmuir fluctuations. In particular, the Langmuir fluctuation plays an important role in the formation and maintenance of nonthermal electrons.

• Journal of Environmental Science International
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• v.9 no.2
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• pp.165-171
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• 2000

A kinetic study for anion exchange was performed for commercially available Cl- type anion exchange resin in use to remove nitrate in water. The obtained results from the batch reactor were applied to the Langmuir and Freundlich models. The constants for Lagmuir model were qmax =29.82 and b=0.202, and for Freundlich model were K=5.509 and n=1.772. Langmuir model showed betterfit than Frendlich model for the experimental results. Ion exchange reaction rate was also calculated and the the approximate first-order reaction, rate constant k1 was 0.16 L/mg.hr. Effective diffusion coefficient was obtained in the range from $9.67$\times$10^{-8} cm^2/sec$ for initial concentration change, and from $6.09$\times$10^{-7} to 3.98$\times$10^{-6} cm^2/sec$ for reaction temperature change. Activation energy during the diffusion was calculated as 26 kcal/mol.

• Journal of the Korean GEO-environmental Society
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• v.12 no.11
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• pp.31-37
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• 2011

This study investigated on the adsorption and photocatalysis of Reactive Black 5(RB5) by the hydroxyapatite(HAP)/Titanium dioxide($TiO_{2}$) media. The adsorption of RB5 on $TiO_{2}$, HAP and $TiO_{2}$/HAP was investigated during a series of batch adsorption experiments. The amounts adsorbed at equilibrium were measured. Langmuir and Freundlich isotherm models were tested for their applicability. The result of equilibrium studies of $TiO_{2}$, HAP and $TiO_{2}$/HAP adsorbent were found to follow Langmuir isotherm model. The adsorbed amounts(Qmax) were found to be 5.28mg/g on single $TiO_{2}$, 12.45mg/g on single HAP and 9.03mg/g on $TiO_{2}$/HAP, respectively. The experimental data were analysed using the pseudo-first-order adsorption and photocatalysis kinetic models. According to these models, RB5 degradation by $TiO_{2}$/HAP was affected by interaction effect of photocatalysis and adsorption.

• Korean Chemical Engineering Research
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• v.56 no.1
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• pp.112-118
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• 2018

Adsorption equilibrium, kinetic and thermodynamic parameters of a brilliant green from aqueous solutions at various initial dye concentration (10~30 mg/L), contact time (1~24 h) and temperature (298~318 K) on zeolite were studied in a batch mode operation. The equilibrium adsorption values were analyzed by Langmuir, Freundlich and Dubinin-Radushkevich model. The results indicate that Langmuir and Freundlich model provides the best correlation of the experimental data. Base on the estimated values of Langmuir dimensionless separation factor ($R_L=0.041{\sim}0.057$) and Freundlich constant (1/n=0.30~0.47), this process could be employed as effective treatment method. calculated values of adsorption energy by Dubinin-Radushkevich model were 1.564~1.857 kJ/mol corresponding to physical adsorption. The adsorption kinetics of brilliant green were best described by the pseudo second-order rate model and followed by intraparticle diffusion model. Thermodynamic parameters such as activation energy, free energy, enthalpy and entropy were calculated to estimate nature of adsorption. negative Gibbs free energy (-10.3~-11.4 kJ/mol), positive enthalpy change (49.48 kJ/mol) and Arrehenius activation energy (27.05 kJ/mol) indicates that the adsorption is spontaneous, endothermic and physical adsorption process, respectively.

• Korean Chemical Engineering Research
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• v.57 no.5
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• pp.679-686
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• 2019

Characteristics of adsorption equilibrium, kinetic and thermodynamic of aniline blue onto activated carbon from aqueous solution were investigated as function of initial concentration, contact time and temperature. Adsorption isotherm of aniline blue was analyzed by Langmuir, Freundlich, Redlich-Peterson, Temkin and Dubinin-Radushkevich models. Langmuir isotherm model fit better with isothermal data than other isotherm models. Estmated Langmuir separation factors ($R_L=0.036{\sim}0.068$) indicated that adsorption process of aniline blue by activated carbon could be an effective treatment method. Adsorption kinetic data were fitted to pseudo first order model, pseudo second order model and intraparticle diffusion models. The kinetic results showed that the adsorption of aniline blue onto activated carbon well followed pseudo second-order model. Adsorption mechanism was evaluated in two steps, film diffusion and intraparticle diffusion, by intraparticle diffusion model. Thermodynamic parameters such as Gibbs free energy, enthalpy and entropy for adsorption process were estimated. Enthalpy change (48.49 kJ/mol) indicated that this adsorption process was physical adsorption and endothermic. Since Gibbs free energy decreased with increasing temperature, the adsorption reaction became more spontaneously with increasing temperature. The isosteric heat of adsorption indicated that there is interaction between the adsorbent and the adsorbate because the energy heterogeneity of the adsorbent surface.

• Journal of Hydrogen and New Energy
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• v.13 no.3
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• pp.214-223
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• 2002

Kinetic and effectiveness factors for methanol steam reforming using commercial copper-containing catalysts in a plug flow reactor were investigated over the temperature ranges of $180-250^{\circ}C$ at atmospheric pressure. The selectivity of $CO_2$/$H_2$ was almost 100%, and CO products were not observed under reaction conditions employed in this work. It was indicated that $CO_2$ was directly produced and CO was formed via the reverse water gas shift reaction after methanol steam reforming. The intrinsic kinetics for such reactions were well described by the Langmuir-Hinshelwood model based on the dual-site mechanism. The six parameters in this model, including the activation energy of 103kJ/mol, were estimated from diffusion-free data. The significant effect of internal diffusion was observed for temperature higher than $230^{\circ}C$ or particle sizes larger than 0.36mm. In the diflusion-limited case, this model combined with internal effectiveness factors was also found to be good agreement with experimental data.

• Journal of Korean Society of Environmental Engineers
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• v.37 no.8
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• pp.450-457
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• 2015

In this research a adsorbent, PVA-Zeolite bead, was prepared by immobilizing zeolite with PVA. The results of XRD and SEM analysis showed that the prepared PVA-Zeolite beads had porous structure and the zeolite particles were in mobilized within the internal matrix of the beads. The adsorption properties of Sr ion and Cs ion with the adsorbent were studied by different parameters such as effect of pH, adsorption rate, and adsorption isotherm. The adsorption of Sr ion and Cs ion reached equilibrium after 540 minutes. The adsorption kinetics of both ions by the PVA-Zeolite beads were fitted well by the pseudo-second-order model more than pseudo-first-order model. The equilibrium data fitted well with Langmuir isotherm model. The maximum adsorption capacities of Sr ion and Cs ion calculated from Langmuir isotherm model were 52.08 mg/g and 58.14 mg/g, respectively. The external mass transfer step was very fast compared to the intra-particle diffusion step in the adsorption process of Cs ion and Sr ion by the PVA-Zeolite beads. This result implied that the rate controlling step was the intra-particle diffusion step.