Isotherm

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K Porkodi - One of the best experts on this subject based on the ideXlab platform.

  • Isotherms and thermodynamics by linear and non linear regression analysis for the sorption of methylene blue onto activated carbon comparison of various error functions
    Journal of Hazardous Materials, 2008
    Co-Authors: Vasanth K Kumar, K Porkodi, Fernando Rocha
    Abstract:

    A comparison of linear and non-linear regression method in selecting the optimum Isotherm was made to the experimental equilibrium data of methylene blue sorption by activated carbon. The r2 was used to select the best fit linear theoretical Isotherm. In the case of non-linear regression method, six error functions, namely coefficient of determination (r2), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter Isotherms and also to predict the optimum Isotherm. For two parameter Isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted Isotherms. In the case of three parameter Isotherm, r2 was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical Isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum Isotherm. In addition to the size of error function, the theory behind the predicted Isotherm should be verified with the help of experimental data while selecting the optimum Isotherm. A coefficient of non-determination, K2 was explained and was found to be very useful in identifying the best error function while selecting the optimum Isotherm.

  • batch adsorber design for different solution volume adsorbent mass ratios using the experimental equilibrium data with fixed solution volume adsorbent mass ratio of malachite green onto orange peel
    Dyes and Pigments, 2007
    Co-Authors: Vasanth K Kumar, K Porkodi
    Abstract:

    Abstract Equilibrium studies were carried out at 305 K for the sorption of malachite green onto orange peel for a fixed operating line condition (solution volume/adsorbent mass ratio or V / M ratio). The experimental data were fitted to the Freundlich, Langmuir and Redlich–Peterson Isotherms by non-linear method. The best fitting Isotherm was found to be the Langmuir and Redlich–Peterson Isotherm. Redlich–Peterson is a special case of Langmuir Isotherm when the constant g equals unity. A single stage batch adsorber was designed for different operating line ( V / M ) ratios using the Redlich–Peterson Isotherm. Equilibrium data were obtained from the Langmuir Isotherm at different V / M ratios using the mass balance equation for the batch adsorber system. A simple linear expression relating the parameters involved in the batch adsorber design was proposed for the studied system.

Vasanth K Kumar - One of the best experts on this subject based on the ideXlab platform.

  • Isotherms and thermodynamics by linear and non linear regression analysis for the sorption of methylene blue onto activated carbon comparison of various error functions
    Journal of Hazardous Materials, 2008
    Co-Authors: Vasanth K Kumar, K Porkodi, Fernando Rocha
    Abstract:

    A comparison of linear and non-linear regression method in selecting the optimum Isotherm was made to the experimental equilibrium data of methylene blue sorption by activated carbon. The r2 was used to select the best fit linear theoretical Isotherm. In the case of non-linear regression method, six error functions, namely coefficient of determination (r2), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter Isotherms and also to predict the optimum Isotherm. For two parameter Isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted Isotherms. In the case of three parameter Isotherm, r2 was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical Isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum Isotherm. In addition to the size of error function, the theory behind the predicted Isotherm should be verified with the help of experimental data while selecting the optimum Isotherm. A coefficient of non-determination, K2 was explained and was found to be very useful in identifying the best error function while selecting the optimum Isotherm.

  • batch adsorber design for different solution volume adsorbent mass ratios using the experimental equilibrium data with fixed solution volume adsorbent mass ratio of malachite green onto orange peel
    Dyes and Pigments, 2007
    Co-Authors: Vasanth K Kumar, K Porkodi
    Abstract:

    Abstract Equilibrium studies were carried out at 305 K for the sorption of malachite green onto orange peel for a fixed operating line condition (solution volume/adsorbent mass ratio or V / M ratio). The experimental data were fitted to the Freundlich, Langmuir and Redlich–Peterson Isotherms by non-linear method. The best fitting Isotherm was found to be the Langmuir and Redlich–Peterson Isotherm. Redlich–Peterson is a special case of Langmuir Isotherm when the constant g equals unity. A single stage batch adsorber was designed for different operating line ( V / M ) ratios using the Redlich–Peterson Isotherm. Equilibrium data were obtained from the Langmuir Isotherm at different V / M ratios using the mass balance equation for the batch adsorber system. A simple linear expression relating the parameters involved in the batch adsorber design was proposed for the studied system.

Keith K H Choy - One of the best experts on this subject based on the ideXlab platform.

  • Langmuir Isotherm Models Applied to the Multicomponent Sorption of Acid Dyes from Effluent onto Activated Carbon
    Journal of Chemical & Engineering Data, 2000
    Co-Authors: Keith K H Choy, John F Porter, Gordon Mckay
    Abstract:

    The adsorption of three acidic dyes, Acid Blue 80 (AB80), Acid Red 114 (AR114), and Acid Yellow 117 (AY117) onto activated carbon, Filtrasorb 400, has been studied. Three single-component and three binary, AB80 + AR114, AB80 + AY117, and AR114 + AY117, Isotherms were determined. Four models for predicting the multicomponent equilibrium sorption Isotherms have been compared in order to determine which is the best fit model to predict or correlate binary adsorption data. These were an extended Langmuir Isotherm, a simplified model based on single-component equilibrium factors, a modified extended Langmuir Isotherm with a constant interaction factor, and a modified extended Langmuir Isotherm incorporating a surface coverage dependent interaction factor.

  • the prediction of sorption from a binary mixture of acidic dyes using single and mixed Isotherm variants of the ideal adsorbed solute theory
    Chemical Engineering Science, 1999
    Co-Authors: John F Porter, Gordon Mckay, Keith K H Choy
    Abstract:

    Abstract Equilibrium Isotherms have been determined for the adsorption of two single-component and one binary acid dye solutions on carbon. The ideal adsorbed solute theory (IAST) has been used to predict Isotherm data for the binary system using the single-component dye sorption data alone. A detailed analysis has been carried out to investigate the effect of different error criteria for determining single-component Isotherm parameters and their influence on the results of IAS model simulations using the Langmuir and Freundlich Isotherm equations. It was found that the “best-fit” single-component Isotherm based on the minimum error criteria did not result in the “best-fit” IAS model predictions. Furthermore, the IAS model producing the closest fit to the binary experimental data did not use the same Isotherm model as the single-component data for one dye. Reasons for this apparently anomalous behaviour have been discussed and the most likely cause appears to be dye–dye interactions in the binary system.

Constantino Suarez - One of the best experts on this subject based on the ideXlab platform.

  • Analysis of the sorptional characteristics of amaranth starch
    Journal of Food Engineering, 1999
    Co-Authors: Andrea N. Calzetta Resio, Roberto J. Aguerre, Constantino Suarez
    Abstract:

    The water vapor adsorption Isotherms of amaranth starch were determined for the temperature range 25‐50∞C and water activity 0.04‐0.90. Comparison with adsorption Isotherms of wheat and corn native starches showed that the three starches have similar adsorption capacities at low aw values. Amaranth starch showed higher sorption capacity than corn and wheat starches at high aw values. Two BET-like Isotherm equations were used to fit the equilibrium data: the GAB Isotherm and a fractal Isotherm. Although the best fit was obtained with fractal Isotherm, the values of C and mm obtained from both equations were practically coincident. The fractal dimension D was in average 2.77 revealing the high degree of surface roughness of the starch. The eAect of temperature on the equilibrium data was satisfactorily modeled by means of a simple two-parameter equation, covering the whole aw range investigated. An analytical expression was used to estimate the variation of the isosteric heat with moisture. The isosteric heat reached its maximum value of 30 kJ/mol at moisture levels of about 5% (db). ” 1999 Elsevier Science Ltd. All rights reserved.

  • A fractal Isotherm for multilayer adsorption in foods
    Journal of Food Engineering, 1996
    Co-Authors: Roberto J. Aguerre, Pascual E. Viollaz, Constantino Suarez
    Abstract:

    Abstract The effect of the fractal surface on physical adsorption has been analysed and a new three-parametric Isotherm equation was derived. The model describes the multilayer adsorption on fractal surfaces within the framework of BET theory. It predicts lower buildup of the multilayer coverage on a fractal surface than on a flat surface. The results of the simulation show that increasing the fractal dimension of the surface affects the adsorption Isotherms; namely, the upward curvature of the Isotherms at high relative pressures is decreased as D increases. For the submonolayer region, the curves become independent of the fractal nature of the absorbent. The Isothermal data for water vapor sorption on grains and other starchy materials were used to evaluate the new Isotherm equation. The parameters of the Isotherms were calculated using computational regression techniques. Fractal dimension ranged from 2.6 to 2.9, approximately, indicating the contribution of the pore structure to the sorption capacity of the products investigated. Results show that the model allows an accurate and simple description of the sorption data for the whole range of water activity.

Gordon Mckay - One of the best experts on this subject based on the ideXlab platform.

  • adsorption of acid dyes on chitosan equilibrium Isotherm analyses
    Process Biochemistry, 2004
    Co-Authors: Y C Wong, Y S Szeto, W H Cheung, Gordon Mckay
    Abstract:

    Abstract The ability of chitosan, derived from deacetylated crab shell chitin, to remove acid dyes from effluent solution by adsorption has been studied. Equilibrium Isotherms for the adsorption of five acid dyes, Acid Green 25 (AG25), Acid Orange 10 (AO10), Acid Orange 12 (AO12), Acid Red 18 (AR18) and Acid Red 73 (AR73), on chitosan were measured experimentally. Results were analysed by the Langmuir, Freundlich and Redlich–Peterson (R–P) equation using a linearised correlation coefficient. The Langmuir Isotherm gave the best correlation for the adsorption of AG25, AR18, AR73 and AO12 while the composite Freundlich Isotherm gave excellent correlation for AO10. The equilibrium data were then analysed using five different non-linear error analysis methods and two significant findings were obtained. Firstly, the order of Isotherm selection was changed showing that the R–P equation had the lowest error values for all five acid dye-chitosan Isotherms. Secondly, the values of the individual Isotherm constants changed with the error methodology selected.

  • Langmuir Isotherm Models Applied to the Multicomponent Sorption of Acid Dyes from Effluent onto Activated Carbon
    Journal of Chemical & Engineering Data, 2000
    Co-Authors: Keith K H Choy, John F Porter, Gordon Mckay
    Abstract:

    The adsorption of three acidic dyes, Acid Blue 80 (AB80), Acid Red 114 (AR114), and Acid Yellow 117 (AY117) onto activated carbon, Filtrasorb 400, has been studied. Three single-component and three binary, AB80 + AR114, AB80 + AY117, and AR114 + AY117, Isotherms were determined. Four models for predicting the multicomponent equilibrium sorption Isotherms have been compared in order to determine which is the best fit model to predict or correlate binary adsorption data. These were an extended Langmuir Isotherm, a simplified model based on single-component equilibrium factors, a modified extended Langmuir Isotherm with a constant interaction factor, and a modified extended Langmuir Isotherm incorporating a surface coverage dependent interaction factor.

  • the prediction of sorption from a binary mixture of acidic dyes using single and mixed Isotherm variants of the ideal adsorbed solute theory
    Chemical Engineering Science, 1999
    Co-Authors: John F Porter, Gordon Mckay, Keith K H Choy
    Abstract:

    Abstract Equilibrium Isotherms have been determined for the adsorption of two single-component and one binary acid dye solutions on carbon. The ideal adsorbed solute theory (IAST) has been used to predict Isotherm data for the binary system using the single-component dye sorption data alone. A detailed analysis has been carried out to investigate the effect of different error criteria for determining single-component Isotherm parameters and their influence on the results of IAS model simulations using the Langmuir and Freundlich Isotherm equations. It was found that the “best-fit” single-component Isotherm based on the minimum error criteria did not result in the “best-fit” IAS model predictions. Furthermore, the IAS model producing the closest fit to the binary experimental data did not use the same Isotherm model as the single-component data for one dye. Reasons for this apparently anomalous behaviour have been discussed and the most likely cause appears to be dye–dye interactions in the binary system.

  • A Comparison of Langmuir Based Models for Predicting Multicomponent Metal Ion Equilibrium Sorption Isotherms on Peat
    Process Safety and Environmental Protection, 1997
    Co-Authors: Gordon Mckay, John F Porter
    Abstract:

    Three models for predicting multicomponent equilibrium sorption Isotherms have been tested for the sorption of cadmium, copper and zinc ions onto peat. The models tested were an extended Langmuir Isotherm, a simplified model based on characteristic equilibrium parameters and a modified extended Langmuir Isotherm incorporating an interaction factor. The experimental system is based on the sorption of three metal ions onto peat in single, binary and ternary component systems.