Intraparticle Diffusion Equation Research Articles

Biosorption of Cu(II) from aqueous solutions by mimosa tannin gel

The biosorption of Cu(II) from aqueous solutions by mimosa tannin resin (MTR) was investigated as a function of particle size, initial pH, contact time and initial metal ion concentration. The aim of this study was to understand the mechanisms that govern copper removal and find a suitable equilibrium isotherm and kinetic model for the copper removal in a batch reactor. The experimental isotherm data were analysed using the Langmuir, Freundlich and Temkin equations. The equilibrium data fit well in the Langmiur isotherm. The experimental data were analysed using four sorption kinetic models – the pseudo-first- and second-order equations, and the Elovich and the intraparticle diffusion equation – to determine the best fit equation for the biosorption of copper ions onto mimosa tannin resin. Results show that the pseudo-second-order equation provides the best correlation for the biosorption process, whereas the Elovich equation also fits the experimental data well. Thermodynamic parameters such as the entropy change, enthalpy change and Gibb's free energy change were found out to be 153.0 J mol −1 K −1, 42.09 kJ mol −1 and −2.47 kJ mol −1, respectively.

Adsorption of Cu(II) ions in aqueous solution using chitosan beads, chitosan–GLA beads and chitosan–alginate beads

Abstract The use of chitosan beads, chitosan–GLA 1:1, 2:1 ratio beads, and chitosan–alginate beads for the removal of Cu(II) ions from aqueous solution at different initial pH, agitation periods, adsorbent dosage, and initial concentrations has been investigated. The equilibrium adsorption data were described by the non-linear Langmuir, Freundlich and Sips isotherms. Chitosan beads, chitosan–GLA 1:1 and 2:1 ratio beads agreed well with the non-linear Freundlich isotherm, though it gave an adsorption capacity of 64.62 mg/g, 31.20 mg/g and 19.51 mg/g, respectively, based on the non-linear Langmuir isotherm. Meanwhile, chitosan–alginate beads showed a better fit to the non-linear Langmuir isotherm giving an adsorption capacity of 67.66 mg/g. Based on the Sips isotherm, chitosan beads, chitosan–GLA 1:1 and 2:1 ratio beads are heterogeneous adsorbents, meanwhile chitosan–alginate beads is a homogeneous adsorbent. The pseudo-first and pseudo-second orders and intraparticle diffusion equation were used to evaluate the kinetic data and the constants are determined.

Equilibrium and kinetic data, and adsorption mechanism for adsorption of lead onto valonia tannin resin

The adsorption of lead onto valonia tannin resin studied using a batch adsorber. The aim of this study was to understand the mechanisms that govern lead removal and find a suitable equilibrium isotherm and kinetic model for the lead removal in a batch reactor. The experimental isotherm data were analyzed using the Langmuir, Freundlich, Temkin and Dubinin–Radushkevich equations. The equilibrium data fit well the Langmuir isotherm. The experimental data were analyzed using four adsorption kinetic models – the pseudo first- and second-order equations, the Elovich equation and intraparticle diffusion equation – to determine the best fit equation for the adsorption of lead-ions onto valonia tannin resin. The characteristic parameters for each kinetic models have been determined and the correlation coefficients have been calculated in order to assess which model provides the best fit predicted data with experimental results. Also, predicted qt values from the kinetic equations were compared with the experimental data. Results show that the pseudo second-order equation provides the best correlation for the adsorption process. Adsorption mechanism was also proposed for the adsorption of lead-ions onto valonia tannin resin.

Sorption kinetics and isotherm studies of a cationic dye using agricultural waste: Broad bean peels

In this paper, broad bean peels (BBP), an agricultural waste, was evaluated for its ability to remove cationic dye (methylene blue) from aqueous solutions. Batch mode experiments were conducted at 30 °C. Equilibrium sorption isotherms and kinetics were investigated. The kinetic data obtained at different concentrations have been analyzed using pseudo-first-order, pseudo-second-order and intraparticle diffusion equations. The experimental data fitted very well the pseudo-first-order kinetic model. Analysis of the temportal change of q indicates that at the beginning of the process the overall rate of adsorption is controlled by film-diffusion, then at later stage intraparticle-diffusion controls the rate. Diffusion coefficients and times of transition from film to pore-diffusion control were estimated by piecewise linear regression. The experimental data were analyzed by the Langmuir and Freundlich models. The sorption isotherm data fitted well to Langmuir isotherm and the monolayer adsorption capacity was found to be 192.7 mg/g and the equilibrium adsorption constant K a is 0.07145 l/mg at 30 °C. The results revealed that BBP was a promising sorbent for the removal of methylene blue from aqueous solutions.

Equilibrium and kinetic data and process design for adsorption of Congo Red onto bentonite

The adsorption of Congo Red onto bentonite in a batch adsorber has been studied. Four kinetic models, the pseudo first- and second-order equations, the Elovich equation and the intraparticle diffusion equation, were selected to follow the adsorption process. Kinetic parameters; rate constants, equilibrium adsorption capacities and correlation coefficients, for each kinetic equation were calculated and discussed. It was shown that the adsorption of Congo Red onto bentonite could be described by the pseudo second-order equation. The experimental isotherm data were analyzed using the Langmuir, Freundlich and Temkin equations. Adsorption of Congo Red onto bentonite followed the Langmuir isotherm. A single stage batch adsorber was designed for different adsorbent mass/treated effluent volume ratios using the Langmuir isotherm.

Pomegranate husk as an adsorbent in the removal of toxic chromium from wastewater

The use of a new sorbent developed from the husk of pomegranate, a famous fruit in Egypt, for the removal of toxic chromium from aqueous solution has been investigated. The batch experiment was conducted to determine the adsorption capacity of the pomegranate husk. The effects of initial metal concentration (25 and 50 mg l−1), pH, contact time, and sorbent concentration (2–6 g l−1) have been studied at room temperature. A strong dependence of the adsorption capacity on pH was observed, the capacity increased as the pH decreased, and the optimum pH value was pH 1.0. Adsorption equilibrium and kinetics were studied with different sorbent and metal concentrations. The adsorption process was fast, and equilibrium was reached within 3 h. The maximum removal was 100% for 25 mg l−1 of Cr6+ concentration on 5 g l−1 pomegranate husk concentration, and the maximum adsorption capacity was 10.59 mg g−1. The kinetic data were analysed using various kinetic models—pseudo-first-order, pseudo-second-order, Elovich, and intraparticle diffusion equations—and the equilibrium data were tested using several isotherm models, Langmuir, Freundlich, Tempkin, Dubinin–Radushkevich, and Generalized isotherm equations. The Elovich and pseudo-second-order equations provided the greatest accuracy for the kinetic data, while Langmuir and Generalized isotherm models were the closest fit for the equilibrium data. The activation energy of sorption has also been evaluated as 0.236 and 0.707 kJ mol−1 for 25 and 50 mg l−1 chromium concentration, respectively.

Treatment of wastewater containing toxic chromium using new activated carbon developed from date palm seed

The use of a new activated carbon developed from date palm seed wastes, generated in the jam industry, for removing toxic chromium from aqueous solution has been investigated. The activated carbon has been achieved from date palm seed by dehydrating methods using concentrated sulfuric acid. The batch experiments were conducted to determine the adsorption capacity of the biomass. The effect of initial metal concentration (25–125 mg l −1), pH, contact time, and concentration of date palm seed carbon have been studied at room temperature. A strong dependence of the adsorption capacity on pH was observed, the capacity increase as pH value decrease and the optimum pH value is pH 1.0. Kinetics and adsorption equilibrium were studied at different sorbent doses. The adsorption process was fast and the equilibrium was reached within 180 min. The maximum removal was 100% for 75 mg l −1 of Cr 6+ concentration on 4 g l −1 carbon concentration and the maximum adsorption capacity was 120.48 mg g −1. The kinetic data were analyzed using various kinetic models – pseudo-first order equation, pseudo-second order equation, Elovich equation and intraparticle diffusion equation – and the equilibrium data were tested using several isotherm models, Langmuir, Freundlich, Koble–Corrigan, Redlich–Peterson, Tempkin, Dubinin–Radushkevich and Generalized isotherm equations. The Elovich equation and pseudo-second order equation provide the greatest accuracy for the kinetic data and Koble–Corrigan and Langmuir models the closest fit for the equilibrium data. Activation energy of sorption has also been evaluated as 0.115 and 0.229 kJ mol −1.

Kinetics and thermodynamics of the adsorption of some dyestuffs from aqueous solution by poplar sawdust

The effect of temperature on the adsorption of metanil yellow (MY) (acidic) and methylene blue (MB) (basic) by poplar sawdust was investigated. In addition, the amounts of NaHCO 3, Na 2CO 3, NaOH and C 2H 5ONa adsorbed by 1 g of poplar sawdust to determine its surface acidity were also determined. Kinetical data obtained at different temperatures (293 K, 313 K and 333 K) for the adsorption of each dyestuff by poplar sawdust were applied to the pseudo first-order, the pseudo second-order and the intraparticle diffusion equations, and the rate constants of first-order adsorption ( k 1), the rate constants of second-order adsorption ( k 2) and intraparticle diffusion rate constants ( k p) at these temperatures were calculated, respectively. In addition, isothermal data obtained at different temperatures (293 K, 313 K and 333 K) for the adsorption of each dyestuff by poplar sawdust were applied to thermodynamical equations, and thermodynamical parameters (Δ G, Δ H and Δ S) were also calculated.

Adsorption of lead onto formaldehyde or sulphuric acid treated acorn waste: Equilibrium and kinetic studies

The adsorption of lead onto formaldehyde or sulphuric acid treated acorn waste was studied using a batch sorber. The aim of this study was to understand the mechanisms that govern lead removal and find a suitable equilibrium isotherm and kinetic model for the lead removal in a batch reactor. The experimental isotherm data were analyzed using the Langmuir, Freundlich and Temkin equations. The equilibrium data fit well the Langmuir isotherm. The experimental data were analyzed using four adsorption kinetic models – the pseudo first- and second-order equations, intraparticle diffusion equation and the Elovich equation – to determine the best fit equation for the adsorption of lead ions onto formaldehyde or sulphuric acid treated acorn waste. The rate constants, equilibrium capacities and related correlation coefficients for each kinetic model were calculated and discussed. Also, predicted q t values from the kinetic equations were compared with the experimental data. Results show that the pseudo second-order equation provides the best correlation for the adsorption process, whereas the Elovich equation also fits the experimental data well.

Adsorption kinetics and thermodynamics of an anionic dye onto sepiolite

The adsorption kinetics of CI reactive blue 221 (RB221), an anionic dye, onto sepiolite was investigated in aqueous solution in a batch system with respect to stirring speed, contact time, initial dye concentration, pH, and temperature. Experimental results have shown that the acidic pH, increasing initial dye concentration and temperature favours the adsorption. Experimental data related to the adsorption of RB221 on sepiolite under different conditions were applied to the pseudo-first-order equation, the pseudo-second-order equation and the intra-particle diffusion equation, and the rate constants of first-order adsorption ( k 1), the rate constants of second-order adsorption ( k 2) and intra-particle diffusion rate constants ( k int) were calculated, respectively. The experimental data fitted very well the pseudo-second-order kinetic model and also followed the intra-particle diffusion model up to 20 min, whereas diffusion is not only the rate controlling step. The activation energy of system ( E a) was calculated as 7.73 kJ mol −1. The thermodynamics parameters of activation such as Gibbs free energy, enthalpy, entropy were also evaluated and found that Δ G ∗, Δ H ∗, and Δ S ∗ are 47.9 (49.4, 50.0, 51.3) kJ mol −1, 5.30 (5.21, 5.13, 5.05) kJ mol −1, and −145.3 (−148.8, −142.7, −143.1) J K −1 mol −1 at 20 (30, 40, 50) °C, respectively. The results indicate that sepiolite could be employed as a low-cost material for the removal of textile dyes from effluents.

Adsorption of lead(II) ions from aqueous solutions by activated carbon prepared from biomass plant material of Euphorbia rigida

Abstract Adsorption of lead(II) ions onto activated carbon prepared from renewable plant material, which is Euphorbia rigida , was investigated with the variation in the parameters of pH, contact time, the amounts of adsorbent, lead(II) ions concentration and temperature. Adsorption data of lead(II) ions onto activated carbon by E. rigida obeys the Langmuir isotherm model. Maximum adsorption capacity ( q max ) of lead(II) ions onto adsorbent was 1.35 × 10 −3 mol g −1 or 279.72 mg g −1 at 40 °C. Three kinetic models are the first-order, pseudo-second-order and intraparticle diffusion equations, were selected to interpret the adsorption data. Kinetic parameters such as the rate constants, equilibrium adsorption capacities and related correlation coefficients, for each kinetic model were calculated and discussed. It was indicated that the adsorption of lead(II) ions onto activated carbon by E. rigida could be described by the pseudo-second-order kinetic model and also followed the simple external diffusion model the initial 10 min and then by intraparticle diffusion model up to 50 min.

Removal of cadmium from aqueous solutions by adsorption onto orange waste

The use of orange wastes, generated in the orange juice industry, for removing cadmium from aqueous solutions has been investigated. The material was characterized by Fourier transform infrared spectroscopy and batch experiments were conducted to determine the adsorption capacity of the biomass. A strong dependence of the adsorption capacity on pH was observed, the capacity increasing as pH value rose. Kinetics and adsorption equilibrium were studied at different pH values (4–6). The adsorption process was quick and the equilibrium was attained within 3 h. The maximum adsorption capacity of orange waste was found to be 0.40, 0.41 and 0.43 mmol/g at pH 4–6, respectively. The kinetic data were analysed using various kinetic models – pseudo-first order equation, pseudo-second order equation, Elovich equation and intraparticle diffusion equation – and the equilibrium data were tested using four isotherm models – Langmuir, Freundlich, Sips and Redlich–Peterson. The data were fitted by non-linear regression and five error analysis methods were used to evaluate the goodness of the fit. The Elovich equation provides the greatest accuracy for the kinetic data and the Sips model the closest fit for the equilibrium data.

Sorption of lead from aqueous solution by chemically modified carbon adsorbents

An indigenously prepared, steam activated and chemically modified carbon from husk and pods of Moringa oleifera ( M. oleifera), an agricultural waste, was comparatively examined as an adsorbent for the removal of lead from aqueous solutions. Studies were conducted as a function of contact time, initial metal concentration, dose of adsorbent, agitation speed, particle size and pH. Maximum uptake capacities were found to be, 98.89, 96.58, 91.8, 88.63, 79.43% for cetyltrimethyl ammonium bromide (CTAB), phosphoric, sulfuric, hydrochloric acid treated and untreated carbon adsorbents, respectively. Bangham, pseudo-first- and second-order, intra-particle diffusion equations were implemented to express the sorption mechanism by utilized adsorbents. Adsorption rate of lead ions was found to be considerably faster for chemically modified adsorbents than unmodified. The results of adsorption were fitted to both the Langmuir and Freundlich models. Satisfactory agreement between the metal uptake capacities by the adsorbents at different time intervals was expressed by the correlation coefficient ( R 2). The Langmuir model represented the sorption process better than the Freundlich one, with R 2 values ranging from 0.994 to 0.998.

A two stage batch adsorber design for methylene blue removal to minimize contact time

The adsorption of methylene blue onto bentonite in a batch adsorber has been studied. Three kinetic models, the intraparticle diffusion equation and the pseudo first and second order equations, were selected to follow the adsorption process. Kinetic parameters, rate constants, equilibrium adsorption capacities and related correlation coefficients for each kinetic model were calculated and discussed. It was shown that the adsorption of methylene blue onto bentonite could be described by the pseudo second order equation. Adsorption of methylene blue onto bentonite followed the Langmuir isotherm. A model has been developed for the design of a two stage batch adsorber based on pseudo second order adsorption kinetics. The model has been optimized with respect to operating time in order to minimize total contact time to achieve a specified amount of methylene blue removal using a fixed mass of adsorbent. The results of two stage batch adsorber design studies showed that the required times for specified amounts of methylene blue removal significantly decreased. This design is particularly suitable for low-cost adsorbents/adsorption systems when minimising contact time is a major operational and design criterion and a significant volume of effluent needs to be treated in the minimum amount of time.

Contact time optimization of two-stage batch adsorber design using second-order kinetic model for the adsorption of phosphate onto alunite

The adsorption of phosphate onto alunite in a batch adsorber has been studied. Four kinetic models including pseudo first- and second-order equation, intraparticle diffusion equation and the Elovich equation were selected to follow the adsorption process. Kinetic parameters, rate constants, equilibrium adsorption capacities and related correlation coefficients, for each kinetic model were calculated and discussed. It was shown that the adsorption of phosphate onto alunite could be described by the pseudo second-order equation. Adsorption of phosphate onto alunite followed the Langmuir isotherm. A model has been used for the design of a two-stage batch adsorber based on pseudo second-order adsorption kinetics. The model has been optimized with respect to operating time in order to minimize total operating time to achieve a specified amount of phosphate removal using a fixed mass of adsorbent. The results of two-stage batch adsorber design studies showed that the required times for specified amounts of phosphate removal significantly decreased. It is particularly suitable for low-cost adsorbents/adsorption systems when minimising operating time is a major operational and design criterion, such as, for highly congested industrial sites in which significant volume of effluent need to be treated in the minimum amount of time.

Kinetics of Chromium Sorption on Biomass Fungi from Aqueous Solution

The kinetics of chromium ions sorption from aqueous solution on fungi biomass have been investigated in a batch system. The experimental data were analysed based on an intraparticle diffusion equation and a pseudo-second-order mechanism, in order to predict the constant rate of sorption and the equilibrium capacity with the effect of initial chromium ions concentration, temperature and initial solution pH. The results indicate that the sorption mechanism is described by a pseudo-second order equation. Intraparticule diffusion was signifiant in the lower concentration systems. The sorption of chromium onto the biomass fungi sorbent is favoured at higher concentrations of chromium solution, low temperatures. An activation energy of sorption was evaluted as 11.7 Kj.mol-1 for the sorption of chromium ions on fungi biomass. The results show that the sorption of the chromium ions on fungi biomass is exothermic nature process.

Determination of the equilibrium, kinetic and thermodynamic parameters of adsorption of copper(II) ions onto seeds of Capsicum annuum

Adsorption of copper ions onto Capsicum annuum (red pepper) seeds was investigated with the variation in the parameters of pH, contact time, adsorbent and copper(II) concentrations and temperature. The nature of the possible adsorbent and metal ion interactions was examined by the FTIR technique. The copper(II) adsorption equilibrium was attained within 60 min. Adsorption of copper(II) ions onto C. annuum seeds followed by the Langmuir, Freundlich and Dubinin–Radushkevich (D–R) isotherm models. Maximum adsorption capacity ( q max) of copper(II) ions onto red pepper seeds was 4.47 × 10 −4 mol g −1 at 50 °C. Three kinetic models including the pseudo-first-order, pseudo-second-order and intraparticle diffusion equations were selected to follow the adsorption process. Kinetic parameters such as rate constants, equilibrium adsorption capacities and related correlation coefficients, for each kinetic model were calculated and discussed. It was indicated that the adsorption of copper(II) ions onto C. annuum seeds could be described by the pseudo-second-order kinetic model and also followed the intraparticle diffusion model up to 60 min, but diffusion is not only the rate controlling step. Thermodynamics parameters such as the change of free energy, enthalpy and entropy were also evaluated for the adsorption of copper(II) ions onto C. annuum seeds.

Effects of calcium competition on lead sorption by palm kernel fibre

The kinetics of sorption of a mono-solute of lead ions and of a bi-solute of lead and calcium ions onto palm kernel fibre was investigated in a batch system. The experimental data were analysed based on an intraparticle diffusion equation and a pseudo-second-order mechanism, in both the mono- and bi-solute sorption systems, in order to predict the rate constant of sorption, the equilibrium capacity, and the initial sorption rate. The results indicate that the sorption mechanism is described by a pseudo-second-order equation. Intraparticle diffusion was significant in the lower-concentration systems. In addition, a modified intraparticle diffusion equation was applied to the sorption systems.

Two-stage batch sorber design using second-order kinetic model for the sorption of metal complex dyes onto pine sawdust

The sorption of metal complex dyes, metal complex blue (MCB) and metal complex yellow (MCY), onto pine sawdust in a batch sorber has been studied. A model has been used for the design of a two-stage batch sorber based on pseudo second-order sorption kinetics. The model has been optimized with respect to contact time in order to minimize total contact time to achieve a fixed percentage of metal complex dyes removal. Three simplified kinetic models including pseudo first- and second-order equation, and intraparticle diffusion equation were selected to follow the sorption process. Kinetic parameters, rate constants, equilibrium sorption capacities and related correlation coefficients, for each kinetic model were calculated and discussed. It was shown that the sorption of metal complex dyes could be described by the pseudo second-order equation. The equilibrium data fit well in the Langmuir isotherm. Results of two-stage batch sorber design studies show that the required times for the 90% efficiencies removal of metal complex dyes are 45.9 and 22.4 min for MCB and MCY, respectively.

A kinetic study of metal complex dye sorption onto pine sawdust

The removal of metal complex dyes, Metal Complex Blue (MCB) and Metal Complex Yellow (MCY), from aqueous solutions by pine sawdust has been studied in single component sorption systems. The aim of this study was to understand the mechanisms that govern metal complex dyes removal and find a appropriate model for the kinetics of removal in a batch reactor. In order to investigate the mechanism of sorption and potential rate controlling steps, pseuso first- and second-order equations, intraparticle diffusion equation and the Elovich equation have been used to test experimental data. Kinetic analysis of the four models has been carried out for system variables—particle size and mass of sawdust, pH and initial dye concentration. The rate constants for the four models have been determined and the correlation coefficients have been calculated in order to assess which model provides the best fit predicted data with experimental results. Both pseudo second-order equation and the Elovich equation provide the best fit to experimental data.