Linear Adsorption Isotherm Research Articles

Simulation of Ca2+ and Mg2+ removal process in fixed-bed column of natural zeolite

In this research, an explicit finite difference scheme is assessed for solving non-linear governing differential equation of contaminant transport to simulate the removal process of Ca2+ and Mg2+ within a fixed-bed zeolite column. Experiments were carried out in a continuous system at pH 7.5, with five samples at concentrations of 120, 50 ppm for Ca2+ and Mg2+, respectively. The required parameters for Langmuir isotherms were obtained using batch experiments. The distribution coefficient of linear adsorption isotherm was evaluated through calibrating the proposed numerical model. In the calibration, the parameter adjusted to obtain the most suitable distribution coefficient by which outflow solution concentration best fits the experimental results. Furthermore, the dispersion coefficient was evaluated using an empirical relationship to calculate dispersivity. The comparison of the proposed numerical model and experimental results indicated that the proposed numerical model that uses linear adsorption isotherm and the utilized empirical relationship to determine dispersivity has considerable capability to simulate Ca2+ and Mg2+ removal processes in fixed-bed column.

Assessment of phenol infiltration resilience in soil media by HYDRUS-1D transport model for a waste discharge site

The movement of contaminants through soil imparts a variety of geo-environmental problem inclusive of lithospheric pollution. Near-surface aquifers are often vulnerable to contamination from surface source if overlying soil possesses poor resilience or contaminant attenuation capacity. The prediction of contaminant transport through soil is urged to protect groundwater from sources of pollutants. Using field simulation through column experiments and mathematical modeling like HYDRUS-1D, assessment of soil resilience and movement of contaminants through the subsurface to reach aquifers can be predicted. An outfall site of effluents of a coke oven plant comprising of alarming concentration of phenol (4-12.2 mg/L) have been considered for studying groundwater condition and quality, in situ soil characterization, and effluent characterization. Hydrogeological feature suggests the presence of near-surface aquifers at the effluent discharge site. Analysis of groundwater of nearby locality reveals the phenol concentration (0.11-0.75 mg/L) exceeded the prescribed limit of WHO specification (0.002 mg/L). The in situ soil, used in column experiment, possess higher saturated hydraulic conductivity (KS = 5.25 × 10(-4) cm/s). The soil containing 47 % silt, 11 % clay, and 1.54% organic carbon content was found to be a poor absorber of phenol (24 mg/kg). The linear phenol adsorption isotherm model showed the best fit (R(2) = 0.977, RMSE = 1.057) to the test results. Column experiments revealed that the phenol removal percent and the length of the mass transfer zone increased with increasing bed heights. The overall phenol adsorption efficiency was found to be 42-49%. Breakthrough curves (BTCs) predicted by HYDRUS-1D model appears to be close fitting with the BTCs derived from the column experiments. The phenol BTC predicted by the HYDRUS-1D model for 1.2 m depth subsurface soil, i.e., up to the depth of groundwater in the study area, showed that the exhaustion point was reached within 12 days of elapsed time. This clearly demonstrated poor attenuation capacity of the soil to retard migration of phenol to the groundwater from the surface outfall site. Suitable liner, based on these data, may be designed to inhibit subsurface transport of phenol and thereby to protect precious groundwater from contamination.

Analytical solution of a two-dimensional model of liquid chromatography including moment analysis

This work presents an analysis of a two-dimensional model of a liquid chromatographic column. Constant flow rates and linear adsorption isotherms are assumed. Different sets of boundary conditions are considered, including injections through inner and outer regions of the column inlet cross section. The finite Hankel transform technique in combination with the Laplace transform method is applied to solve the model equations. The developed analytical solutions illustrate the influence and quantify the magnitude of the solute transport in the radial direction. Comparing Dirichlet and Danckwerts boundary conditions, the predicted elution profiles differ significantly for large axial dispersion coefficients. For further analysis of the solute transport behavior, the temporal moments up to the fourth order are derived from the Laplace-transformed solutions. The analytical solutions for the concentration profiles and the moments are in good agreement with the numerical solutions of a high resolution flux limiting finite volume scheme. Results of different case studies are presented and discussed covering a wide range of mass transfer characteristics. The derived analytical solutions provide useful tools to quantify jointly occurring longitudinal and radial dispersion effects.

Removal of 99Tc(VII) by organo-modified bentonite

99Technetium is one of the largest components of nuclear waste material. In aqueous solutions 99Tc is present as the pertechnetate oxoanion, 99TcO4−, which is highly soluble and mobile in groundwater under oxidizing conditions, thus posing a major environmental concern. In this study, a series of organo-modified bentonite clay samples was tested as adsorbents for the removal of radioactive 99TcO4− from aqueous solution at room temperature. The influence of the hexadecyl trimethylammonium (HDTMA)/bentonite ratio on the adsorption ability of the organobentonites was investigated. It was found that the adsorbent in which the exchangeable cations were only partially substituted with HDTMA showed very low affinity toward pertechnetate. On the other hand, the adsorbents in which the HDTMA loading exceeded the cation exchange capacity (CEC) value had high efficiency. The behavior of such adsorbents was best described by a Freundlich isotherm, while for the sample in which the HDTMA loading was equal to the CEC, the linear adsorption isotherm was the most appropriate. The difference in adsorption performance of several adsorbents was discussed from the point of view of the interlayer arrangement of the HDTMA. The kinetics of pertechnetate adsorption on HDTMA–bentonites was tested and analyzed using different surface reaction- and diffusion-based kinetic models. For all the investigated adsorbents, the most appropriate kinetic model was the pseudo-second-order kinetics model. The obtained adsorption capacities were and HDTMA-bentonites with HDTMA loadings exceeding CEC value should be regarded as very promising adsorbents for the remediation of 99Tc polluted waters.

Effect of temperature on the equilibrium and kinetics of galactose, glucose, and lactose adsorption on a cation exchanger

AbstractGalacto-oligosaccharides are typically produced by an enzymatic reaction when the post-reaction mixture contains considerable amounts of lactose and glucose and a smaller amount of galactose. In order to develop a process of chromatographic removal of saccharide impurities, adsorption equilibria and kinetics of these di- and monosaccharides were investigated for Diaion UBK 530, an industrialgrade strong cation-exchanger in the Na+ form. Frontal chromatographic experiments were carried out in the temperature range of 30–70°C and a broad interval of saccharide concentrations up to 350 g L−1. Breakthrough curves were described using the equilibrium-dispersive model with the linear adsorption isotherm. Both the distribution and the axial dispersion coefficient values depended on the saccharide molecule type and size. No significant effect of temperature or concentration on the distribution coefficient was observed. The apparent dispersion coefficients of all saccharides exhibited some decrease with the temperature, which was caused by the decrease of the intraparticle mass transfer resistance. An analysis showed that both the intraparticle mass transfer and the axial dispersion had a significant influence on the front dispersion.

Thermodynamic Properties of Chromium (III) Ion Adsorption by Sweet Orange (<i>Citrus sinensis</i>) Peels

The adsorption of Cr (III) ion from aqueous solution using orange peels as adsorbent was investigated using batch equilibrium technique. The research is significant as it’s aimed at investigating the suitability of orange peel, a waste product as adsorbent for the adsorption of Cr (III) ions from aqueous solution. Orange peel as an adsorbent is resource-saving and has an environmental friendly behavior. Adsorption envelope experiment was conducted using a constant Cr (III) ion concentration of 0.1 M, adsorbent dose of 2.5 g and a temperature of 30°C at varying solution pH of 2, 4, 7, 9 and 12 respectively with pH of 2 having the highest adsorption and therefore it was selected for use in the adsorption isotherm experiment. Adsorption isotherm experiment was conducted at varying temperatures (30°C, 40°C, 50°C, 60°C), concentration (0.1 M, 0.2 M and 0.3 M) Cr(NO3)3. Thermodynamic parameters such as ΔG, ΔH, ΔHr, ΔA, and ΔS were calculated from the experimental data which showed that the adsorption process is feasible, spontaneous and followed physisorption mechanism 9H2O and adsorbent dosage (1 g, 1.5 g and 2 g) respectively. The experimental results were tested using Langmuir, Freundlich, Linear and Temkin adsorption isotherm models. The experimental data best fitted the Freundlich isotherm model. The experimental results revealed the suitability of orange peel which is a waste product as effective adsorbent for the sorption of chromium (III) ions from aqueous solution.

Analytical solutions and moment analysis of general rate model for linear liquid chromatography

The general rate model (GRM) is considered to be a comprehensive and reliable mathematical model for describing the separation and mass transfer processes of solutes in chromatographic columns. However, the numerical solution of model equations is complicated and time consuming. This paper presents analytical solutions of the GRM for linear adsorption isotherms and different sets of boundary conditions at the column inlet and outlet. The analytical solutions are obtained by means of the Laplace transformation. Numerical Laplace inversion is used to transform back the solution in the time domain because analytical inversion cannot be obtained. The first four temporal moments are derived analytically using the Laplace domain solutions. The moments of GRM are utilized to analyze the retention times, band broadenings, front asymmetries and kurtosis of the elution profiles. Relationships are derived among the kinetic parameters to match the first four moments of GRM and the simpler lumped kinetic model (LKM). For validation, the analytical solutions are compared with numerical solutions of a second order finite volume scheme. Good agreements in the results verify the correctness of analytical solutions and the accuracy of the numerical scheme.

Rhamnolipid surface thermodynamic properties and transport in agricultural soil

Rhamnolipid is a biosurfactant produced by several Pseudomonas species, which can wet hydrophobic soils by lowering the cohesive and/or adhesive surface tension. Because of its biodegradability, rhamnolipid applications bring minimal adverse impact on the soil and groundwater as compared with that of chemical wetting agents. Subsequently, rhamnolipid applications have more advantages when used to improve irrigation in the agricultural soil, especially under draught conditions. In the presence of rhamnolipid, water surface tension dropped linearly with the increase of rhamnolipid concentration until the rhamnolipid critical micelle concentration (CMC) of 30mg/L was reached. Below the CMC, rhamnolipid had linear adsorption isotherms on the soil with a partition coefficient of 0.126L/kg. Rhamnolipid transport breakthrough curves had a broad and diffuse infiltration front, indicating retention of rhamnolipid on the soil increased with time. Rhamnolipid transport was found to be well represented by the advection–dispersion equation based on a local equilibrium assumption. When applied at concentrations above the CMC, the formed rhamnolipid micelles prevented rhamnolipid adsorption (both equilibrium adsorption and kinetic adsorption) in the soil. It was discovered in this research that rhamnolipid surface thermodynamic properties played the key role in controlling rhamnolipid transport. The attractive forces between rhamnolipid molecules contributed to micelle formation and facilitated rhamnolipid transport.

Analytical solutions and moment analysis of chromatographic models for rectangular pulse injections

This work focuses on the analysis of two standard liquid chromatographic models, namely the lumped kinetic model and the equilibrium dispersive model. Analytical solutions, obtained by means of Laplace transformation, are derived for rectangular single solute concentration pulses of finite length and breakthrough curves injected under linear conditions. In order to analyze the solute transport behavior by means of the two models, the temporal moments up to fourth order are calculated from the Laplace-transformed solutions. The limiting cases of continuous injection and negligible mass transfer limitations are evaluated. For validation, the analytical solutions are compared with the numerical solutions of models using the discontinuous Galerkin finite element method. Results of different case studies are discussed for linear and nonlinear adsorption isotherms. The discontinuous Galerkin method is employed to obtain moments for both linear and nonlinear models numerically. Analytically and numerically determined concentration profiles and moments were found to be in good agreement.

Adsorption of Hg2+ Ions onto Super Paramagnetic Poly (Acrylamide-co-Crotonic Acid) Hydrogel: Kinetic and Thermodynamic Studies

The sorption efficiency of super paramagnetic nano iron oxide loaded poly (acrylamide-co- crotonic acid) hydrogel (super paramagnetic PAC hydrogel), for toxic Hg2+ ions from aqueous solutions has been investigated as a function of appropriate equilibrium time, adsorbent dose, temperature, adsorbate concentrations and pH in a batch system. The synthesized copolymer was magnetized insitu and the size, structure and coating of magnetic nano particles were characterized by TEM, XRD and FTIR analysis respectively. Different thermodynamic parameters ΔG0, ΔH0 and ΔS0 have also been evaluated and it has been found that the sorption was feasible, spontaneous and exothermic in nature. The kinetics of the sorption was analyzed using the pseudo-first-order and pseudo-second-order kinetic models. Kinetic parameters, rate constants, equilibrium sorption capacities and related correlation coefficients for each kinetic model were calculated and discussed. The sorption data was analyzed and fitted to linearized adsorption isotherm of the Langmuir, Freundlich and Temkin equations respectively. Equilibrium data fitted very well to the Freundlich model. This hydrogel has been found to be an efficient adsorbent for toxic Hg2+ ions removal from water (>92% removal) and could be regenerated efficiently and used repeatedly for further experiments.

Facile optimization for chromatographic separation of liquiritin and liquiritigenin

A reversed phase chromatographic system, composed of a stationary phase of C18 silica gel (ODS, 20μm) and a mobile phase of ethanol/water, was used to separate liquiritin and liquiritigenin in the raw material of flavonoids. The linear adsorption isotherm and the equilibrium-dispersive model were adopted to approximatively describe the chromatographic separation behaviors of liquiritin and liquiritigenin in the raw material under different column temperatures, ethanol contents and flow rates of the mobile phase, sample concentrations and feeding times. Combined with orthogonal design, the ED model was used to optimize the chromatographic separating conditions, the corresponding experimental result with a good agreement was obtained and the overload separation was realized.

Adsorption of nickel by Indian soils

Adsorption of metals from liquid into solid phase is one of the most important chemical processes which affect the behaviour and bioavailability of metals in soils, thereby exerts a major influence on their uptake by plant roots. Indian soils, representing the various soil types of tropics, were subjected to Ni treatment of different concentrations and equilibrated at room temperature. The Ni adsorbed by each soil was calculated as the difference between the amount of Ni present in the solution initially and that remaining after equilibration. Results indicated that all the soils under study follow Freundlich and linear adsorption isotherms with highly significant positive correlation. In general, adsorption capacity of the soils for Ni increased with an increase in pH of the soil, whereas, the reverse was found to be true for the rate of adsorption. Significant positive correlations (p = 0.1 – 0.001) were obtained between Freundlich’s K (adsorption capacity) and pH, CEC and CaCO 3 content of the soils. Also, eight soils of Maharashtra, India, were found to fit in all the three adsorption isotherms, namely, Freundlich, Langmuir and linear. The distribution coefficient (K d ) values of these soils, in general, increased with an increase in pH and CEC of the soils. Adsorption of Ni in soils followed the order: vertisol > entisol > alfisol/ultisol.

Theoretical study of using simulated moving bed chromatography to separate intermediately eluting target compounds

This study deals with the separation of ternary mixtures based on Simulated Moving Bed chromatography to isolate target components with intermediate adsorption strength. To overcome the limitations of conventional SMB systems, which are designed for binary separations and unable to perform center-cut separations, several modifications have been proposed. The purpose of this study was to provide a theoretical comparison of several of advanced SMB configurations capable to separate ternary mixtures. Emphasis is given to those techniques, which have already been used in practice, and to those having potential for future industrial application. SMB cascades connected in series via the extract or raffinate ports of the first unit are analyzed and compared are as well as an integrated 8-zone SMB unit with internal recycle. Additionally, the commercialized pseudo SMB process (JO process) was evaluated. The performance of these modified SMB systems was investigated based on the assumption of linear adsorption isotherms for all three components considering three separation problems characterized by different separation difficulty. Besides the influence of separation factors, the concentrations of the impurities in the feed mixture and the purity requirements for the target product were studied systematically.

Adsorbents and columns in analytical high‐performance liquid chromatography: A perspective with regard to development and understanding

A brief historical survey is presented on the evaluation of silica adsorbents in analytical HPLC. The theory of analytical HPLC is mostly still being based on the height equivalent to a theoretical plate concept and the van Deemter equation that was derived from gas phase adsorption involving a linear adsorption isotherm and fast mass transfer kinetics. One can obviously wonder whether the use of the van Deemter equation is relevant and valid for the evaluation of the performance of HPLC systems, where most often the liquid solutes involve charged molecules in electrolytes and in very many cases the adsorbates are macromolecules having diffusion coefficients of small magnitude. Instead of the van Deemter equation, a multi-scale modelling approach that involves microscopic and macroscopic dynamic non-linear mass-transfer-rate models should be employed. Furthermore, advanced experimental methods for the characterisation of porous media and the distribution of the density of immobilised active sites (e.g., ligands) on surfaces as well as microscopic pore-network modelling and molecular dynamics modelling and simulation methods could be used for the design of novel adsorbents whose porous structures and immobilised active sites would provide effective mass transport and adsorption rates for realising efficient separations as well as high dynamic capacities when larger throughputs are required.

Nanoporous Polymeric Material for Remediation of PAHs Polluted Water

A new nanoporous polymer was prepared using non covalent molecular imprinting technique to remediate PAHs contaminated water. The molecularly imprinted polymer (MIP) microspheres size range between 10 and 20 μm were synthesized in acetonitrile using 4 PAHs mix as the template, methacrylic acid as the functional monomer, and ethylene glycol dimethacrylate as the cross-linking monomer. The removal efficiency of the nanoporous polymeric material (NPM) for mixed PAHs (benzo[a]anthracene, benzo[a]pyrene, benzo[k]fluoranthene, and chrysene) was studied using adsorption equilibrium experiments. The linear adsorption isotherm and the independent adsorption in binary isotherm indicated that the selected PAHs are mainly adsorbed onto the NPM by a partition mechanism. The adsorption capacity of the NPM (4.25 μg g−1) was 3-fold higher than the commercially used activated carbon. Washing with methanol/acetic acid, the NPM could be regenerated for re-adsorption of PAHs. No significant decline in the PAHs removal efficiency of the NPM was observed repeated used for 25 adsorption-desorption cycles. This study demonstrated that the NPM has potential to remediate PAHs polluted water.

Bypass chromatography – design and analysis of an improved strategy for operating batch chromatography processes

The possibility to improve the performance of batch chromatographic separations by using so-called bypass method is analyzed for the first time. In bypass chromatography, only a part of the feed is introduced into the column and purified to purity larger than the desired value. The resulting fractions are then blended with fresh feed to match the given purity constraints. A general approach is presented for designing bypass batch chromatography. Analytical design equations, based on equilibrium theory of chromatography, are presented for the case of binary systems with linear or competitive Langmuir adsorption isotherms under ideal conditions. The approach allows direct calculation of optimal loading and amount of bypass so that arbitrary purity requirements are satisfied without waste streams. It is shown that the bypass strategy enhances productivity of batch chromatography without an increase in the eluent consumption. In the case of a Langmuir isotherm, maximum productivity and minimum eluent consumption are always obtained when the less retained component is collected from the column at 100% purity. In contrast, the optimal purity of the second fraction from the column is typically less than 100% and depends on the purity constraint of the more retained component. In the case of linear isotherms, operation with touching bands is preferred.

Tracer adsorption in sand-tank experiments of saltwater up-coning

Summary This study aims to substantiate otherwise unresolved double-peaked plumes produced in recent saltwater up-coning experiments (see Jakovovic et al. (2011) , Numerical modelling of saltwater up-coning: Comparison with experimental laboratory observations, Journal of Hydrology 402, 261–273) through additional laboratory testing and numerical modelling. Laboratory experimentation successfully reproduced the double-peaked plume demonstrating that this phenomenon was not an experimental nuance in previous experiments. Numerical modelling by Jakovovic et al. (2011) was extended by considering adsorption effects, which were needed to explain the observed up-coning double peaks of both previous and current laboratory experiments. A linear adsorption isotherm was applied in predicting dye tracer (Rhodamine WT) behaviour in the sand-tank experiments using adsorption parameters obtained experimentally. The same adsorption parameters were tested on all laboratory experiments and it was found that adsorption had insignificant effect on experiments with high pumping rates. However, low pumping rates produced pronounced spatial velocity variations within the dense salt plume beneath the pumping well, with velocities within the plume increasing from the centre of the plume towards the interface. The dye tracer was retarded relative to the salt and was transported preferentially along the higher-velocity paths (i.e. along the edges of the salt plume) towards the well forming double-peaked up-coning patterns. This illustrates the sensitive adsorptive nature of Rhodamine WT and that care should be taken when it is used in similar sand-tank experiments. Observations from this study offer insight into the separation of chemicals in natural systems due to different adsorption characteristics and under conditions of density-dependent flow.

Two-dimensional numerical finite volume modeling of processes controlling distribution and natural attenuation of BTX in the saturated zone of a simulated semi-confined aquifer

This paper presents a two-dimensional finite volume model to predict multi-species reactive transport processes in the saturated zone of a simulated semi-confined aquifer. A multipurpose commercial software called PHOENICS was used to solve model equations numerically. Capability of the present model was first confirmed using experimental data and the results obtained by a published one-dimensional finite element reactive transport model by other researchers taking different scenarios into consideration. The model was then expanded to a two-dimensional case to simulate reactive transport of BTX compounds with discontinuous source in the saturated zone of the groundwater flow system. In addition to the physical transport processes, the two-dimensional model also incorporates linear and nonlinear adsorption isotherms, first order and Monod kinetics. The two-dimensional model considers both static and dynamics modes into account. The results show that considering chemical reactions during reactive transport of contaminants could successfully predict the contaminated zone. The results of such studies can be used for monitoring of contaminated areas, designing methods to control pollution transport, and minimize its harmful effects on aquifer systems.

Quantification of the adsorption of phenolic compounds on the geotextile and bentonite components of four geosynthetic clay liners

ABSTRACT: The aim of this paper is to present the experimental results obtained regarding the adsorption on various constitutive geotextiles and bentonites of geosynthetic clay liners of phenol, o-cresol, p-cresol, 2-chlorophenol, 4-chlorophenol, 2,4-dimethylphenol, 3,4-dimethylphenol, 2,4-dichlorophenol, 2,4,6-trichlorophenol, 2,3,4,6-tetrachlorophenol, 2,3,5,6-tetrachlorophenol, pentachlorophenol, and bisphenol A. These contaminants, including certain derivatives of halogenated phenols, are known to be toxic even at very low concentrations. Geotextiles and bentonites were sampled from four geosynthetic clay liners (GCLs) representative of the GCLs commonly used in bottom liner systems in France. Adsorption was studied through batch adsorption tests. The effect of the nature of the bentonite (sodium versus calcium activated) was studied. Results obtained in this study show that, contrary to what has been observed for volatile organic compounds (VOCs), the adsorption isotherms are non-linear. For VOCs, linear adsorption isotherms are obtained both for geotextiles and for bentonites. The contrast between the adsorption on geotextiles and bentonites is smaller than for VOCs. Up to two orders of magnitude difference can be obtained between the low adsorption coefficient for bentonite as compared with the large adsorption coefficient for geotextiles when adsorption of VOCs is considered. For phenolic compounds, the adsorption coefficients are of the same order of magnitude for bentonite and geotextiles. Two different trends were observed for woven and nonwoven needle-punched geotextiles as regards the adsorption parameters measured. For chlorophenols, polarity appears to affect adsorption: the adsorption coefficients increased with increasing number of chlorine atoms.

Determination of adsorption isotherm and diffusion coefficient of toluene on activated carbon at low concentrations

Adsorption is one of the most effective technologies for indoor gas pollutant removal. To guide the design and modeling of sorbent-based air cleaners, it is necessary to characterize a sorbent material (e.g., activated carbon) in advance. A new dynamic volumetric adsorption test method was developed in this study. The adsorption capacity of toluene on activated carbon was determined in the concentration range of 0.1–100 ppm at three relative humidity conditions (20%, 50%, and 80%). The obtained adsorption isotherm was used to evaluate the validity of Langmuir model, Freundlich model and Dubinin-Radushkevich (D-R) model, respectively. Langmuir model gave the best fit. A linear adsorption isotherm was observed when the concentration was below 1.5 ppm. The measured data was then used to determine the model parameters (partition coefficient, mass transfer coefficient and diffusion coefficient) by least-square fitting to a mechanistic numerical model. Results show that the diffusion coefficient increases with increased concentration, indicating the dominating role of surface diffusion during VOC adsorption on activated carbon.