Adsorption plays an important role in water and wastewater treatment. The analysis and design of processes that involve adsorption rely on the availability of isotherms that describe these adsorption processes. Adsorption isotherms are usually estimated empirically from measurements of the adsorption process variables. Unfortunately, these measurements are usually contaminated with errors that degrade the accuracy of estimated isotherms. Therefore, these errors need to be filtered for improved isotherm estimation accuracy. Multiscale wavelet based filtering has been shown to be a powerful filtering tool. In this work, multiscale filtering is utilized to improve the estimation accuracy of the Freundlich adsorption isotherm in the presence of measurement noise in the data by developing a multiscale algorithm for the estimation of Freundlich isotherm parameters. The idea behind the algorithm is to use multiscale filtering to filter the data at different scales, use the filtered data from all scales to construct multiple isotherms and then select among all scales the isotherm that best represents the data based on a cross validation mean squares error criterion. The developed multiscale isotherm estimation algorithm is shown to outperform the conventional time-domain estimation method through a simulated example.

Liquid-phases adsorption equilibrium of phenol onto two naturally available soils namely Kalathur soil (Kr) and Adhanur soil (Ar) were studied. The experimental data were analyzed using fourteen isotherm models, ranging from single-parametric model to multi-parametric models (up to 5 parameters) of the system. Results show that in general the accuracy of models to fit experimental data improves with the degree of freedom. To understand the mechanism involved with different types of sorbate-sorbent system as well as to find out the best fitting isotherm model, the correlation coefficients, and average percentage error and student t-test were carried out. Temkin isotherm model, Langmuir-Freundlich isotherm model and Fritz-Schlunder model as well as Baudu model were found to be the best fit models amongst the two-parametric models, three parametric models and four parametric isotherms modeling, respectively. This study brings out the need of simultaneous solution of multi-parametric equations (using relevant softwares, MATLAB, in present case) than solution of their linearized forms, which is mostly followed by contemporary investigators.

The removing of ferric ions (Fe3+) from aqueous solution using natural feldspar (NF) has been studied in a batch operation mode. The factors affecting of the sorption equilibrium, such as contact time, initial concentration of the ferric ions (Fe3+), feldspar dosage concentration and temperature, were investigated. The maximum removal is 93 % (approx.) using low-level concentration of Fe3+ions (30 mg L-1) and high dosage concentration (40 g L-1). The adsorption equilibrium is achieved during the first 90 min. Freundlich model has successfully analyzed the equilibrium of isotherms with R 2 = 1. The adsorption mechanism of aqueous ferric ion on NF follows Freundlich isotherm models (R 2 = 0.997). The capacity (K f) and intensity (1/n) of Freundlich adsorption are 1.70 and 0.621, respectively. The results reveal that the adsorption mechanism of ferric ion on NF is chemisorptions, heterogeneous multilayer and spontaneous in nature (DG = -19.778 kJ mol-1). Adsorption reaction kinetic models, such as pseudo-first order and pseudo-second order, and adsorption diffusion model, such as Weber-Morris intraparticle diffusion model, have been used to describe the adsorption rate and mechanism of the ferric ion onto NF surface. Adsorption of ferric ion on the NF has achieved Lagergren pseudo-second-order model (R 2 = 1.0 approx.) more than Lagergren pseudo-first-order model. The kinetic parameters, rate constant and sorption capacities have been calculated. The new information in this study suggests that NF could be used as a novel filtering materials for removing ferric ions from water.

The optimization of adsorption-based operations requires an accurate model to represent the separation process. In the present study, single-component adsorption data of L-lysine on its imprinted polymer were fitted to Freundlich, Langmuir-type and Jovanovic-type models. L-Lysine imprinted polymer (LLIP) was prepared by free radical solution polymerization. The best estimate of the parameters of these models by regression analysis was obtained. The statistical analysis of results showed that the experimental data fit the Jovanovic-Freundlich mode, better than other models in terms off value. The best prediction of retention capacity equal to 0.186 mmol lysine per g of LLIP, which is the nearest value to the experimental data, was obtained by applying the Jovanovic model.

This study investigated the adsorption process of methylene blue cationic dye by silver nanoparticles synthesized using extract Tragopogon buphthalmoides. The effectiveness of various parameters, including adsorbent dosage, pH, contact time, and temperature, was evaluated in terms of their effects on the efficiency of dye removal. The study determined that the optimal conditions for dye removal were a pH of 10, an adsorbent dosage of 0.2 g, a contact time of 60 min, and a temperature of 25°C. Then, Ten different isotherm models including Langmuir, Dubinin-Radushkevich (DR), Harkins-Jura, Freundlich, Jovanovic, Temkin, Fowler-Guggenheim, Halsey, Flory-Huggins, and Hill-de Boer were performed based on the optimal conditions. The calculations were fully presented to obtain the constants of each isotherm, and for greater accuracy in selecting the dominant isotherm, some other error functions, such as SSE (sum of squared errors), MSE (mean squared error), and RMSE (root mean square error) were also used. The Freundlich and Halsey isotherms were identified as the dominant models with the highest degree of correlation coefficient (R2= 0.9913) and least error values (SSE= 0.0229, MSE= 0.00229, RMSE= 0.0047). According to the values of the isotherm constants of Freundlich, n= 1.5087 and Kf = 27.0287, it is quite clear that the adsorption process has occurred physically and there is weak interaction between the adsorbate and adsorbent due to the heterogeneous adsorption of multiple layers on the surface of the adsorbent. The Langmuir isotherm determined the qmax (maximum adsorption capacity) to be 181.8182 mg/g, and the RL (separation factor) was found to be 0.5677, indicating favorable adsorption. The results of this study showed that the order of dye adsorption conformity in the studied isotherms was Temkin