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.

Adsorption of p-Cresol by three different activated carbons was carried out at 301 K and at controlled pH conditions. Langmuir-Freundlich isotherm equations were studied and relative parameters were found. In acidic conditions that pH of solution is well below the pKa of p-cresol (in molecular form), it was observed that the adsorb ate solubility and the electron density of aromatic ring were the influencing factors on the extent of the adsorption by affecting the extent of London dispersion forces. It was found that the uptake of the molecular form of the aromatic solute was dependent on the PZC and surface area of the carbon. In higher solution pH conditions (in ionic form), the electrostatic forces played a significant role on the extent of adsorption. The effect of pH must be considered from its combined effects on the carbon surface and on the solute molecules. Adsorption capacity (Qmax) and affinity (K) decrease with pH. Adsorption of the solute in higher pH values was found to be dependent on the concentration of anionic form of the solute. All isotherms were fitted in to Langmuir-Freundlich isotherm equations to find the relative factors.

Heavy metals are present in different types of industrial effluents, being responsible for environmental pollution. Biosorption is a promising alternative method to treat industrial effluents, mainly because of its low cost and high metal binding capacity. In this work application of Langmuir and Freundlich sorption models for chromium, copper and nickel biosorption process by Sargassum seaweed biomass was studied in batch system. The work considered the effects of some important parameters such as retention time and initial concentration on remained concentration of heavy metals. Dried Sargassum was contacted with metal solution on different retention times (10, 20, 30, 45 and 60 min) and variation of initial concentration (10, 25, 50, 75 and100mg/l) at constant pH and temperature. The obtained charts were linear for Langmuir and Freundlich equilibriums and their slopes and y-intercepts were calculated (Constants a, b, n, k). Results showed that the constants were in a same range; therefore Langmuir and Freundlich sorption models were in good agreement with experimental results.

In this work, the micro powder was the product of cedar leaf (MPCL) is used as a low-cost adsorbent for the removal of Pb2+ions from aqueous solutions. Bath experiments were used to determine the best adsorption conditions The adsorption percentage of Pb2+ions MPCLsamples at different initial pH, contact time (tc), adsorbent dosage and temperature (T) were investigated. Effective removal of metal ions was demonstrated at pH values of 5. Metal adsorption onto MPCLwas evaluated by Langmuir and Freundlich isotherms. Results indicate that the Langmuir isotherm model is the most suitable one for the adsorption process using MPCL (R2=0.9987), thus indicating the applicability of monolayer coverage of Pb (II) ion on MPCL surface. The relationship between thermodynamic parameters was used to predict the absorption process. According to Thermodynamic analysis, the process exothermic and natural (DH=-21.65 kJmol-1 and DS=- 56.4 Jmol-1 K-1).

Quality water resources are limited. The use of biological adsorbents in reducing water salinity is a new and environmentally friendly method. The purpose of this article is to determine the amount of salinity removal by the rice husk adsorbent and estimate the amount of absorption by Freundlich and Langmuir adsorption isotherm models and their evaluation. In this study, a tank (part of the physical model) with a height of approximately 50 cm and a diameter of 20 cm was used, and it was divided into two parts based on the height of the tank. In the center of the location of the absorber under study, a specific thickness of 8 cm was considered. On both sides of the absorbent layer, either upwards (reservoir surface) or downwards (reservoir bottom), layers of silica sand with 0.3, 0.6 and 1 cm granularity were placed in a height of 5 cm. Water quality treatments including calcium and magnesium, sodium and chlorine (salinity) at four salinity concentrations of 0.2, 0.5, 0.7 and 1 dS/m were passed through the rice husk adsorbent and the amount of cat ions and anions absorbed by the adsorbent It was measured. The results showed that for different concentrations, absorption is very high at the beginning and decreases over time. The equilibrium time for qualitative parameters of calcium and magnesium, sodium and chlorine obtained between 60 and 90 (at a water temperature of 25 degrees Celsius and an acidity of 7.4) minutes. The results showed that on average, a high percentage of calcium, magnesium and sodium cat ions in water (about 50-60%) have been absorbed by rice husk. The results of the adsorption isotherm model showed that the adsorption isotherm model of the Freundlich has a better estimate than the Langmuir model (10 to 15 percent).

Organic pollutants, such as dyes, widely used in textile, dyeing, and chemical industries, pose significant risks to human health and the environment if introduced into water resources. In modeling the transport of dissolved pollutants, three processes are commonly considered: advection, dispersion, and chemical mechanisms. Studies have shown that the third mechanism is often overlooked in practical modeling. Additionally, qualitative models are calibrated based on limited data, making their parameters subject to uncertainty. In this study, the Freundlich and Langmuir isotherms were analyzed. First, their parameters were estimated and calibrated using a simple optimization model. To analyze parameter uncertainty, a Bayesian approach employing the Markov Chain Monte Carlo method was adopted, utilizing the Metropolis-Hastings and Gibbs algorithms, and the results were compared. The study was conducted based on experimental data for the adsorption of Malachite Green onto activated carbon. While laboratory data allow for precise control of conditions, they may not fully represent field data due to scale and environmental constraints. Therefore, extending this research to field data could enhance the generalizability of the results and prove valuable in high-accuracy engineering designs and environmental management. The results indicated that the Langmuir isotherm performed better than the Freundlich isotherm at all temperatures, providing lower RMSE values. For instance, at 323 K, the Langmuir model demonstrated 13. 55 units more accuracy than the Freundlich model. Confidence interval analysis revealed that the Metropolis-Hastings algorithm generally produced narrower and more symmetrical intervals, yielding more precise estimates. For example, for the KL parameter of the Langmuir model at 323 K, the 95% confidence interval obtained using the Metropolis-Hastings algorithm was [0. 03, 0. 04], compared to [0. 007, 0. 05] with the Gibbs algorithm. However, the Gibbs algorithm exhibited a higher convergence speed, making it suitable for scenarios where computational efficiency is a priority. The Metropolis algorithm’s runtime was 5. 8 times that of the Gibbs algorithm. This study highlights the superiority of the Langmuir model and the Metropolis-Hastings algorithm in adsorption data analysis and uncertainty evaluation.