Sorption Model Research Articles

Effect of particle size on the transport of polystyrene micro- and nanoplastic particles through quartz sand under unsaturated conditions

Micro- and nanoplastics (MNPs) are contaminants of emerging concern recently found in soil ecosystems. Their presence in terrestrial environments and their migration to aquatic environments may become a risk for the health of ecosystems and, through them, of humans. Understanding the interaction between particle properties and physicochemical and hydrodynamic factors is crucial to evaluate their fate and their potential infiltration towards groundwater. This study investigates the impact of particle size on MNPs transport through sand under unsaturated conditions. Infiltration column experiments with polystyrene MNPs ranging from 120 to 10,000 nm were conducted and supported by numerical modelling to derive reactive transport parameters. Results show a significant effect of particle size on the transport of MNPs, with higher recovery values observed for smaller particles (120 nm; 95.11%) compared to larger particles (1,000 nm; 71.44%). No breakthrough was observed for 10,000 nm particles, indicating a complete retention within the quartz sand matrix. DLVO theory confirmed the dominance of electrostatic repulsive forces between MNPs and sand grains, suggesting an unfavourable environment for MNPs to adhere to quartz sand. Consequently, particle retention in the sand matrix occurs predominantly by physical processes. Equilibrium sorption modelling reveals that larger particles (1,000 nm) tend to be immobilized in small pores throats due to straining, resulting in lower recoveries. When they are not trapped, particles tend to travel faster through preferential flows due to a size exclusion effect, evidenced by shorter arrival times at the column outlet compared to tracers. These findings highlight the influence of particle size on the transport and retention of MNPs in quartz sand under unsaturated conditions and contribute to a better understanding of their transport dynamics and environmental fate.

Применение моделей адсорбции при исследовании поглощения ионов никеля почвой

The aim of the presented work is to study the absorption of nickel ions by soils of the Udmurt Republic using four sorption models. Humus horizons (0–20 cm) of Albeluvisols Umbric, Leptosols Rendzinic and Phaeozems Albic soils widely distributed in Udmurtia were selected as objects of nickel adsorption research. According to the Langmuir model, good sorbents are characterized by high Amax values and low – KL, therefore, the best sorbent of nickel ions is Albeluvisols Umbric (Amax=0.0562 mol/kg, KL=2075.19 dm3/mol), and a weaker absorber is Phaeozems Albic (Amax=0.0192 mol/kg, KL=19474.48 dm3/mol), Leptosols Rendzinic occupies an intermediate position (Amax=0.0289 mol/kg, KL=14766.47 dm3/mol). The negative value of the Gibbs energy (∆G=–17.97 kJ/mol for Albeluvisols Umbric, –22.59 kJ/mol for Leptosols Rendzinic and –23.24 kJ/mol for Phaeozems Albic) indicates the spontaneous nickel adsorption by soil absorbing complex (SAC). In accordance with the Freundlich model, in all types of studied soils, the nickel ion – SAC binding energy decreases as the surface is filled, herewith the studied soils are characterized by heterogeneity of sorption centers. The approximation coefficient of the Temkin model is in the range of 0.80–0.85, therefore, the discrepancy between the experimental data of the theoretical model indicates the absence of interaction between the adsorbed particles. The Dubinin – Radushkevich model allows us to determine the nature of adsorption forces, as well as the value of the average free energy of adsorption: E=8,325 kJ/mol in Albeluvisols Umbric, 9.5477 kJ/mol in Leptosols Rendzinic and 9.6296 kJ/mol in Phaeozems Albic. Consequently, chemisorption is characteristic of all soils, and proceeds by an ion-exchange mechanism.

Removal of Lead Cations by Novel Organoclays Derived from Bentonite and Amphoteric and Nonionic Surfactants.

For many decades, natural and modified clay minerals have been used as adsorbents to clean up aquatic and soil ecosystems contaminated with organic and inorganic pollutants. In this study, organoclays based on bentonite and various amphoteric and nonionic surfactants were synthesized and tested as effective sorbents for lead ions. The maximum values of R were obtained when describing the sorption processes using the Langmuir model, which ranged from 0.97 to 0.99. The adsorption of lead ions by these organoclays was investigated using different sorption models including the Langmuir, Freundlich, and BET. It was found that, according to the values of limiting adsorption to the Langmuir equation, the synthesized organoclays formed an increasing series: organoclay with cocamide diethanolamine < bentonite < organoclay with lauramine oxide < organoclay with sodium cocoiminodipropionate < organoclay with disodium cocoamphodiacetate < organoclay with alkyl polyglucoside. The Gibbs energy for all of the analyzed samples was calculated and found to be negative, indicating the spontaneity of the cation adsorption process in the forward direction. The maximum value of the adsorption capacity of lead cations on organoclay-based bentonite with alkyl polyglucoside was 1.49 ± 0.05 mmol/g according to the Langmuir model, and 0.523 ± 0.003 mmol/g as determined by the BET model. In the process of modifying bentonite, there was an increase in negative values of the zeta potential for organoclays compared to the initial mineral, which clearly enhanced their electrostatic interactions with the positively charged lead ions. It was hypothesized, based on the physicochemical principles, that exchange adsorption is the main mechanism for lead absorption. Based on chemical approaches, organoclays based on amphoteric surfactants absorb lead mainly through the mechanisms of electrostatic attraction, ion exchange, and complexation as well as the formation of insoluble precipitates. Organoclays based on nonionic surfactants, on the other hand, absorb lead through mechanisms of complexation (including chelation) and the formation of insoluble chemical precipitates. The comparison of isotherms from different models allows us to find the most accurate match between the model and the experimental data, and to better understand the nature of the processes involved.

Regulation of the co-transport of toluene and dichloromethane by adsorbed phase humic acid under different hydro-chemical conditions

The transport behavior of combined organic pollutants in soil and groundwater has attracted significant attention in recent years. Research on the influence of humic acid (HA) on organic pollutant transport behavior mainly focuses on the study of the mobile phase HA, with less research on the adsorbed phase HA, especially regarding its interaction with combined pollutants. To enhance understanding of the regulation of co-transport and retention of combined pollutants by adsorbed phase HA, in this study, tests were conducted to investigate how toluene (TOL) and dichloromethane (DCM) are transported in the presence of adsorbed phase HA at different pH levels and ionic strengths. As the proportions of HA-coated sand increased, so did its adsorption capacity for TOL and DCM, which can be attributed to adsorbed phase HA providing more adsorption sites compared to plain sand, thereby reducing the transport potential of the pollutants. The presence of both TOL and DCM facilitated their mutual transportation due to competitive adsorption controlled by the adsorbed phase HA content in the porous medium. Furthermore, it was observed that pH levels influenced the transport behavior of TOL and DCM when adsorbed phase HA was present since adsorbed phase HA transformation into mobile phase was regulated by pH levels. The transport patterns can be effectively simulated using the chemical nonequilibrium two-site sorption model in HYDRUS-1D, accurately reflecting the retardation coefficients and transport distances based on model parameters. This work sheds new light on the regulatory role of adsorbed phase HA in TOL and DCM transport under diverse hydrochemical conditions, with implications for accurately depicting the behavior of combined pollutants, optimizing the remediation strategies and improving remediation efficiency in contaminated sites.

Photoaged tire wear particles hinder the transport of Pb(II) in urban soils under acid rain: Experimental and numerical investigations

Rapid urbanization brought lots of serious environmental contamination, including the accumulation of heavy metals, acid rain, and the emission of tire wear particles (TWPs), with detrimental effects for terrestrial ecosystems. Nevertheless, how naturally aged TWPs affect the mobilization of heavy metals in soils under acid rain is still unclear. Here, we investigate the adsorption and transport mechanisms of Pb(II) co-existing with acid rainwater in soil-TWP mixtures via batch experiments, column experiments and modeling. Results showed that photoaged TWP significantly prolonged the Pb(II) adsorption equilibrium time (1 to 16 h) and enhanced the Pb(II) adsorption capacity of soils. Soil column profiles confirmed that TWP effectively boosted the initial accumulation of lead in the topsoil and thus impeded the downward transport of lead. The retardation factor (R) estimated by the linear two-site sorption model (TSM) fitting the Pb(II) breakthrough curves gradually increased from 1.098 to 16.38 in soils with TWP (0–10 %). Comparative results of linear or nonlinear TSM suggested nonlinear sorption replacing linear sorption as the main Pb(II) sorption mechanism under 1 % and 10 % TWP. This research provides significant insights into the implications of TWP on the Pb(II) retention behaviors and highlights the severer potential remobilization risks of Pb(II) in urban soils under different acid rain environments.

Migration of naphthalene in a biochar-amended bioretention facility based on HYDRUS-1D analysis

Biochar has been proved as a promising and efficient filler in bioretention facilities for enhancing the stormwater pollutants removal. However, the migration behaviors of stormwater pollutants in biochar filled bioretention facilities is unclear. In this study, as one of the most typical stormwater pollutants, naphthalene was selected as an example and a HYDRUS-1D model was first used to understand the migration behavior of naphthalene in a bioretention facility. In comparison with the conventional bioretention soil media (sandy loam), the amended biochar filled bioretention cell showed that the naphthalene removal rate was enhanced by up to 10.1%. Meanwhile, the experimental data was well-fitted by the “two-site sorption model” in HYDRUS-1D model. Another, the effect of rainfall intensity on the naphthalene migration in both bioretention columns was further investigated. The HYDRUS-1D model fitting indicated that the increase in rainfall intensity promoted naphthalene migration by increasing hydraulic conductivity and water flux. In addition, static batch experiments revealed that the biochar filled fillers achieved about 50% higher adsorption capacity than sandy loam. The sensitivity analysis from the HYDRUS-1D model data verified adsorption coefficient Kd and longitudinal dispersivity λ are the main factors affecting naphthalene migration. Finally, the model simulation displays that the proportion of naphthalene retained by the fillers was highest during high rainfall intensities, indicating that the fillers remain the most important fate for naphthalene. This study presents research on the behavior and mechanisms of stormwater pollutant transport through improved bioretention facilities.

Insights on influence of polymer molecular weight on gas sorption, transport and plasticization in glassy 6FDA-DAM polyimide membranes

It is well-known that spinning of defect-free asymmetric polyimide hollow fibers is promoted by using high polymer molecular weight. On the other hand, effects of polymer molecular weight on microstructure and separation performance of dense film 6FDA-based polyimide membranes relevant to sheath layers of composite membranes are less well-explored. In this work, gas sorption, diffusion and permeation of CO2, N2 and CH4 for 6FDA-DAM dense films are considered for 45 kDa and 176 kDa weight average molecular weights. Such molecular weights are relevant for practical hollow fiber spinning of membranes. Earlier results for polystyrene samples show similar trends in dual mode sorption model results like those noted here for the 6FDA-DAM polyimide case; however, effects on permeation like those considered here were not addressed for the polystyrene case. Here we also address actual pure and mixed gas CO2 and CH4 permeation and show higher free volumes, higher gas permeability but lower 50:50 CO2/CH4 selectivity associated with the higher molecular weight sample. Analysis using the self-consistent dual-mode sorption and transport models help understand the observed trends. Our results suggest denser packing of polymer segments exists in the Henry's law environment of the low molecular weight sample. Moreover, the higher polymer segmental packing in the Henry's law environment suppresses CO2 plasticization with a dual-mode microstructure controlling separation performance and plasticization behavior for this important member of the 6FDA polyimide family. We show evidence of effects of charge transfer complexes as possible main features in these trends. These dense film results help guide future work on dense sheath layers on composite hollow fiber membranes.

Numerical and Experimental Approach to Evaluate Microplastic Transport in Saturated Porous Media

Under varying flow rate conditions, the transport and retention of polydisperse microplastics (MPls), with an average particle size of 16 ± 6 µm, were investigated in saturated porous media. First-order reversible and irreversible kinetic sorption models were used to describe the sorption kinetics. Sensitivity analyses provided insight into the effects of each sorption parameter. Both numerical modeling and experimental measurements were utilized to evaluate the retention rates of sand filters. The influence of flow rate on sorption was reflected in variations in the distribution coefficient (Kd), the mass transfer coefficient (β), and the irreversible sorption rate (K1). Lower flow rates were associated with higher Kd and β values, indicating increased sorption and reduced mass transfer rates. An increase in Kd resulted in a more gradual sorption process, with a decrease in peak concentration, whereas changes in β had a comparatively smaller impact on sorption rate and peak concentration. Lower K1 values were linked to higher peak concentrations and decreased retention efficiency. Numerical modeling revealed retention rates of 28 ± 1% at a flow rate of 31 mL min−1 and 17 ± 1% at 65 mL min−1. The introduction of MPls into saturated sand environments modifies the transport dynamics within the medium. Consequently, these alterations affect the hydrological characteristics of porous media, impacting groundwater quality and agricultural output. The mean absolute error (MAE) of 6% between the modeled and observed retention rates indicated a high level of accuracy. This study underscores the importance of examining retention efficiency and the accuracy of numerical models in understanding MPl transport in porous media.

The effect of traditional processing craft on the hygroscopicity of palm leaf manuscripts

Palm leaf manuscripts, which are crucial carriers of historical, religious, scientific, and artistic information in East and Southeast Asia, specifically encapsulate significant aspects of Buddhist culture and thus require comprehensive research and preservation efforts. The base material of palm leaf manuscripts is processed palm leaves, which are hygroscopic and profoundly affected by environmental humidity. Currently, there is a research gap regarding the impact of traditional processing crafts and natural aging on the hygroscopicity of palm leaf manuscripts. Utilizing dynamic water vapor sorption (DVS), the hygroscopic properties of palm leaves from various years were assessed before and after traditional processing in Yunnan Province, China. The results show that traditional processing slightly increases the equilibrium moisture content (EMC) in environments with 0 to 60% relative humidity (RH), but significantly lowers EMC in high humidity environments, with reductions up to 19.01%. Additionally, hysteresis doubled post-processing, indicating enhanced stability under fluctuating humidity conditions. Sorption models suggest that traditional processing increases the number of adsorption sites while reducing physical adsorption or capillary condensation. FT-IR (Fourier-transform infrared spectroscopy) analysis indicates that the relative contents of cellulose and hemicellulose were reduced by 39.90% and 3.97%, respectively. Degradation occurring in both the crystalline and amorphous regions of cellulose. After natural aging, the hygroscopicity of processed palm leaves improved across the entire humidity range of 0 to 95%, and there was a slight increase in hysteresis. This is due to the increase in both adsorption sites and physical adsorption capabilities. FT-IR results also indicate that the relative contents of cellulose and hemicellulose were decreased by 57.52% and 19.83% after nature aging, respectively. These findings confirm that traditional processing improves the writability and humidity resilience of the leaves, while natural aging enhances their overall hygroscopic properties. This research contributes to our understanding of how humidity damages palm leaf manuscripts. aids in determining optimal RH ranges for storage, and assesses the effectiveness of consolidation treatments in their long–term preservation.

Non-Invasive, Continuous, Quantitative Detection of Solvent Content in Vacuum Tray Drying

A non-invasive capacitance instrument was embedded in the base of a vacuum-drying tray to monitor continuously the residual amount of solvent left in a pharmaceutical powder. Proof of concept was validated with Microcrystalline Cellulose laced with water, as well as water/acetone mixtures absorbed in a spray-dried Copovidone powder. To illustrate the role of impermeability of the base, we derive a model of vapor sorption that reveals the existence of a kinetic limit when solids are thinly spread, and a diffusion limit with greatly diminished effective diffusivity at large powder thickness. By monitoring the residual solvent content of powders, this new in situ technique offers advantages over indirect methods like mass spectrometry of vapor effluents, but without complications associated with probe fouling. To prescribe design guidelines and interpret signals, we model the electric field shed by the probe when a powder holds variable solvent mass fraction in the vertical direction.Graphical abstract

Differences and implications of strontium distribution coefficient on various granite compositional materials.

The distribution coefficient (Kd) of radionuclides is a crucial parameter in assessing the safety of high-level radioactive waste (HLW) geological repository. It is determined in the laboratory through batch and column experiments. However, differences in obtained Kd values from distinct experiments have not been thoroughly assessed and compared. This study evaluated strontium (Sr) sorption on different granite materials using static batch and dynamic experiments (column and core-flooding experiments). The results from batch sorption experiments showed higher Sr sorption on granite under acidic and strongly alkaline conditions, low solid-liquid ratios, and low ionic strength. In column experiments, a two-site sorption model was used to simulate Sr transport in crushed granite and mixed pure minerals. The sorption of Sr on crushed granite exhibited a higher affinity than that of mixed pure minerals. The dual-porosity transport model was employed to investigate Sr transport behavior in fractured granite in the core-flooding experiment. Kd obtained from batch sorption experiments are four to twenty times higher than those from column experiments, and two to three orders of magnitude higher than that from a core-flooding experiment. The results of this study provide valuable insights into safety assessment for the HLW geological repository.

On languaging a simulation engine: Rapid modeling of nanoporous media sorption by hierarchical language model

Language model intelligence is revolutionizing the way we program materials simulations. However, the diversity of simulation scenarios renders it challenging to precisely transform human language into a tailored simulator. Here, using three types of expert language model, we propose a language-to-simulation (Lang2Sim) framework that enables interactive navigation on languaging a simulation engine, by taking a scenario instance of water sorption in porous matrices. Unlike line-by-line coding of a target simulator, the language models interpret each simulator as an assembly of invariant tool function and its variant input–output pair. Lang2Sim enables the precise transform of textual description by functionalizing and sequentializing the language models of, respectively, rationalizing the tool categorization, customizing its input–output combinations, and distilling the simulator input into executable format. Importantly, depending on its expert type, each language model features a distinct processing of chat history to best balance its memory limit and information completeness, thus leveraging the model intelligence to unstructured nature of human request. Overall, this work establishes language model as an intelligent platform to unlock the era of languaging a simulation engine.

Beltanol Sorption Modelling in the Soil Column using High Performance Liquid Chromatography Technique

Beltanol Sorption Modelling in the Soil Column using High Performance Liquid Chromatography Technique

Trivalent lanthanide sorption onto illite in the presence of carbonate: A study combining thermodynamic sorption modeling, time-resolved laser fluorescence spectroscopy, and parallel factor analysis

Formation of aqueous actinide complexes with dissolved inorganic carbon (DIC) in groundwater decreases the sorption of actinides onto clay minerals in a geological disposal environment. Hence, the effect of DIC on actinide sorption must be evaluated quantitatively. In this study, batch sorption experiments using Eu(III) and Sm(III) as the chemical analogs of trivalent actinides were performed to assess their sorption behavior onto illite in the presence of DIC. In the studied pH region between 8.4 and 11, the sorption was significantly lower in the presence of DIC, with the largest effect being observed at pH 9–10. The effect increased with increasing DIC from 10 to 50 mM. A thermodynamic sorption model (TSM) was used to evaluate the results of batch sorption experiments. The experimental results can only be predicted when ternary-surface complexes with carbonate ions are considered. Moreover, information on the chemical forms of sorbed Eu on illite was obtained via time-resolved laser fluorescence spectroscopy (TRLFS) measurements. Parallel factor analysis of TRLFS data indicated the presence of two chemical species of Eu. These chemical species exhibited pH dependence, which is consistent with that of the surface species predicted using the TSM. In the presence of DIC, the dominant chemical species showed a long fluorescence lifetime and was inferred to coordinate with carbonate ions, supporting the validity of the TSM.

Experimental and theoretical investigation of water sorption on lemon leaves: New perspectives with statistical physical modeling

A deeper analysis of the water sorption isotherms on lemon leaves (40, 50, and 60 °C) was carried out using statistical physical modeling to obtain information about the sorption mechanism and better understand the process. For this, a theoretical model was developed based on the grand canonical potential to describe the experimental data, and the isotherms were analyzed using the finite multilayer sorption model. The experimental sorption isotherms obtained for lemon leaves are Type II. The model used to analyze the process showed excellent predictive capacity, with coefficient of determination values above 0.97 and root mean square error below 0.08. The interpretation of the estimated parameters indicated that the water molecules are parallel to the surface of the lemon leaves, which allows the formation of finite layers of water. The system is directly affected by temperature, where increasing temperature decreases the density of receptor sites. The process occurs through physisorption since the calculated sorption energies are less than 50 kJ mol−1. The thermodynamic analysis of the process shows that water sorption on leaves is exothermic and spontaneous. This work contributes to a better understanding the drying process through the results obtained.

Polypyrrole-coated zinc/nickel oxide nanocomposites as adsorbents for enhanced removal of Pb(II) in aqueous solution and wastewater: An isothermal, kinetic, and thermodynamic study

One common heavy metal that is extremely harmful to the kidneys, reproductive system, and nervous system of humans is lead (Pb). This study aimed to investigate the effectiveness of a novel nanocomposite adsorbent, synthesised from polypyrrole, zinc oxide, and nickel (PPy/ZnO-NiO), in eliminating Pb(II) ions from a water-based solution. This adsorbent offers excellent metal selectivity, environmental stability, ease of manufacture, and reusability. Several techniques, namely XRD, FTIR, TGA, SEM, TEM, EDX, and BET, were employed to characterize the synthesised nanocomposite adsorbent. The study examined the impact of multiple factors influencing the adsorption process, including pH, temperature, contact period, metal ion concentration, and adsorbent dose, along with isotherms, kinetics, and thermodynamics processes. The adsorption of Pb ions was examined via various isotherm models, including the Temkin, Freundlich, and Langmuir, and thus various factors inherent to pseudo-first-order, pseudo-second-order, and Elovich kinetics were determined. The data revealed that both the Langmuir sorption model and pseudo-second-order kinetics match the adsorption data well. The highest adsorption capacities of the PPy/ZnO-NiO nanocomposite adsorbent for Pb(II) metal ions were 436.48, 450.48, and 469.56 mg/g at 298, 305, and 310 K, respectively, and the optimal pH was 5. An actual water sample that had been tainted with Pb(II) ions was used to test the applicability of the PPy/ZnO-NiO nanocomposite for the removal of Pb(II) ions. Based on the available data, the PPy/ZnO-NiO nanocomposite appears to be effective in terms of elimination of Pb(II) from five different raw water samples, such as tap water, surface water, groundwater, sewage plant wastewater, and domestic wastewater.

Sorption modelling of crude oil-contaminated soils using a derived spectral index

Theoretical models to describe and evaluate sorption of hydrocarbons on soil particles are well documented but experimental results in the literature are scarce. This study describes the use of a spectral index to evaluate sorption phenomena in oil-contaminated soils at micro and macro levels. Experiments involved oil-dosing from 0.25 mL to 4 mL and the application of a spectral index to estimate the sorption capacity of different soils based on change in statistically derived Critical Point (CP). Results show that sorption of oil varies with soil type, specifically the proportion of clay in a soil/sediment and the clay species, in the order smectite > illite > kaolinite. In support of theoretical models, this work proposes a model from experimental data that explains observed phenomena of soil-oil interaction with changing soil composition. The location and prominence of the CP is also strongly affected by soil moisture, particularly in coarse-grained soils, potentially providing insight to soil-oil–water interaction. The methods developed using a simple synthetic crude provide potential to explore other contamination scenarios including different soil compositions, types of petroleum products and different environmental controls.

Water sorption modeling and monolayer of biological and food materials

Despite water molecules are strongly hydrogen bonding to hydrophilic solids, the Brunauer-Emmet-Teller (BET) and Guggenheim-Anderson-de Boer (GAB) surface adsorption models have been widely accepted to describe water sorption properties of biological and food materials. These mathematically quite similar models use parameters which include a theoretical ‘monolayer’ value and one or two other parameters which describe ‘surface affinity’ in thermodynamic terms as heat of sorption. A high surface affinity indicates a strong surface binding of water molecules and preferential monolayer adsorption prior to multilayer sorption. Conversely, biological materials are water plasticized and suffer physicochemical changes at various stages of water sorption. Dynamic water sorption measurements often show regions where time-dependent changes in material characteristics, such as viscous flow and crystallization, may occur as a result of the glass transition. The two or three parameters of the BET and GAB models, respectively, are useful in the analysis of water sorption characteristics of individual substances, although the existence of a monolayer particularly in multicomponent materials may not be justified. Fitting the models to experimental data may occur rather for empirical than theoretical reasons.

Analysis of bulk-surface reaction-sorption-diffusion systems with Langmuir-type adsorption

We consider a class of bulk-surface reaction-adsorption-diffusion systems, i.e. a coupled system of reaction-diffusion systems on a bounded domain Ω⊆Rd (bulk phase) and its boundary Σ=∂Ω (surface phase), which are coupled via nonlinear normal flux boundary conditions. In particular, this class includes a heterogeneous catalysis model with Fickian bulk and surface diffusion and nonlinear adsorption of Langmuir type, i.e. transport from the bulk phase to the active surface, and desorption. For this model, we obtain well-posedness, positivity and global-in-time existence of solutions under some realistic structural conditions on the chemical reaction network and the sorption model. We work in appropriate Sobolev-Slobodetskii settings, where we aim for a wide range for the integrability index, including in particular values p<d.

Comparative Evaluation of Boron Sorption Dynamics on Zeolites in Irrigation Waters: An Isothermal Modeling Approach.

Efficient boron removal from irrigation waters is crucial for sustainable agriculture, as elevated levels of boron can be toxic to many plants, limiting growth and crop productivity. In this context, the present study investigated the sorption equilibrium of boron using zeolites in two types of aqueous matrices: a synthetic solution containing only boron and natural irrigation waters. Through the application of various isothermal sorption models (Langmuir, Freundlich, Sips, Toth, Jovanovic, Temkin, Dubinin-Radushkevich, and Redlich-Peterson), the efficacy of zeolite for boron removal under controlled and real conditions was evaluated. The results indicated a notable difference in sorption behavior between the two matrices, reflecting the complexity and heterogeneity of interactions in the boron-zeolite system. In the synthetic solution, the Freundlich model provided the best fit (R2 = 0.9917), suggesting heterogeneous and multilayer sorption, while the Sips model showed high efficacy in describing the sorption in both matrices, evidencing its capability to capture the complex nature of the interaction between boron and zeolite under different environmental conditions. However, in natural irrigation waters, the Jovanovic model demonstrated the most accurate fit (R2 = 0.999), highlighting the importance of physical interactions in boron sorption. These findings underscore the significant influence of the water matrix on the efficacy of zeolite as a boron removal agent, emphasizing the need to consider the specific composition of irrigation water in the design of removal treatments. Additionally, the results stress the importance of selecting the appropriate isothermal model to predict boron sorption behavior, which is crucial for developing effective and sustainable treatment strategies. This study provides a basis for optimizing boron removal in various agricultural and industrial applications, contributing to the design of more efficient and specific water treatment processes.