Adsorption Kinetic Models and Their Applications: A Critical Review

Adsorption Kinetic Models and Their Applications: A Critical Review

Abidemi Anthony Sangoremi

Department of Chemistry, Federal University Otuoke, Bayelsa State, Nigeria

DOI: https://doi.org/10.51244/IJRSI.2025.120500019

Received: 02 May 2025; Accepted: 07 May 2025; Published: 29 May 2025

ABSTRACT

Adsorption kinetic models are essential tools to understanding the rates and mechanisms by which adsorbates interact with adsorbents. These models facilitate the prediction of pollutant removal rates and the determination of time-dependent concentrations of residual adsorbates in solutions. Commonly employed models include the pseudo-first-order and pseudo-second-order models, which are particularly effective in describing adsorption processes involving heavy metals and organic contaminants. The intraparticle diffusion model is instrumental in elucidating the diffusion mechanisms within porous adsorbents, while the Elovich model is frequently applied to systems with heterogeneous surfaces. These kinetic models have practical applications across various fields, including environmental remediation, wastewater treatment, gas storage and separation, catalysis, and the pharmaceutical and biomedical sectors. They are particularly valuable in evaluating the performance of adsorbents and investigating adsorption mass transfer mechanisms. However, challenges persist in accurately interpreting the physical meanings and solving methods of these models, especially when applied to complex real-world systems. Recent advancements have focused on developing comprehensive analytical solutions and new approaches to address these complexities, thereby enhancing the applicability and reliability of adsorption kinetic models in various applications.

Keywords: Mechanism, adsorbent, adsorption, pollutants, wastewater

Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface (Guruge, 2021). This process creates a film of the adsorbate on the surface of the adsorbent. This process differs from absorption, in which a fluid (absorbate) is dissolved by or permeates a liquid or solid (absorbent). While adsorption does often precede absorption, which involves the transfer of the absorbate into the volume of the absorbent material, alternatively, adsorption is distinctly a surface phenomenon, wherein the adsorbate does not penetrate through the material surface and into the bulk of the adsorbent (Atkins et al., 2018).

Like surface tension, adsorption is a consequence of surface energy. In a bulk material, all the bonding requirements (be they ionic, covalent or metallic) of the constituent atoms of the material is fulfilled by other atoms in the material. However, atoms on the surface of the adsorbent is not wholly surrounded by other adsorbent atoms and therefore can attract adsorbates. The exact nature of the bonding depends on the details of the species involved, but the adsorption process is generally classified as physisorption (characteristic of weak van der Waals forces) or chemisorption (characteristic of covalent bonding) (Ferrari et al., 2010). It may also occur due to electrostatic attraction (Khosrow Shahi et al., 2022). The nature of the adsorption can affect the structure of the adsorbed species. For example, polymer physisorption from solution can result in squashed structures on a surface (Carroll et al., 2010).

Adsorption is present in many natural, physical, biological and chemical systems and is widely used in industrial applications such as heterogeneous catalysts, activated charcoal, capturing and using waste heat to provide cold water for air conditioning and other process requirements (adsorption chillers), synthetic resins, increasing storage capacity of carbide-derived carbons and water purification. Adsorption, ion exchange and chromatography are sorption processes in which certain adsorbates are selectively transferred from the fluid phase to the surface of insoluble, rigid particles suspended in a vessel or packed in a column (Czelej et al., 2016). Pharmaceutical industry applications, which use adsorption as a means to prolong neurological exposure to specific drugs or parts thereof, are lesser known (Ali et al., 2024).

Principles of Adsorption Kinetics in Chemical Processes

Adsorption kinetics describe how adsorbate molecules like ions, gases, or liquids stick to the surface of a solid or liquid adsorbent as time passes. This process plays a key role in chemistry shedding light on the workings behind important functions such as biosorption, enzyme immobilization, and drug delivery. To improve these applications in areas like pharmaceutical manufacturing, wastewater treatment, and biotechnology, we need to grasp adsorption kinetics well (Patel et al. 2020). Biosorption and Environmental Cleanup Biosorption uses living materials to soak up and remove pollutants such as heavy metals and organic contaminants, from water. The speed of absorption in biosorption helps determine how fast these pollutants can be eliminated and provides essential information to turn lab results into industrial applications. In the field of chemistry, biosorption has an impact on environmental cleanup offering green and affordable ways to fight pollution. Studies show that chemical interactions between the biosorbent and the absorbed substance often control biosorption processes, following pseudo- second-order kinetics (Jiang et al. 2021).

Enzyme Immobilization

Fixing enzymes to solid supports is a crucial method in chemical engineering. This process boosts enzyme stability, allows for reuse, and improves catalytic performance. Scientists study adsorption kinetics to understand how enzymes interact with immobilization materials how they attach, and what conditions lead to the best activity. Many industries, like food processing and drug making, use immobilized enzymes. The adsorption process helps keep enzyme activity steady and extends how long they can work (Zhou et al. 2019).

Drug Delivery Systems

In the pharmaceutical world, adsorption kinetics play a key role in creating drug delivery systems. These systems use carrier surfaces to adsorb active molecules for targeted and controlled release. To regulate how drugs are released, these systems depend on knowing adsorption mechanisms like physisorption and chemisorption. Smaller drug molecules often follow pseudo-first-order kinetics when they adsorb. More complex systems might need kinetic models that factor in intraparticle diffusion and surface reactions (Li et al. 2020).

Adsorption equilibrium in Chemical systems

Adsorption equilibrium occurs when the rate at which adsorbate molecules stick to the surface of an adsorbent matches the rate at which they release. This balance leads to a consistent concentration of adsorbate on the adsorbent’s surface. In chemical contexts, grasping adsorption equilibrium is crucial for understanding processes like enzyme-substrate interactions and how biomolecules bind to surfaces. These interactions play a significant role in various biological and industrial applications, such as removing pollutants through biosorption and regulating enzyme activity in immobilized systems (Moghaddam et al., 2021). In biological settings, adsorption equilibrium sheds light on how biomolecules engage with different surfaces, which is a key aspect in both natural and engineered systems. For example, enzymes that are immobilized on solid supports are commonly utilized in industrial processes, and achieving equilibrium is essential for maintaining their optimal activity and stability. Likewise, in biosorption, biological materials such as algae, fungi, or bacteria serve as adsorbents to eliminate toxic pollutants from water. These processes depend heavily on the balance between adsorbed and unadsorbed states to enhance pollutant removal efficiency (Moghaddam et al., 2021). A particular instance of adsorption equilibrium in chemistry is competitive adsorption, where various biomolecules vie for binding sites on an adsorbent. This concept is vital for comprehending how proteins interact on surfaces, especially in multi-component systems. For example, proteins with stronger binding affinities can displace others, leading to redistribution of adsorbates. Such dynamics are important in applications like drug delivery, biosensors, and diagnostics, where selective binding is crucial. Environmental factors such as pH, temperature, and ionic strength frequently affect the equilibrium state, underscoring the complexity of these interactions in real-world situations (Singh et al., 2020).

Kinetic Models of Adsorption

Pseudo-First Order Kinetic Model

Pseudo-first-order model assumes that the rate of adsorption is proportional to the number of unoccupied sites on the adsorbent. Therefore, such modes serve processes at low adsorbate concentrations. Referring to the area such as in chemistry that often collects it: this model applied to define the adsorption of small molecules or contaminants to biological adsorbents (Jiang et al., 2021).

The pseudo-first-order kinetic model is among the earliest models used to describe adsorption kinetics. It assumes that the rate of adsorption is proportional to the difference between the amount of adsorbate adsorbed at equilibrium and at any given time. This model is particularly applicable in systems where physical adsorption dominates, relying on weak van der Waals forces for interaction between the adsorbate and the adsorbent (Lagergren, 2018).

The pseudo-first-order model operates under specific assumptions. Firstly, adsorption occurs on a homogeneous surface where all sites have equal energies and no interaction occurs between adsorbed molecules. Secondly, the adsorption process is controlled by diffusion through the boundary layer around the adsorbent particles, emphasizing the role of external mass transfer.

Applications of this model extend across various fields. In water treatment, it is frequently employed to describe the adsorption of organic pollutants and dyes onto activated carbon. The model is also applied in studying the adsorption of gases onto homogeneous surfaces, particularly in controlled environmental conditions. Additionally, it is used to understand adsorption dynamics for light metals and small organic compounds in environmental remediation processes (Ho & McKay, 2021).

Despite its advantages, the pseudo-first-order model has notable limitations. It is not suitable for systems where chemisorption dominates, as it fails to account for electron exchange or sharing between adsorbent and adsorbate. Furthermore, the model’s accuracy diminishes in heterogeneous systems, where surface energies vary significantly. Linearization of the kinetic equation can also lead to inaccuracies in parameter estimation, particularly when equilibrium adsorption capacities are low (Azizian, 2024). The non-linear form of Pseudo-First order is shown in equations 1 and 2, while the linear form is shown in equation 3

                                                                                                      (1)

)                                                                                                       (2)

The linear form is given as;

                                                                                  (3)

The plot of log (q_e-q_t) against t gives the slope k₁/2.303 and intercept log q_e

Pseudo-Second-Order Kinetic Model

The pseudo-second-order model assumes that the adsorption rate is proportional to the-square of the number of unoccupied sites. Usually, this type of model is applied when adsorption is characterized by the chemisorption mechanism as well as the strong binding formed between adsorbate and adsorbent. Therefore, it is very much relevant in chemistry for explaining metal ions or organic molecules’ adsorption by biomaterials (Zhou et al., 2019).

The pseudo-second-order kinetic model is often applied in the description of adsorption processes, especially when chemisorption dominates. In chemisorption, there is sharing or exchange of electrons between adsorbent and adsorbate leading to stronger bonds than in physisorption. The model postulates that the rate of adsorption is directly proportional to the square of the number of available adsorption sites on the adsorbent (Ho & McKay, 2021).

The pseudo-second-order model is based on particular assumptions. First, it postulates that the rate-limiting step involves chemisorption. In this mechanism, valence forces relate to the sharing or transfer of electrons between the adsorbent and adsorbate molecules. Furthermore, the model assumes that adsorption takes place uniformly over the surface of the adsorbent; this assumption makes mathematic interpretation of kinetic data easier (Ho, 2016).

The applicability of the pseudo-second-order model is cut across various disciplines. It has been particularly used in effective remediation of environments to explain the adsorption phenomena in the removals of heavy metals like lead (Pb) and cadmium (Cd) from contaminated waters. The model was also used in treatment processes of wastewater through the adsorption of organic pollutants, which comprise dyes and phenols (Vijayaraghavan et al., 2019). Apart from environmental applications, thepseudo-second-order model applies very well to gas adsorption studies, especially in the storage and separation of greenhouse gases like CO2 and in catalysis where it is involved in determining the adsorption behavior of reactants on catalyst surfaces (Blanchard et al., 2024).

Despite its usefulness, the pseudo-second-order kinetic model is not free of limitations. This model is most appropriate for adsorption systems where chemisorption is the dominant mechanism; thus, it is least suitable for physical adsorption processes, systems that involve multilayer adsorption, or heterogeneous surfaces. Furthermore, applicability relies highly on the quality of experimental data obtained to fit and validate the model appropriately (Sparks, 2023).

The non-linear forms of Pseudo-Second order are shown in equations 4 and 5, while the linear form is displayed in equation 6.

                                                                                                 (4)

                                                                                                        (5)

The linear form of pseudo second order is given as;

                                                                                                   (6)

The plot of t/q_t against t gives a slope 1/q_e and intercept (1/k₂q_e²)

The Elovich Model

The Elovich model is a kinetic model of adsorption which is accepted widely, especially when dealing with chemisorption on heterogeneous adsorbents. It takes the name of the scientist who first developed it, and it is assumed that as the number of adsorbed species increases, the rate of adsorption will decrease exponentially with respect to that. This behavior makes the Elovich model particularly useful for systems wherein surface activation energy varies significantly (Chen & Zhao, 2024). Within the frame of several assumptions, this model asserts that adsorption takes place on a heterogeneous surface with a cause of energy large enough to cover a range of potential energies for adsorption in the material. Thus, it is the most applicable case, and the rate of adsorption follows an exponential decrease with adsorption from saturation of adsorption sites. The model also presents itself where chemisorption has been adopted as an adsorption-practice process (Kumar & Singh, 2023).

The Elovich model has very extensive applications spread from one field to another. In environmental remediation, it is known for accounting the adsorption of heavy metals, dyes, and organic pollutants from the aqueous phase, which gives an account of the performance of adsorbents under different conditions (Patel et al., 2023). In catalysis, it helps to understand the adsorption of reactants on the surfaces of catalysts, which will direct the design, evaluation, and optimization of catalytic processes (Smith & Brown, 2023). In addition, the Elovich model evaluates gas adsorption as a characteristic baseline for the storage of different gases on active carbons or zeolites, giving very crucial information for the design of efficient storage applications (Johnson &Andrews, 2024).

 Despite its versatility, the Elovich model has some shortcomings. It is not applicable to systems that are essentially characterized by physical adsorption since chemisorption is assumed to be the predominant process. In addition to this, since the model is based on the assumption of a heterogeneous surface, it would compromise its application towards homogeneous adsorbents. The equations 7 and 8 represent non-linear and linear Elovich equations respectively.

                                                                                   (7)

                                                                           (8)

The plot of q_t versus lnt gives the slope and intercept

Intraparticle Diffusion Model

This model of intraparticle diffusion is a multiple-stage mechanism of adsorption. It is during which adsorbate can diffuse into the pores of the adsorbent, which conveys an important understanding of the diffusion limitations existing in biosorption, whereby adsorbate could experience resistance on its way to the active sites inside the adsorbent (Bhatnagar et al., 2020).

All these materials used in chemistry, such as activated carbon or natural biopolymers, are porous, hence demand this model to understand how adsorption occurs. The intraparticle diffusion model is a key kinetic model used to describe adsorption processes where the rate-limiting step involves the diffusion of adsorbate molecules into the internal pores of the adsorbent. This model is particularly relevant for porous adsorbents, where internal diffusion governs the overall rate of adsorption (Weber & Morris, 2023). The model assumes a three-stage mechanism: the initial stage involves external mass transfer from the bulk solution to the adsorbent surface; the second stage, which is often rate-limiting, is the diffusion of adsorbate molecules into the pores; and the final stage involves the adsorption onto the internal active sites.

A linear relationship between the amount adsorbed and the square root of time indicates that intraparticle diffusion is the rate-controlling step, but deviations from linearity suggest the involvement of additional mechanisms, such as surface adsorption or film diffusion.

The intraparticle diffusion model has diverse applications. In environmental remediation, it describes the adsorption of heavy metals, dyes, and organic pollutants onto porous adsorbents such as activated carbon and zeolites. In wastewater treatment, it aids in modeling contaminantremoval processes influenced by pore diffusion. Additionally, the model is employed in gas storage and separation studies, where it evaluates gas diffusion into materials like metal-organic frameworks and activated carbons. Despite its utility, the model has limitations. It assumes a homogeneous adsorbent structure, which may not be valid for heterogeneous systems.

Furthermore, it does not account for multiple diffusion mechanisms occurring simultaneously, and its accuracy depends on correctly identifying the rate-limiting steps under various experimental conditions.

The non-linear and linear Intra-Particle Diffusion Model are represented by equations 9 and 10

                                                                                  (9)

                                                              (10)

The plot of log R against log t gives the slope and the intercept

Avrami Model

The Avrami model is a kinetic model originally developed to describe phase transformations in materials science and has been adapted to study adsorption kinetics in heterogeneous systems. It is particularly useful for processes involving complex interactions and multilayer adsorption, known for its ability to capture non-linear adsorption behaviors and dynamic systems with evolving rates (Chen & Zhang, 2022).

The model assumes heterogeneous adsorption, where adsorption occurs on a surface with varying energy sites, making it applicable to complex systems. It also accounts for the dynamic growth of the adsorbed layer, where the rate of adsorption changes over time as adsorbates accumulate, and non-linear adsorption kinetics, accommodating deviations from simple kinetic behaviors such as multilayer adsorption or external influences like temperature or pH (Lee & Wang, 2023).

Applications of the Avrami model include multilayer adsorption, which describes adsorption processes where multiple layers of adsorbates form on an adsorbent surface, commonly observed in gas or complex organic molecule adsorption. The model is also used in dynamic biological systems, such as the adsorption of proteins or enzymes on heterogeneous surfaces like membranes or nanoparticles. Additionally, it plays a role in environmental remediation by modeling the adsorption of pollutants with non-linear behaviors, such as dyes, heavy metals, and emerging contaminants on adsorbents like activated carbon or biochar, as well as in catalysis to evaluate interactions between reactants and catalytic surfaces with evolving adsorption dynamics.

Despite its versatility, the Avrami model has limitations, including complex calculations that require advanced computational tools, the assumption of surface heterogeneity, which may not apply to all adsorbents, particularly those with uniform characteristics, and the need for extensive experimental data to validate its predictions, especially in systems with fluctuating conditions (Smith & Brown, 2021).

Factors Affecting Adsorption Kinetics

Several factors have an impact on the adsorption kinetics in chemical systems shaping how well and how the process works. To improve systems like bioremediation, biosorption, and enzyme- driven reactions, it’s essential to grasp these factors. These systems see widespread use in environmental and industrial settings.

Surface Area and Pore Size of Adsorbent

The surface area and pore size of an adsorbent have a major impact on how much and how fast adsorption happens. Adsorbents with a big surface area, like activated carbon, biochar, or microbial cell surfaces, give more places for binding, which makes adsorption work better.

Bigger pore sizes help adsorbate molecules larger biomolecules or pollutants, move into the adsorbent more . For instance, people often use activated carbon with tiny and medium-sized pores to clean up organic pollutants in wastewater (Smith & Carter, 2023). In chemical systems changing the surface properties of adsorbents such as by activating them or coating them with functional groups, can make adsorption work even better.

Temperature

Temperature has a significant impact on the adsorption process, especially when chemisorption is the primary mechanism. As temperatures rise, the kinetic energy of adsorbate molecules increases, allowing them to more easily overcome the activation energy barrier needed to bind to the adsorbent surface. In systems involving enzymes or microbes, temperature also influences the activity and stability of these biomolecules, adding another layer of complexity. For example, in biosorption, moderate temperature increases can enhance the uptake of pollutants by microorganisms, but excessively high temperatures may denature enzymes or kill microbes, ultimately reducing system efficiency (Brown & Johnson, 2024). Therefore, choosing the right temperature is crucial for balancing adsorption efficiency with biological functionality.

Concentration of Adsorbate

The concentration of the adsorbate in the surrounding medium is a key factor in adsorption kinetics. Higher concentrations create a stronger driving force for adsorbate molecules to move toward the adsorbent surface, which boosts adsorption rates. This effect is particularly noticeable in wastewater treatment, where increased pollutant concentrations typically lead to more effective biosorption. However, at very high concentrations, the adsorbent can become saturated, resulting in a plateau in adsorption efficiency (Thompson et al., 2022). In chemical systems, managing adsorbate concentration is vital to avoid verloading and to ensure the effectiveness of the process.

Contact Time

Contact time determines how long adsorbate molecules interact with the adsorbent surface. Longer contact times allow the system to approach equilibrium, ensuring maximum adsorption capacity. In biological systems, the interaction time is especially crucial for processes like microbial uptake of nutrients or pollutants. For example, in biosorption, longer exposure times enable pollutants to bind to microbial cell surfaces or penetrate the cell walls, leading to higher removal efficiencies. However, prolonged contact times can sometimes lead to secondary reactions, such as desorption or degradation of adsorbed molecules, which must be managed for optimal system performance (Davis & Lee, 2023).

Rate-Determining Step

The rate-determining step is the slowest step in the adsorption process, which ultimately limits the overall kinetics. In chemical systems, this could involve external mass transfer (movement of adsorbates from the bulk solution to the adsorbent surface), internal mass transfer (diffusion of adsorbates into the pores of the adsorbent), or the binding process itself. For example, in microbial biosorption, the diffusion of pollutants through the microbial cell wall or their interaction with specific binding sites on the cell surface can act as the rate-determining step (Smith & Carter, 2023). Identifying and optimizing the rate-determining step is crucial for improving the efficiency of adsorption processes.

Methods for Evaluating Adsorption Kinetics

Evaluations of the adsorption kinetics are required to establish how fast adsorbates are captured by adsorbents. There is no shortage of experimental and analytical procedures for that work, in which the concentration of adsorbates is monitored as they increase with time, and the data treatment adopting a suitable kinetic model should provide information regarding not only performance and capture mechanisms but also possible optimization within any particular process application notably involving wastewater treatment, environmental protection, or chemical industries in general.

Types of Adsorption Experiments

Batch Adsorption Experiments

In this method a certain amount of adsorbent is taken in a batch reactor having known  concentration of adsorbate. The reaction mixture is allowed to attain the equilibrium and then the concentration of the adsorbate in solution is measured at different time intervals. The obtained experimental data can be used for calculation of rate and fitting of kinetic model. This method is simple and frequently used to study adsorption on different materials like activated carbon, zeolites, bioadsorbents etc. (Arias et al., 2021).

Column Adsorption Experiments

Column experiments are conducted to mimic adsorption processes with continuous flows. An adsorbent is packed into a column, and an adsorbate solution is allowed to flow through the column. At certain specified intervals, samples of the effluent are collected and analyzed for adsorbate concentration. Column experiments are especially useful for assessing long-term performance of adsorbents under realistic conditions and for evaluating the dynamics of adsorption in continuous flow systems (Vargas et al., 2023).

Dynamic light scattering (DLS)

DLS can be used to examine size distribution of adsorbates in solution during impact. This method is useful to determine the aggregation of particles upon adsorption or to investigate the interaction between adsorbates and adsorbents at the nanoscale. It provides a time-resolved measurement that can monitor the whole process of adsorption kinetic mechanisms involving small molecules, colloids, or nanoparticles (Liu et al., 2023).

DATA ANALYSIS METHODS

Regression Analysis and Model Fitting

One of the most commonly used techniques for evaluating adsorption kinetics is fitting the experimental data to various kinetic models (e.g., pseudo-first-order, pseudo-second-order, or intraparticle diffusion models). Regression analysis helps determine the rate constants and other parameters that describe the adsorption process. The goodness of fit is evaluated using statistical methods such as the coefficient of determination (R²) or chi-square tests (Li & Wang, 2024).

Non-Linear Fitting

In many cases, linear regression may not adequately describe the kinetics, particularly when the system involves non-linear adsorption processes (e.g., multilayer adsorption). Non-linear fitting methods use optimization techniques to fit experimental data directly to the models, providing amore accurate representation of complex adsorption behaviors (Zhao et al., 2023).

Adsorbent characterization

Surface Area and Pore Size Analysis

Techniques like the Brunauer-Emmett-Teller (BET) method are used to determine the surface area and pore volume of adsorbents, which are crucial factors in adsorption kinetics. This information can help identify the adsorption mechanisms (physical vs. chemical adsorption) and the role of pore diffusion in the overall process (Chen et al., 2023).

Scanning Electron Microscopy (SEM)

SEM is used to visualize the surface morphology of adsorbents before and after adsorption. It provides insight into the changes in surface characteristics, such as pore structure or the formation of surface complexes. This technique is valuable for understanding the physical and chemical interactions between the adsorbate and the adsorbent during the kinetic study (Nguyen & Xu, 2023).

Thermogravimetric Analysis (TGA)

TGA measures changes in the weight of the adsorbent material as a function of temperature. This method is useful for studying the desorption kinetics and the stability of adsorbed species. By analyzing the temperature at which desorption occurs, researchers can infer the strength of adsorption bonds and the types of interactions involved (Gao & Li, 2022).

Applications of Adsorption Kinetic Models

While adsorption kinetic models serve as valuable instruments to comprehend adsorption mechanisms and their intricacies, optimizing applications across diverse domains necessitates unpacking the rates at which pollutants and compounds adhere to sorbents. Such models afford a strategic means to both gauge adsorptive uptake over time and disentangle the intricate interactions that facilitate separation, thereby permitting enhanced conceptualization and functionality of engineered remediation and purification schemes. Furthermore, calibrating designs in response to kinetic insights gleaned from systematically parsing the progression of pollutant sequestration promises to refine adsorbent materials and treatment workflows toward improved environmental, industrial and medical outcomes.

Environmental Remediation

Adsorption kinetic models are widely used in environmental remediation to study and improve pollution removal processes.

Removal of heavy metals

Adsorption kinetics help in evaluating how effectively adsorbents such as activated carbon, biochar, and functionalized clays remove toxic heavy metals like arsenic, lead, and mercury. These models, especially the pseudo-second-order kinetic model, provide insights into the adsorption capacity and predict the performance of adsorbents under varying environmental conditions (Liu et al., 2023).

Removal of organic pollutants: The removal of persistent organic pollutants including dyes, pesticides, and pharmaceutical chemicals benefits greatly from adsorption studies Kinetic models enable characterization of adsorption efficiency, and affect adsorbents a selection and effect of operating conditions in wastewater treatment (Chen & Zhao, 2022).

Wastewater treatment

Adsorption kinetics plays an important role in strengthening wastewater treatment systems, ensuring efficient removal of contaminants and designing the system.

Industrial effluents: Many industries produce effluents containing oils, chemicals and heavy metals. Kinetic models are used to understand the adsorption rates of these pollutants, enabling companies to develop treatment plans that comply with environmental regulations (Gupta et al., 2024).

Emerging pollutants: New adsorbents and adsorption models are being developed to address pollutants such as microplastics and endocrine disruptors, which require improved understanding for effective removal (Smith & Brown, 2023).

Gas Storage and Separation

Adsorption kinetic models provide insights into gas adsorption and desorption rates, crucial for applications such as energy storage and air purification.

Energy Storage: Hydrogen and methane storage systems use advanced adsorbents like metal-organic frameworks (MOFs). Kinetic models determine optimal conditions for efficient storage and release of these gases (Kim et al., 2022).

Carbon Capture: Adsorption kinetics are applied to carbon dioxide capture systems to optimize the adsorbent materials and operational parameters for reducing greenhouse gas emissions (Wang & Li, 2023).

Catalysis and Industrial Processes: Kinetic models are essential for catalytic processes, were adsorption of reactants onto catalysts determines reaction rates and yields.

Heterogeneous Catalysis: Adsorption kinetics help optimize conditions for chemical reactions, such as hydrogenation, oxidation, and polymerization, by characterizing reactant interactions with catalyst surfaces (Nguyen et al., 2023).

Adsorbent Regeneration: Understanding desorption kinetics allows industries to efficiently regenerate spent adsorbents, reducing operational costs and environmental impact (Ali &Khan, 2024).

Pharmaceutical and Biomedical Applications

In the biomedical field, adsorption kinetic models contribute to the design of systems for drug delivery, biosorption, and other applications.

Drug Delivery Systems: The release of drugs from carriers like hydrogels, nanoparticles, or porous materials is governed by adsorption and desorption mechanisms. Kinetic models enable precise control over drug release profiles for therapeutic purposes (Chandra et al.,2024).

Biosorption: In medical and environmental biotechnology, biological materials like algae, fungi, and bacteria are used to adsorb toxins, heavy metals, and other contaminants. Adsorption kinetics help evaluate and optimize these systems for both environmental cleanup and medical applications (Singh et al., 2023).

Case Studies in Adsorption Applications

Water Purification: Activated carbon and biochar have been extensively studied using kinetic models for removing heavy metals and dyes, contributing to cleaner water systems (Zhao & Lin, 2023).

Soil Remediation: Adsorption kinetics help in developing strategies to remove contaminants from soil using microbial and chemical adsorbents (Wang et al., 2022).

Air Purification: Advanced adsorbents like zeolites and MOFs are evaluated using adsorption kinetics to remove volatile organic compounds (VOCs) and other air pollutants (Liu et al., 2023).

Challenges in Adsorption Kinetics

Real-world systems often involve complex matrices with multiple components, including pollutants, competing ions, and other interfering substances. These complexities make it challenging to predict adsorption behaviors accurately using conventional kinetic models. For example, the simultaneous adsorption of organic and inorganic pollutants often deviates from idealized models (Gupta et al., 2023).

Many traditional adsorption kinetic models, such as pseudo-first-order and pseudo-second-order models, rely on assumptions of homogeneity, linearity, or single-layer adsorption. However, real adsorbent surfaces are often heterogeneous and may involve multilayer adsorption, making these models less applicable (Smith & Brown, 2023).

In many adsorption processes, mass transfer both external (film diffusion) and internal (pore diffusion)—can limit the adsorption rate. Differentiating between these rate-limiting steps in kinetic studies is difficult, leading to potential inaccuracies in model fitting (Wang et al., 2022).

Factors such as temperature, pH, ionic strength, and adsorbent dose can significantly influence adsorption kinetics. Variability in experimental setups across studies often leads to inconsistencies in reported data, complicating the comparison and reproducibility of results (Nguyen et al., 2023).

Recent Advances in Adsorption Kinetics

Recent years have seen the introduction of more sophisticated kinetic models, such as fractal-like kinetic models, distributed reaction rate models, and modified intraparticle diffusion models. These models account for surface heterogeneity, non-linear adsorption dynamics, and complex interaction mechanisms, providing more accurate predictions of adsorption behavior (Liu et al., 2023).

Advances in materials science have led to the development of high-performance adsorbents such as nanomaterials, bio-based adsorbents, and metal-organic frameworks (MOFs). These materials offer unique properties, such as high surface areas, tunable pore sizes, and selective adsorption capabilities. Kinetic studies on these materials have expanded our understanding of adsorption dynamics (Kim et al., 2022).

Computational tools, including molecular dynamics (MD) simulations, density functional theory (DFT), and artificial intelligence (AI), are increasingly being used to model adsorption kinetics. These approaches allow for the prediction of adsorption behaviors and optimization of process parameters with greater accuracy and reduced experimental costs (Chandra et al., 2024).

Hybrid systems, such as adsorbent-membrane combinations and photocatalytic adsorption processes, have gained attention for their enhanced efficiency. Kinetic studies on these systems provide insights into synergistic effects and mechanisms that improve adsorption performance (Ali & Khan, 2024).

The use of environmentally friendly and cost-effective adsorbents, such as agricultural waste- derived biochar and algal biomass, has gained traction. Recent kinetic studies focus on optimizing these sustainable materials for applications in water purification, gas capture, and soil remediation (Thompson et al., 2022).

CONCLUSION

Adsorption kinetic models are vital for understanding and optimizing chemical processes. These models, including pseudo-first-order, pseudo-second-order, Elovich, and intraparticle diffusion, elucidate the mechanisms and rates of adsorption in systems like enzyme-substrate interactions, biosorption for pollutant removal, and biomolecule immobilization. In chemistry, these models are particularly relevant for improving processes such as the removal of heavy metals through biosorption or the modulation of enzyme activity on immobilized systems.

Although challenges such as system complexity, model limitations, and experimental variability remain, recent advancements in computational modeling, high-performance adsorbents, and hybrid systems have significantly expanded their applicability. Novel materials like bio-based adsorbents and nanomaterials further enhance the scope of these models. By addressing these challenges, adsorption kinetic models continue to offer transformative potential for biotechnological innovations, enabling sustainable solutions to complex chemical and environmental challenges.

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