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In this study, the experimental and kinetic modeling investigations were performed to evaluate the ability of mesoporous and microporous canola stalk-derived activated carbon (CSAC) on 2,4-dichlorophenoxyacetic acid (2,4-D) removal from synthetic and natural water in both batch and continuous systems. Three empirical models (pseudo-first-order equation (PFOE), pseudo-second-order equation (PSOE), and the Elovich equation (EE)) and three theoretical models (film diffusion model (FDM), particle diffusion model (PDM), and second-order chemical reaction rate model (SOCRRM)) were compared in terms of diffusion coefficients, maximum 2,4-D adsorption, and rate constants at various operating conditions. CSAC was prepared at 600 °C and activated with water steam under a controlled flow and subsequently characterized by various analytical methods. The results showed that the maximum 2,4-D uptake by CSAC was achieved as 135.8 mg g −1 under a pH of 2 and an initial 2,4-D concentration of 150 mg L −1 . The CSAC removed 38.3% of Na + , 43.49% of K + , 8.96% of Mg 2+ , 45.14% of Ca 2+ , 17.2% of Cl −1 , 39.48% of HCO 3 − , 63.74% of SO 4 2− , and 100% of the herbicide from agricultural subsurface drainage water and also retained its usability after regenerated by acetone for five cycles. It was concluded that the 2,4-D was adsorbed on the surface of the CSAC through its aromatic ring interaction with the reactive functional groups of the adsorbent. The model result indicated that the PDM is the best-fitting kinetic model for the adsorption of 2,4-D by CSAC, followed by FDM, SOCRRM, PSOE, PFOE, and EE. The mass balance equation based on PDM describes the dynamic behavior of the column satisfactorily. Graphical abstract

This study aims to assess kinetic modelling of the solid–liquid extraction process of total polyphenolic compounds (TPC) from apple pomace (AP). In this regard, we investigated the effects of temperature and solvent (i.e. water, ethanol, and acetone) on TPC extraction over various periods. The highest TPC yield of 11.1 ± 0.49 mg gallic acid equivalent (GAE)/g db (dry basis) was achieved with a mixture of 65% acetone–35% water (v/v) at 60 °C. The kinetics of the solvent-based TPC extraction processes were assessed via first-order and second-order kinetic models, with an associated investigation of the kinetic parameters and rate constants, saturation concentrations, and activation energies. The second-order kinetic model was sufficient to describe the extraction mechanism of TPC from AP. This study provides an understanding of the mass transfer mechanism involved in the polyphenolic compound extraction process, thus facilitating future large-scale design, optimization, and process control to valorize pomace waste.

The correct determination of the kinetic model and the kinetic parameters that describe a heterogeneous process is key to accurately predicting its progress within a wide range of conditions, which is one of the main purposes of kinetic analysis. Albeit ideal kinetic models continue to be used to gain insight about the process mechanism, they are constrained by certain assumptions that are rarely met in real experiments and limit their applicability. This is the case of contracting (or interface) kinetic models, which are one of the most commonly used. Thus, the ideal kinetic model R 2 is derived by assuming a cylindrical contraction in the radial direction but not contemplating the possibility of a contraction in the direction of the axis of the cylinder. Moreover, in the case of the ideal model R 3, it is assumed that contraction takes place simultaneously in particles of identical dimensions in all three directions of space (spheres or cubes). Here, it is revisited this type of model, and it is considered the contraction of particles with different geometries, namely cylinders with different aspect ratios and rectangular cuboids. Besides, a novel generalized interface reaction model is proposed, which covers all the studied cases and broadens the range of applicability to more complex situations involving different geometries and inhomogeneous particle sizes. Finally, the proposed model is applied to the analysis of the experimental thermal dissociation of ammonium nitrate, previously described in the literature as a sublimation process. It is proved that the novel kinetic model provides a more accurate description of the kinetics of the reaction and better prediction capabilities.

High phosphate content in water causes eutrophication, leading to many risks to the aquatic environment and human health. This study used biochar derived from macadamia husks at the pyrolysis temperatures (300, 450, and 600℃) to remove P from water. Adsorption parameters such as initial pH, biochar dosage, initial P concentration, and adsorption time when biochar was exposed to the P solution were determined. The results show that pH 4 is optimal for P removal with biochar pyrolyzed at 300 and 450°C, while pH 6 gives biochar 600°C, biochar dosage 10 g.L−1, concentration Initial P 25-200 mg.L−1 and adsorption time 40 minutes for 3 types of biochar. The maximum P adsorption capacity is 20.07, 20.03, and 20.03 mg.L−1 corresponding to 3 forms of biochar 300, 450, and 600°C. P adsorption data were consistent with the Freundlich isotherm model for all three biochar forms. The pseudo-second-order kinetic model was suitable for all three types of biochar, showing that the main adsorption mechanism is a surface chemical reaction. The study suggested that hydrogen bonding plays an important role in the adsorption of P onto biochar derived from macadamia husks. This study indicates that biochar derived from macadamia husks pyrolyzed at temperatures of 300, 450, and 600°C are all potentially effective and low-cost adsorbents for phosphate removal from water.

Crystal violet (CV) synthetic dyes are well known in the dyeing industry for their mitotic and mutagenic poisoning. CV dye being a toxic organic dye is responsible for serious health issues as well as environmental damage. In this study, an inexpensive biosorbent (white clover: Trifolium repens ) stem powder was tested for the adsorption of CV dye (cationic dye) from an aqueous solution. The batch adsorption measurements were designed to find out the influence of contact time, pH, adsorbent dose, and dye concentration, for dye removal. The operation parameters studied are the contact time (20 to 160 min), initial dye concentration (10–100 mg/L), dose (0.1–1 g), and pH, (1–10). At optimum conditions, maximum percent removal of 92.997% and adsorption capacity value of 1.952 mg/g was achieved at pH 2, adsorbent dose (1 g), and contact time (140 min), and dye concentration (70 ppm). The results suggested that the removal of CV rose with the contact time and adsorbent dose. Langmuir and Freundlich isotherm models were applied to the equilibrium adsorption data, and data were perfectly fitted to Langmuir isotherm model. Pseudo-first-order and pseudo-second-orders were applied to the data, and it was found that the pseudo-second-order kinetic model was best fitted to the experimental data. It was also revealed that the stem powdered of the Trifolium repens plant can be employed as a useful adsorbent to remove cationic CV dye from different water samples (tap, river and distilled). Furthermore, the performance of adsorbent was also evaluated in saline water containing sodium chloride, potassium chloride and manganese chloride salts to check the effect of various ions on the performance of adsorbent and it was observed that the adsorbent showed excellent performance in saline water. Moreover, a comparative study was performed to check the efficiency of different commercial adsorbents (silica gel and active carbon) and to compare their performance with our study. All these experiments revealed that the biosorbent used in this study effectively removes contaminating dyes from industrial wastewater and as well as saline water and thus, can be used for the treatment of wastewater at the commercial level.

Purpose:This study characterized the chemical components and nutrient release patterns of filter cake, filter cake biochar, and sugarcane bagasse ash—by-products of the sugarcane industry, a globally significant crop.Method:The chemical composition of each material was analyzed, nutrient release kinetics were examined using water extraction during 336 h, and kinetic models were applied.Results:The studied materials were rich in various elements and exhibited alkaline properties. Carbon and Si were the primary components, followed by Ca, Al, P, and K. All materials released substantial amounts of K and P, with minimal N release. Filter cake had the highest cumulative release of water-soluble P (7,701±87.4 mg/kg), followed by filter cake biochar (2,982±27.3 mg/kg) and sugarcane bagasse ash (1,194±3.66 mg/kg), representing 32.2%, 7.8%, and 21.7%, respectively, of total P. Conversely, the cumulative release of water-soluble K was highest in sugarcane bagasse ash (7,295±418 mg/kg), followed by filter cake (3,999±124 mg/kg) and filter cake biochar (2,312±107 mg/kg), accounting for 23.3%, 30.3%, and 11.0%, respectively, of total K. The nutrient release kinetics showed that the magnitude of release was controlled by the inherent elemental concentrations of each material and exhibited good fits with the Elovich and power function models (R² = 0.836–0.990 and 0.810–0.996). Nutrient release depended mainly on diffusion through heterogeneous and homogeneous surfaces.Conclusion:These sugarcane by-products have the potential to improve soil fertility through nutrient releases. Transforming filter cake into biochar slows the initial release of nutrients while ensuring a more sustained and steady long-term release.Highlight· Filter cake, its biochar and sugarcane bagasse ash are alkaline and rich in C and Si.· Filter cake releases the most water-soluble P among the three materials.· Sugarcane bagasse ash shows the highest cumulative release of water-soluble K.· Each material shows distinct nutrient release influencing agricultural use.Biochar transformation of filter cake slows nutrient release for long-term use.

Industry represents a fundamental component of modern society, with the generation of massive amounts of industrial waste being the inevitable result of development activities in recent years. Red mud is an industrial waste generated during alumina production using the Bayer process of refining bauxite ore. It is a highly alkaline waste due to the incomplete removal of NaOH. There are several opinions in both the literature and legislation on the hazards of red mud. According to European and national legislation, this mud is not on the list of hazardous wastes; however, if the list of criteria are taken into account, it can be considered as hazardous. The complex processing of red mud is cost-effective because it contains elements such as iron, manganese, sodium, calcium, magnesium, zinc, strontium, lead, copper, cadmium, bismuth, barium and rare earths, especially scandium. Therefore, the selection of an extraction method depends on the form in which the element is present in solution. Extraction is one of the prospective separation and concentration methods. In this study, we evaluated the kinetic modelling of the solid–liquid acid extraction process of predominantly scandium as well as other elements present in red mud. Therefore, three acids (HCl, HNO3 and H2SO4) at different concentrations (10, 20 and 30%) were targeted for the extraction of Sc(III) from solid red mud. Specific parameters of the kinetics of the extraction process were studied, namely the solid:liquid ratio, initial acid concentration, contact time and temperature. The extraction kinetics of Sc(III) with acids was evaluated using first- and second-order kinetic models, involving kinetic parameters, rate constants, saturation concentration and activation energy. The second-order kinetic model was able to describe the mechanism of Sc(III) extraction from red mud. In addition, this study provides an overview on the mechanism of mass transfer involved in the acid extraction process of Sc(III), thereby enabling the design, optimization and control of large-scale processes for red mud recovery.

In this study, we explore a new method based on color variation data to derive the kinetics of the entire process of the hydration of alkali-activated slag (AAS). Using this image analysis technique, we can monitor the induction period that cannot be observed using conventional microcalorimetry techniques. Color variation was recorded across a sequence of 9999 images, which were processed via MATLAB software package. Further, an average pixel value (APV) was determined to represent the color in each image. Reaction parameters, such as color variation velocity v(t), reaction speed ε(t), and hydration degree α(t), that govern the entire hydration process were determined. On the basis of the reaction parameters and a Krstulovic–Dabic kinetic model, integral and differential equations were derived to simulate the three basic processes of AAS hydration. Equations describing the reaction kinetics of AAS with solutions of three different concentrations of NaOH were extracted using this method.

Background The members of the genus Caldicellulosiruptor have the potential for future integration into a biorefinery system due to their capacity to generate hydrogen close to the theoretical limit of 4 mol H2/mol hexose, use a wide range of sugars and can grow on numerous lignocellulose hydrolysates. However, members of this genus are unable to survive in high sugar concentrations, limiting their ability to grow on more concentrated hydrolysates, thus impeding their industrial applicability. In this study five members of this genus, C. owensensis, C. kronotskyensis, C. bescii, C. acetigenus and C. kristjanssonii, were developed to tolerate higher sugar concentrations through an adaptive laboratory evolution (ALE) process. The developed mixed population C. owensensis CO80 was further studied and accompanied by the development of a kinetic model based on Monod kinetics to quantitatively compare it with the parental strain. Results Mixed populations of Caldicellulosiruptor tolerant to higher glucose concentrations were obtained with C. owensensis adapted to grow up to 80 g/L glucose; other strains in particular C. kristjanssonii demonstrated a greater restriction to adaptation. The C. owensensis CO80 mixed population was further studied and demonstrated the ability to grow in glucose concentrations up to 80 g/L glucose, but with reduced volumetric hydrogen productivities (\\(Q_H_2 \\)) and incomplete sugar conversion at elevated glucose concentrations. In addition, the carbon yield decreased with elevated concentrations of glucose. The ability of the mixed population C. owensensis CO80 to grow in high glucose concentrations was further described with a kinetic growth model, which revealed that the critical sugar concentration of the cells increased fourfold when cultivated at higher concentrations. When co-cultured with the adapted C. saccharolyticus G5 mixed culture at a hydraulic retention time (HRT) of 20 h, C. owensensis constituted only 0.09–1.58% of the population in suspension. Conclusions The adaptation of members of the Caldicellulosiruptor genus to higher sugar concentrations established that the ability to develop improved strains via ALE is species dependent, with C. owensensis adapted to grow on 80 g/L, whereas C. kristjanssonii could only be adapted to 30 g/L glucose. Although C. owensensis CO80 was adapted to a higher sugar concentration, this mixed population demonstrated reduced \\(Q_H_2 \\) with elevated glucose concentrations. This would indicate that while ALE permits adaptation to elevated sugar concentrations, this approach does not result in improved fermentation performances at these higher sugar concentrations. Moreover, the observation that planktonic mixed culture of CO80 was outcompeted by an adapted C. saccharolyticus, when co-cultivated in continuous mode, indicates that the robustness of CO80 mixed culture should be improved for industrial application.

Purpose Modeling relative biological effectiveness (RBE) is central to carbon ion radiotherapy treatment planning. The modified Microdosimetric Kinetic Model (mMKM) is a clinically established RBE framework that has guided treatment protocols at many existing carbon centers, while the Mayo Clinic Florida Microdosimetric Kinetic Model (MCF MKM) is a recently developed alternative. This work aims to implement the MCF MKM in the open‐source treatment planning system matRad and to quantitatively compare its RBE‐weighted dose predictions with those of the clinically established mMKM using identical physical dose distributions across multiple disease sites. These findings will help assess their dosimetric equivalence and inform protocol development for carbon ion radiotherapy at MCF. Methods Monte Carlo simulations of the MCF carbon beamline were performed to generate physical (IDD, LET, lateral spread) and biological base data for integration of each RBE model into matRad. Treatment plans were generated for six patients, each corresponding to a different disease site, using clinical beam configurations with carbon‐reference dose prescriptions, and plans were optimized using the MCF MKM. To isolate differences attributable solely to the RBE model, the resulting physical dose distributions were held fixed and RBE‐weighted doses were recalculated using the mMKM. Dose volume histogram (DVH) metrics and spatial dose‐difference maps were used to compare target coverage and organ‐at‐risk doses between the two models. Results Across patient cases, RBE‐weighted dose distributions from MCF MKM and mMKM showed strong agreement. Differences in target coverage were small, with CTV D95% differing by less than 1.6% across all disease sites and maximum target dose differences not exceeding 0.88%. Organ‐at‐risk dose deviations were limited, with differences of 3.0% or less across evaluated DVH metrics. Spatial dose‐difference maps showed that the largest discrepancies occurred in regions of steep dose gradients near target to organ‐at‐risk interfaces, while overall dose conformity and plan quality remained comparable between the two models. Conclusions: This study served as the first systematic model comparison of the MCF MKM and mMKM within a treatment planning environment. These findings suggest that the MCF MKM and mMKM produce dosimetrically consistent RBE‐weighted dose predictions under realistic planning conditions using carbon‐reference parameters. Accordingly, the fractionation schemes developed from years of clinical experience with mMKM implementations may serve as a practical foundation for protocol development at MCF.