This research is focused on investigating the utilization of Bayesian methodologies, specifically the Markov Chain Monte Carlo method, as well as filter sampling by importance and sequential resampling. The objective is to estimate kinetic parameters and state variables associated with the uranium bioleaching process by Acidithiobacillus ferrooxidans. Experimental data of cell concentration, uranium concentration, and concentrations of ferrous and ferric ions, obtained from literature, were employed. These measurements were evaluated using a mathematical model expressed by a system of ordinary differential equations. Three different mathematical models were evaluated, considering different uncertainties in experimental measurements and mathematical models (1% and 5%). The estimation results presented a good fit to the experimental data, with coefficients of determination in the range of 0.95 to 0.99. The validation of the mathematical models was obtained by reproducing the experimental measurements and the Bayesian techniques proved to be suitable for application in the bioleaching process.

The increase in emissions of toxic gasses such as hydrogen sulfide (H₂S) and carbon dioxide (CO₂), resulting from growing urbanization and industrialization, has caused environmental and public health problems, making the implementation of air purification techniques through adsorption important. Thus, modeling the gas adsorption process is fundamental for good agreement with experimental data, employing mathematical models that enable the prediction of adsorption capacity. In this way, the present work aimed to compare different analytical breakthrough curve models (Thomas, Yoon–Nelson, Adams–Bohart, and Yan) for the adsorption of H₂S and CO₂ in fixed-bed columns, using experimental data from the literature, estimating the curve parameters through the Markov Chain Monte Carlo (MCMC) method with the Metropolis–Hastings algorithm, and ranking using the determination coefficients (R² and R²_Adjusted) and the Bayesian Information Criterion (BIC). The models showed better agreement using the estimation of maximum adsorption capacity (q_s, N₀) and the constants of each model (k_th, k_yn, and k_ba). In the adsorption of H₂S, the Yan model stood out for its precision in estimating q_s. For the adsorption of CO₂, the Adams–Bohart model achieved better results with the estimation of N₀, along with the Yoon–Nelson model. Furthermore, the use of this method allows for a reduction in computational effort compared to models based on complex differential equations.

The treatment of industrial effluents has great environmental and human health importance. The purification of water from polluting components, such as metals and organic compounds, can be considered one of the main applications in this field, with adsorption being one of the main treatment methods. Therefore, with the objective of describing the dynamics of the process in an adsorption column and estimating the parameters involved, in this work, an algorithm for the Method of Lines (MOL) was used in order to numerically solve the model formed by the mass balance in liquid phase, the linear driving force equation (LDF), and the Langmuir isotherm for equilibrium. In addition, a sensitivity analysis of the phenomenon was carried out in relation to the parameters and a subsequent estimation of these was made through the Monte Carlo technique via the Markov chain (MCMC). The validation algorithm was created using data from actual breakthrough curves found in the literature. The experimental data were obtained from the literature for the adsorption of Cadmium (Cd), Copper (Cu), Nickel (Ni), Zinc (Zn), and Chrome (Cr) ions. Among all the estimates, the one that had the lowest adjustment to the data was that related to zinc metal, which had an R² equal to 0.8984. For the other metals, the correlation coefficient had a value closer to unity. This demonstrates that, in general, the estimates were good enough to represent the dynamics of adsorption.

The present study modeled the adsorption process of the drug diclofenac sodium on activated charcoal. For this purpose, a mass balance-based model was used considering a fixed bed column. The mass transfer rate in the solid phase was represented by a driving force model proposed in this study, and a gamma exponent with a range of $0>\gamma \le 2$ was assigned to the model. Different isotherms were adopted to represent the equilibrium at the solid/liquid interface: the Langmuir, Freundlich, Sips and Redlich-Peterson isotherms. The modeling was approached from the perspective of Bayesian statistics, and the Markov chain Monte Carlo method was used for parameter estimation. Model validation was performed with experimental data obtained under different operating conditions of initial concentration ($C_{0

Currently, petroleum-derived plastics are widely used despite the disadvantage of their long degradation time. Natural polymers, however, can be used as alternatives to overcome this obstacle, particularly cornstarch. The tensile properties of cornstarch films can be improved by adding plant-derived nanofibers. Sisal (Agave sisalana), a very common low-cost species in Brazil, can be used to obtain plant nanofibers. The goal of this study was to obtain sisal nanofibers using low concentrations of sulfuric acid to produce thermoplastic starch nanocomposite films. The films were produced by a casting technique using commercial corn starch, glycerol, and sisal nanofibers, accomplished by acid hydrolysis. The effects of glycerol and sisal nanofiber content on the tensile mechanical properties of the nanocomposites were investigated. Transmission electron microscopy findings demonstrated that the lowest concentration of sulfuric acid produced fibers with nanometric dimensions related to the concentrations used. X-ray diffraction revealed that the untreated fibers and fibers subjected to acid hydrolysis exhibited a crystallinity index of 61.06 and 84.44%, respectively. When the glycerol and nanofiber contents were 28 and 1%, respectively, the tensile stress and elongation were 8.02 MPa and 3.4%. In general, nanocomposites reinforced with sisal nanofibers showed lower tensile stress and higher elongation than matrices without nanofibers did. These results were attributed to the inefficient dispersion of the nanofibers in the polymer matrix. Our findings demonstrate the potential of corn starch nanocomposite films in the packaging industry.

Adsorption is a frequently used technique for pollutant removal due to its efficiency and versatility. Mathematical modeling of these processes enables understanding of adsorbent and adsorbate interactions and prediction of system dynamics, especially when experimental data are limited. Among adsorption isotherm models, the Langmuir model is one of the most applied; however, its formulation does not explicitly consider temperature variation, limiting predictive capability in practical applications. This article proposes an adaptation of the Langmuir model by incorporating temperature dependence, enabling inference of isotherms at temperatures without experimental data. The model was first validated using data from the literature at different temperatures, considering the adsorption of amoxicillin, phosphate, methylene blue, and caffeine. Subsequently, it was applied to experimental data of copper ion adsorption by 5A zeolite obtained in this work, allowing estimation of Q_max and K_L. Based on these estimates, hypotheses regarding their temperature dependence were formulated, and isotherms at 55 °C, 65 °C, and 75 °C were inferred and compared with experimental data. Finally, the model was applied to infer isotherms from 25 °C to 95 °C, demonstrating its ability to represent experimental dynamics and predict adsorption at temperatures without available data, contributing to the analysis and optimization of adsorption processes.