Atmospheric pollution results from toxic gases in low concentrations, originating from natural processes and human activities. These gases interact with each other in the presence of solar radiation, forming much more complex compounds that contribute to the formation of photochemical smog. This study presents a mathematical model to estimate the daily concentrations of primary and secondary pollutants, assuming that spatial variation is not considered within a control volume. The model includes nitrogen oxides, ozone, hydrocarbons, aldehydes, alcohols, and other gases, which are related through 52 chemical and photochemical reactions with rate constants that depend on factors such as the time of day and temperature. The model formulation results in 31 ordinary differential equations that are solved using a variable-step algorithm in MATLAB R2019a. Two scenarios are simulated: the “closed-box” model (CBM), where there are no inflows or outflows of gaseous flux, and the “open-box” model (OBM), which includes inflows and outflows within the control volume. The OBM is particularly useful for predicting concentrations during thermal inversion episodes. The results show that several pollutants reach their maximum concentrations at midday, suggesting an increase in the formation of secondary pollutants under high solar radiation, especially in the closed-box model. In the open-box model, concentration peaks shift toward the afternoon. To compare both models, the closed-box system conditions are considered, incorporating airflow into the open-box model without accounting for pollutants transported by this flow. The complex nonlinear dynamics observed in the pollutants highlight the combined influence of solar radiation, temperature, and emission rates on air quality. This study underscores the usefulness of mathematical models in developing effective mitigation strategies and assessing environmental and public health impacts.

Accurate prediction of contaminant transport and self-purification processes in rivers remains challenging because pollutant dispersion, biochemical reactions, and hydrodynamic conditions interact across multiple spatial scales. This study aims to develop and compare mathematical models for soluble contaminant transport and biodegradable organic matter removal in channels and rivers. Unsteady advection–diffusion–reaction equations were formulated for one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) transport scenarios and solved through numerical techniques based on the transformation of partial differential equations into systems of ordinary differential or algebraic equations. In parallel, the classical Streeter–Phelps model and an extended formulation incorporating turbulent diffusion were implemented to evaluate organic load degradation and oxygen deficit dynamics. Simulations were performed using a Matlab R2019a-based computational framework under representative hydraulic and reaction conditions obtained from literature data and empirical correlations. The results showed that, under specific conditions, the 3D model reproduced trends comparable to those predicted by the 2D model, while the latter approached the behavior of the 1D formulation. The Streeter–Phelps model predicted an organic load removal efficiency of 97.74%, a purification index of 1.9564, a critical time of 18.43 h, and a critical distance of 6.93 km. These findings provide a useful framework for river water-quality assessment and support future applications involving complex hydrodynamic and pollutant-loading scenarios.

The objective of this study was to evaluate the solar photocatalytic degradation of the disperse textile dye 2-(4-amino-2-nitrophenyl)-1,3-benzothiazole using titanium dioxide nanoparticles (TiO₂ P25) under a mean solar irradiance of 492 ± 58 W/m², evaluating the effects of pH, photocatalyst concentration, and continuous aeration on process efficiency. The degradation of the dye was determined by monitoring its concentration by UV–Visible spectrophotometry, while the mineralization was evaluated by chemical oxygen demand (COD). Likewise, kinetic behavior was analyzed using pseudo-first-order and pseudo-second-order models. The results showed that the degradation efficiency increased with the concentration of TiO₂, reaching the highest yield with 400 ppm of TiO₂ and continuous aeration, which confirms that both variables are determining operating factors for maximizing photocatalytic efficiency. pH exerted a significant influence on the activity of the system, obtaining the highest degradation efficiencies and the greatest reductions in COD under slightly alkaline conditions (pH 8–9), a behavior attributed to the greater colloidal stability of TiO₂ and the modification of its surface properties with respect to its point of zero charge (pHpzc ≈ 6.2). The pseudo-second-order model generally provided an adequate empirical description of the experimental data; however, the best-fitting model varied depending on the experimental condition. The simultaneous decrease in the concentration of the dye and the COD confirmed that the treatment produced not only the decolorization of the solution, but also the progressive oxidation of the organic matter. Integrating kinetic analysis with the simultaneous assessment of decolorization and COD enabled clear experimental differentiation between adsorption and photocatalysis, strengthening the interpretation of TiO₂-based solar photocatalytic systems. In conclusion, solar photocatalysis using TiO₂ and the optimization of operational variables constitute an effective treatment strategy that takes advantage of solar irradiation as the primary energy source, thereby reducing dependence on conventional artificial UV irradiation. Within the scope of this study, the combination of solar radiation, continuous aeration and appropriate operating conditions demonstrated promising potential for the treatment of textile wastewater containing persistent dyes.