In this work, a mathematical model to describe drug delivery from polymer coatings on implants is proposed. Release predictability is useful for development and understanding of drug release mechanisms from controlled delivery systems. The proposed model considers a unidirectional recursive diffusion process which follows Fick’s second law while considering the convective phenomena from the polymer matrix to the liquid where the drug is delivered and the polymer–liquid drug distribution equilibrium. The resulting model is solved using Laplace transformation for two scenarios: (1) a constant initial condition for a single drug delivery experiment; and (2) a recursive delivery process where the liquid medium is replaced with fresh liquid after a fixed period of time, causing a stepped delivery rate. Finally, the proposed model is validated with experimental data.

Adsorption is one of the most crucial processes in water treatment today. It offers a low-cost solution that does not require specialized equipment or state-of-the-art technology while efficiently removing dissolved contaminants, including heavy metals. This process allows for the utilization of natural or artificial adsorbents or a combination of both. In this context, polymeric materials play a fundamental role, as they enable the development of adsorbent materials using biopolymers and synthetic polymers. The latter can be used multiple times and can absorb large amounts of water per gram of polymer. This paper focuses on utilizing adsorption through hydrogels composed of poly(acrylamide-co-itaconic acid) for removing Cu²⁺ ions dissolved in aqueous media in a semi-continuous process. The synthesized hydrogels were first immersed in 0.1 M NaOH aqueous solutions, enabling OH⁻ ions to enter the gel matrix and incorporate into the polymer surface. Consequently, the copper ions were recovered as Cu(OH)₂ on the surface of the hydrogel rather than within it, allowing the solid precipitates to be easily separated by decantation. Remarkably, the hydrogels demonstrated an impressive 98% removal efficiency of the ions from the solution in unstirred conditions at 30 °C within 48 h. A subsequent study involved a serial process, demonstrating the hydrogels’ reusability for up to eight cycles while maintaining their Cu2+ ion recovery capacity above 80%. Additionally, these hydrogels showcased their capability to remove Cu²⁺ ions even from media with ion concentrations below 100 ppm.

In this paper, we present the synthesis of composite materials comprised of α-cellulose and sugarcane bagasse cellulose fibers grafted with lactic acid and ε-caprolactone. These fibers were incorporated as reinforcements into a PLA matrix by extrusion, producing composite materials with improved mechanical properties. The grafting of lactic acid and ε-caprolactone onto the fibers was confirmed by FTIR spectroscopy, demonstrating the chemical modification of the fibers. The morphology of the fibers and composites was analyzed through scanning electron microscopy (SEM), showing that the fibers are encapsulated within the polymeric matrix. This suggests good PLA–fiber interaction for the 90 PLA/10 α-Cel, 90 PLA/10 LAC-g-α-Cel, and 90 PLA/10 ε-CL-g-α-Cel composite materials. The obtained composite materials were tested under tensile loading. Incorporating 10 wt% of LAC-g-FBA-Cel and α-Cel-g-FBA-Cel grafted fibers into the PLA matrix improved the tensile modulus by 28% and 12%, respectively, compared with PLA. The maximum tensile strength values obtained were for composite materials with 10 wt% PLA/α-Cel, LAC-g-α-Cel, and FBA-Cel with 23, 27, and 37% concerning PLA. DSC thermal studies showed a reduction in the glass transition temperature in the composites with grafted fibers. The results suggest better interfacial adhesion between the PLA matrix and both grafted and non-grafted α-cellulose fibers, which contributes to the observed improvements in the mechanical and thermal properties of the composite materials. The results demonstrate that the composites can be produced through extrusion. Once the optimal concentration has been determined, α-cellulose or sugarcane bagasse grafted with lactic acid and ε-caprolactone can be incorporated into the PLA matrix, exhibiting adjustable properties.

High-quality water availability is substantial for sustaining life, so its contamination presents a serious problem that has been the focus of several studies. The presence of heavy metals, such as cadmium, is frequently studied due to the increase in the contamination levels caused by fast industrial expansion. Cadmium ions were removed from aqueous solutions at pH 7.0 by chitosan–magnetite (ChM) xerogel beads and chitosan–FeO (ChF) xerogel beads in batch systems. Kinetic studies were best modeled by the Elovich model. The adsorption isotherms obtained showed an inflection point suggesting the formation of a second layer, and the BET model adjusted to liquid–solid systems was adequate for the description of the experimental data. Maximum uptake capacities of 36.97 ± 0.77 and 28.60 ± 2.09 mg Cd/g xerogel were obtained for ChM and ChF, respectively. The studied composites are considered promising adsorbent materials for removing cadmium ions from aqueous systems.

The improper management of fats, oils, and grease (FOG) from food services is a major cause of sewer blockages and environmental damage. This study examines FOG management in the restaurant sector of the Guadalajara Metropolitan Area, Mexico, from three complementary perspectives: the performance of the authorized formal collection system, management practices in food establishments, and the physicochemical characteristics of grease trap residues. These perspectives were addressed using official administrative records and reports from environmental authorities, structured surveys applied to kitchen staff, and laboratory analyses of grease trap samples collected in restaurants. The results reveal important institutional and structural constraints affecting FOG management. Only a limited number of authorized collectors operate actively, serving a small fraction of potential generators, while most food service establishments are micro- or small-sized businesses with limited technical and financial capacity to comply with regulations. A large portion of the sector consists of small, low-cost food service establishments with intensive oil use (e.g., street food vendors, sandwich shops, and set-menu restaurants), which contribute to widespread oil reuse and inadequate disposal practices. Laboratory analyses showed a high free fatty acids (FFAs) content and compositional profiles consistent with repeated oil use, with negative implications for sewer systems and waste management. Overall, the findings highlight the need for stronger regulatory enforcement, collection schemes tailored to micro-scale generators, and awareness campaigns while also indicating opportunities for FOG valorization within circular economy approaches, particularly through energy recovery pathways.