Biosorption has great potential in removing toxic effluents from wastewater, especially heavy metal ions such as cobalt, lead, copper, mercury, cadmium, nickel and other ions. Mathematically modeling of biosorption process is essential for the economical and robust design of equipment employing the bioadsorption process. However, biosorption is a complex physicochemical process involving various transport and equilibrium processes, such as absorption, adsorption, ion exchange and surface and interfacial phenomena. The biosorption process becomes even more complex in cases of multicomponent systems and needs an extensive parametric analysis to develop a mathematical model in order to quantify metal ion recovery and the performance of the process. The biosorption process involves various process parameters, such as concentration, contact time, pH, charge, porosity, pore size, available sites, velocity and coefficients, related to activity, diffusion and dispersion. In this review paper, we describe the fundamental physical and chemical processes involved in the biosorption of heavy metals on various types of commonly employed biosorbents. The most common steady state and dynamic mathematical models to describe biosorption in batch and fixed-bed columns are summarized. Mathematical modeling of dynamic process models results in highly coupled partial differential equations. Approximate methods to study the sensitivity analysis of important parameters are suggested.

Deagglomeration of ultrafine powders poses an important challenge towards their efficient and effective utilization. In the present study, we investigate the effect of frequency on the hydrodynamics of pulsed fluidized beds of ultrafine powders that show strong agglomeration behavior. We have carefully selected square waves of three different frequencies: 0.05 Hz, 0.10 Hz, and 0.25 Hz. The lowest frequency used here allowed the fluidized bed to settle completely before another pulse was introduced whilst the highest frequency ensured that the bed remained in a state of continuous turbulence between occurrences of consecutive pulses. On the other hand, the intermediate frequency pulse was just sufficient to complete the process of bed collapse before the start of the next pulse. Both local and global bed dynamics in all the three cases were rigorously monitored using fast response pressure transducers. The pressure transient data during the bed collapse were processed using the bed collapse model reported in the literature to compute the effective hydrodynamic diameter of agglomerates. Though there was substantial decrease in the agglomerate size, the effect of the frequency appeared to be rather insignificant as the global pressure transients remained rather insensitive to the change of the fluidization velocity.

This study investigates the development of sustainable nanocomposites using recycled polyethylene terephthalate (RPET) and polyamide 11 (PA-11) blends reinforced with graphene nanoplatelets (GNPs). RPET/PA-11 blends were compatibilized with 2 phr Joncryl^® and processed using melt blending followed by injection moulding. The effects of varying GNP contents (1–4 phr) on mechanical, thermal, and flame-retardant properties were analysed. The nanocomposite with 1 phr GNPs exhibited an optimal balance of mechanical, flame-retardant, and thermal properties, along with improved dispersion compared to higher GNP loadings. Higher GNP concentrations led to increased stiffness but also promoted agglomeration, which negatively impacted tensile and impact strength. Thermal analysis revealed that GNPs influenced the cold crystallization behaviour of RPET, while the TGA results indicated a moderate enhancement in thermal stability. The maximum degradation temperature (T_max) increased from 410.38 °C to 430.06 °C with 1 phr GNPs but declined at higher loadings. Similarly, flammability tests showed an improvement in the limiting oxygen index (LOI) from 19 to 24. Morphological analysis confirmed that GNPs facilitated PA-11 dispersion within the RPET matrix, particularly at lower GNP concentrations (1 phr). These findings highlight the potential of RPET/PA-11/GNP nanocomposites for multifunctional applications, providing an optimal balance between mechanical performance, thermal stability, and flame resistance. This research highlights the synergistic effect of GNPs in achieving sustainable, high-performance materials, addressing the challenges of plastic waste management and the need for eco-friendly engineering solutions for industries such as automotive, packaging, and construction.