The Soxhlet extraction of β-carotene from the fruit peel of Momordica cochinchinensis was modeled, yielding valuable insights into the kinetic parameters for operation and optimization.

In the manufacturing of granular urea and ammonium nitrate, the technique of prilling is utilized rather frequently. The liquid droplets that are produced fall along the tower to the ground and become solid due to the removal of heat by the cooling air, which flows in the opposite direction of the stream. Generally, three sequential thermal intervals for the solidification of urea droplets are considered: the cooling of liquid drops, solidification at the freezing temperature of the liquid phase, and cooling of complete solid particles. In this study, the solidification of the urea droplets was considered as a two-phase Stefan problem with a convective flux boundary condition rather than dividing the whole process into three sequential steps. The heat transfer problem was solved numerically using the enthalpy method. The particles were assumed to attain the terminal velocity immediately. The convective heat transfer was determined from the terminal velocity. The temperature distribution of the droplets and the minimum height for complete solidification at different particle diameters were investigated.

Dye pollutants, mainly discharged from the textile industry, have caused severe risks to human health and the ecosystem because of their toxicity, non-biodegradability, and carcinogenicity. This study investigated the use of commercial biochar derived from melaleuca wood as an adsorbent for the removal of methylene blue (MB) using a packed-bed column. The selected biochar was characterized by nitrogen adsorption-desorption isotherms, Fourier transform infrared spectroscopy, and scanning electron microscopy. The experiments were performed to determine breakthrough curves (BTCs) with varying pH (3–9), inflow rate (5–20 mL min–1), bed height (16–65 cm), and initial MB concentration (0.75–9 mg L–1). The biochar (particle size of 1–2 mm) exhibited a low adsorption capacity for MB (~21 mg kg–1), resulting in a short breakthrough time. The Thomas, Bohart-Adams, Yoon-Nelson, and Bed Depth Service Time models were quite suitable for describing the experimental BTCs, with R2-values ranging from 0.92 to 0.98. The obtained BTCs were not in the typical S-shape, which characterizes diffusion-controlled adsorption. Therefore, a serial logistic-exponential model, which accounts for both the mass transfer and interaction contributions, was proposed. The experimental data effectively fit this proposed model, as indicated by high R2-values (>0.998). The dominant influence of mass transfer compared to interaction in controlling the adsorption rate of MB was highlighted.