Understanding the flow state inside twin-screw extruders and continuous mixers is important in order to improve the mixing performance and production capacity of the mixers. Numerical simulations are effective in understanding the flow state, but past studies considering partially filled state in the mixer have not progressed sufficiently due to the difficulty of the partially filled simulation. In recent years, however, the development of mesh-free methods such as the particle method has led to the studies of partially filled flow in the mixers. In this study, the authors conducted partialy filled simulations using the Element-Free Galerkin Method, which is a kind of mesh-free method, and marker particle tracking and investigated the relationship between operating conditions and filling rate, average residence time, and residence time distribution of a counter-rotating continuous mixer. It was found that the filling rate had a linear relationship with the ratio of flow rate to rotational speed, Q/n, as in the case of the co-rotating twin-screw extruder. The residence time distribution normalized by the average residence time was similar for each rotor shape in the range of 1.0 ≤ Q/n ≤ 1.5, regardless of the operating conditions, while the probability density of long and short residence times became larger for Q/n < 1.0 and 1.5 < Q/n. Even though the residence time distribution gradually becomes bimodal and changes significantly for 1.5 < Q/n, the average residence time increases linearly with 1/Q as in the results for Q/n ≤ 1.5. In addition, the average residence time calculated from the mean value of the marker particles and that from the filling rate did not match when the axial filling ratio was non-uniform. Therefore, the filling ratio estimated from the average residence time in the experiment is a good estimate when the axial distribution of the filling ratio is uniform, but an overestimate when the axial filling ratio is non-uniform.

In a horizontal cylindrical vessel, it has been experimentally demonstrated that a device-specific self-induced oscillation occurs due to the release of bubbles from the aeration pipe installed at the bottom of the tank. In this study, we first investigated the two-phase flow model and analysis conditions necessary to reproduce the self-induced oscillation using Computational Fluid Dynamics (CFD). As a result, it was found that by setting the grid resolution in the analysis domain to less than twice the measured average bubble diameter, it is possible to reproduce self-induced oscillation using only the drag coefficient of a single bubble without applying a special drag coefficient for bubble clusters. We evaluated the effects of vessel diameter and gas flow rate as factors influencing the device and flow conditions on the oscillation frequency and obtained results that closely match the experimental data. Furthermore, by varying the vessel diameter and evaluating the self-oscillation frequency, it was found that predictions were within ±3% difference compared to previous experimental correlation equations. This study also found that in CFD, the self-oscillation frequency depends only on the vessel diameter D. Subsequently, using this model, we investigated the influence of placing baffle plates inside the vessel on the self-induced oscillation phenomenon. It was revealed that inserting baffle plates at the upper part of the aeration pipe could alter the oscillation of the bubble flow and suppress the occurrence of primary mode oscillations. As a result, the mechanism behind the self-induced oscillation phenomenon was clarified to consist of two stages: 1. The self-induced oscillation of the bubble flow, which repeats the process of vortex layers generated in regions with a strong velocity gradient on the side of the bubble flow, bending and stretching due to circulation flow, and the splitting and ejection of vortex layers when the bubble flow moves in the opposite direction. 2. The synchronous oscillation phenomenon, where a single primary mode is generated when the length of the bubble flow from the center of the aeration pipe to the liquid surface matches the vessel radius, due to synchronization between the oscillation of the bubble flow and the wave motion on the liquid surface.

Pb²⁺ adsorption equilibrium and kinetic of spray-dried zeolites were investigated. Spray-drying of synthesized Na-FAU zeolite (Si/Al ratio=3.2, primary particle size=0.34 µm) obtained spherical agglomerate with hollow structure, preserving the crystal and micropore structures. The geometric mean diameters and tapped densities of the spray-dried zeolite varied with heating temperature and zeolite concentration, ranging from 0.93–1.64 µm and 0.28–0.32 g/cm³, respectively. Spray-dried zeolite showed saturated Pb²⁺ adsorption amount of 385 mg-Pb²⁺/g, consistent to the powder dried in a thermostatic oven at 80°C (Pow-Y). Spray-dried zeolite reached Pb²⁺ adsorption equilibrium in about 10 s, significantly faster than Pow-Y. The Pb²⁺ adsorption kinetics of the samples were analyzed by the film-pore-surface diffusion model. The Biot number, which represents the ratio of external mass transfer to intraparticle diffusion, was higher than 200, indicating that intraparticle diffusion is the rate-limiting step for Pb²⁺ adsorption in spray-dried zeolite. Furthermore, the time for adsorptive removal of Pb²⁺ below the effluent standard (0.01 mg/L) for spray-dried zeolite was estimated to be more than 1000 times shorter than that for Pow-Y, using the film-pore-surface diffusion model.

We enclosed lithium ion adsorbent of several micrometer in diameter in microcapsules with larger diameter than the adsorbent to achieve ease of handling. We selected hydrophobic polymethyl methacrylate (PMMA) as the wall material of the capsules based on Hansen solubility parameter. PMMA has excellent mechanical strength. However, the hydrophobicity inhibit permeation of water and lithium ions. Therefore, polyethylene glycol (PEG) was incorporated into the PMMA microcapsules and then, removed to make water channels in the capsules. The created micropores promote the diffusion of lithium ions, and adsorption performance of lithium ions was improved by adding the PEG. When evaluated in terms of adsorption kinetics, the pseudo-second-order kinetics were in good agreement with the experimental data. The Langmuir adsorption isotherm model was in good agreement when the equilibrium adsorption amount of lithium ions was evaluated using adsorption isotherms.