## 4 Results and Discussion  
### Particle Evolution Regularities in the Three-Phase Mixing Process  
The physical space of gas, liquid, and solid is a complex turbulent environment, and the existence of flow baffle elements causes turbulent flows to be a disorder at the rotating speed. It will be further investigated and compared to how different aeration settings affect fluid flow and solid particle suspension in the mixed area in order to acquire the fluid-solid multiphase coupling and interphase mass-transfer characteristics. Figure 4 shows particle velocity distribution in the three-phase mixing course. In Figure 4a, the particle is located at the bottom of the container, and the particle takes on the concentrating forms. The particles are sucked under impeller rotating effects. The impeller rotation increases shear energies and fluid axial speeds. In Figure 4b, the particles are in contact with the impeller and diffused to the container wall and baffle since the rotating effect. The particles in the impeller center have a large speed value in Figure 4c, and the particle speed is concentrated at 0.75 m/s-1.0 m/s. Still, the particle speed at the bottom of the impeller can be concentrated at 0 m/s-0.5 m/s. In Figure 4d, the impeller disperses particles and slows down local particles. Under the action of the rotating impeller, some of the particles rise to the free liquid level while others are stopped by the baffle and fall to the container bottom. The particles may be completely mixed, and the fluid field may be in extremely nonlinear turbulence. The radial velocity distribution can be obtained to investigate particle evolution features (Figure 5). This section is centrally located above the aeration port and represents the radial distribution of particles at the mixing space. Particle speed distribution in the initial state is uniform in Figure 5a, and there is no large value. At this time, the particles can be mainly influenced by gravity and vertical upward suction, showing a central convergence state. In Figure 5b, the particles move upward under the effect of impeller rotation, and the local particles reach a high-velocity peak. Many particles show uniform \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Granule density/(kg/m\({}^{3}\)) & 1100 \\ Granule number & 10,000 \\ Granule Young module/MPa & 1 \\ Granule Poisson ratio & 0.25 \\ Granule diameter/mm & 1 \\ Paddle speed/rpm & 400 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Fluid and granule medium characteristics. velocity variation characteristics. Figure 5c shows no significant change in particle velocity, and only one particle has a mutation peak. In Figure 5d, after the mixed flow field reaches a completely turbulent state, the velocity amplitude of the particles fluctuates greatly, a large number of particles have random velocity values, and the velocity distribution is nonlinear. It can be seen from the above characteristics that after full mixing, the disorder and randomness of particle motion in the entire flow field become more complex, and the material mixing efficiency will inevitably increase. Figure 4: Particle velocity distributions in the three-phase mixing process. (**a**) Initial state. (**b**) Particle rise. (**c**) Particle dispersion. (**d**) Particle mixing. Figure 5: Particle velocity curves in the three-phase mixing process. (**a**) Initial state. (**b**) Particle rise. (**c**) Particle dispersion. (**d**) Particle mixing. Based on the above, the energy evolution trends of particles in this cross-section are obtained, as shown in Figure 6. The total energy of particles has a high randomness in the evolution process. In Figure 6a, the particle capacity varies within a small fluctuation range, wherein the particles are mainly affected by kinetic energies generated by impeller rotating effects. In Figure 6b, when the flow field begins to disturb, the particle energy changes obviously, showing more random energy pulses.