## 4 Results and Discussion
### Experimental Results of Pressure Attenuation and Particles Dispersion  
In order to obtain the pressure variation characteristics during the interaction process, the quartz sand particles with an average diameter of 0.95 mm and a filling mass of 5 g were used for the shock wave experiment. The experimental results were compared with the pressure data measured in the blank experiment (without particles), as shown in Figure 5.  
It can be seen from Figure 5 that there was only one peak pressure at the P\({}_{1}\) position in the blank experiment, which was the incident shock overpressure (149 kPa). Peak pressure at the P\({}_{2}\) position was  
Figure 4: Variation of the temperature, pressure, and velocity of the gas and solid phases during the interaction process. (**a**); Velocity evolution (**b**); Temperature evolution (**c**) Pressure evolution. The subscript \(p\) represents the solid phase; \(U\) is the shock velocity; \(T\) is the temperature; \(P\) is the pressure; and the subscripts \(1\), \(2\), and \(\infty\) indicate the wave front, transition zone, and infinity, respectively. Figure 5: Comparison of pressure in the blank experiment and the shock wave experiment with solid particles. 107 kPa. However, in the shock wave experiment with solid particles, there were two peak pressures at the P\({}_{1}\) position; the first was the incident shock overpressure (156 kPa) and the second was the reflected shock overpressure (310 kPa). The peak pressure at the P\({}_{2}\) position was the transmitted shock overpressure (75 kPa). This phenomenon indicates that the presence of solid particles caused the reflection and transmission of the shock wave, thus the shock intensity decreased significantly. In addition, the pressure attenuated 42 kPa in the blank experiment and 71 kPa in the experiment with solid particles. The results are attributed to two aspects. First, the pressure attenuation of the shock front was caused by the volume expansion of the airflow outside the tube. Second, the shock wave exchanged momentum with the solid particles during the interaction process, and part of the energy was used to do work on the particles to drive their dispersion. To study the influence of the size on the particle dispersion process under the shock wave, three types of solid quartz sand particles with average diameters of 2.5, 0.95, and 0.42 mm were used individually for the shock wave experiments, and the filling mass was 5 g. The same batch of diaphragms was employed to ensure the consistency of shock intensity for different experiments. The Mach number  
It can be seen from Figures 6-8 that after the shock wave acted on the quartz sand particles, the dispersion distance of the solid particles increased continuously within 6 ms, and the particles presented a gradually opened \"umbrella\" shape during the dispersion process. It indicated that in the early stage, the energy provided by the shock wave with 1.47 Mach was enough to cause the 5 g of solid quartz sand particles to overcome the gravity and air resistance, and exhibit an overall upward movement. The drag force of the shock wave on the particles dominated in this period. With the passage of time, the drag force decreased, and the gravity of particles gradually became the dominant force that affected the particle movement. In addition, according to the comparison of Figures 6-8, there were some differences in the dispersion process of quartz sand particles with different sizes. At the same time, the solid particles with a small size were scattered faster, and the farther the dispersion distance, the clouds that formed were more dispersed. In Figure 8, the experimental particle dispersion shown is not symmetric. The reason is that the particle size was very small and the particles were easily disturbed by the airflow during the experiment, thus the symmetry was not as well-developed as that shown in Figures 6 and 7. Figure 11: The simulated dispersion process of the quartz sand particles with an average diameter of 0.42 mm.