Effect of Impact Angle on Particle Fracture Phenomenon

12 The effect of terephthalic acid particle properties on particle fracture phenomena was 13 investigated in this study. Furthermore, to evaluate the fracture characteristics in real process, the 14 effect of the particle impact angle on particle fracture phenomena was also investigated. The 15 results of this study indicated that: (i) the crystallite size correlated with the fracture stress of the 16 particle; (ii) the crystallite size also showed a correlation with the critical fracture velocity and the 17 kinetic energy of the particle; and (iii) the particle fractured more easily at impact angles under 18 45°.


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In various industrial processes involving particle movement, such as a powder pneumatic 27 transportation system and a solid-gas septarian using air filtration, particles often fracture because 28 of the impact with a pipe's inner wall or with the surface of a fiber in an air filter. Particle 29 fracturing may cause several problems, such as an increase in the apparent volume, clogging of 30 the powder transfer pipe, and deterioration in flowability because of a relative increase in the 31 adhesion force. Additionally, this phenomenon may significantly affect a subsequent process and 32 the final product quality. Thus, the investigation of particle fracturing is very important. 33

A C C E P T E D M A N U S C R I P T
5 A terephthalic acid powder was used as a test sample. A large quantity of this powder was used 82 as a raw material for the polyethylene terephthalate (PET) resin. Reportedly, problems are caused 83 by particle fracturing in a pneumatic transportation process at a PET manufacturing plant.

EVALUATION OF PHYSICAL PROPERTIES 90
The physical properties of particles, such as particle size distribution, crystallite size, and 91 fracture stress, were measured. The particle size distribution was measured using a laser 92 diffraction method (MicrotracBEL Corp., Microtrac FRA). The crystallite size was calculated 93 using a powder X-ray diffraction (XRD) pattern. This pattern was determined via powder XRD 94 using a diffractometer (Rigaku Corp., MiniFlex II) equipped with a Cu-Kα radiation source. The 95 scan rate was 2.0 ° min -1 , the step interval was 0.02 °, and the scan range was in the 10 °-70 ° 2θ 96 range. The fracture stress measurement of a single particle was based on the JIS R1639-5 (JIS 97 R1639-5, 2007) using a micro-compression tester (Shimazu Crop., MCT-510). The particles were 98 compressed to the point of fracture, and the fracture load F1 (N) was recorded. One hundred Using this mechanism, a particle can be impacted on the plate for a wide range of impact 110 velocities and impact angles. The distance from the nozzle outlet of the cascade impactor to the 111 impact plate is 5.5 mm. The particle impact test process is described as follows. Initially, the gas 112 suction pump was set to a constant flow rate. The particles were poured into the inlet of the 113 cascade impactor. After the pouring was completed, almost all particles in the cascade impactor 114 and membrane filter were collected. A change of 50 % particle diameter was evaluated. Table 1  115 summarizes the nozzle size, the flow velocity at the nozzle, and the theoretical cut off diameter of 116 50 % collection. Theoretically, the expansion of gas passing through the nozzle must be 117  Table 2 summarizes the calculated crystallite size and the 50 % particles diameter. 132 Generally, the higher the crystallinity, the higher the energy required to break a crystal structure. 133 Thus, it can be assumed that the particles' strength or, in other words, the particles' hardness 134 satisfies the expression A > B > C > D. 135 136 Fig. 4 shows a representative load-displacement curve of each sample for a single-particle 138 compression test. The horizontal axis in the graph was normalized to a 50 % particle diameter. It 139 can be observed that the applied load increases at the early stage of particle compression. As the A C C E P T E D M A N U S C R I P T 8 particle compression continues, the applied load does not vary with the displacement. At this 141 point, it was considered that the particle fractured. Consequently, using this particular fracture 142 load and Eq. (1), the fracture stress S of a single particle was calculated. Generally, the fracture 143 stress of a single particle exhibits a wide distribution. Similar behavior was observed in this 144 experiment. Fig. 5 shows the relationship between the calculated crystallite size and a 50 % 145 fracture stress. In this figure, the straight line is a regression line obtained by applying the least-146 squares method. There is a correlation of the crystallite with the 50 % fracture stress. Thus, the 147 assumption that a particle's strength depends on the order of its crystallinity was confirmed. 148 nozzle with the 50 % particle diameter after performing the particle impact test. In this figure, the 152 solid line trend can be easily explained. For each sample, its 50 % particle diameter decreases at 153 the flow velocity value indicated by a dashed line. It was assumed that many particles fractured at 154 this point. The particles used in this experiment were relatively large; their Stokes number was 155 over 450 at the maximum nozzle diameter condition. It can be considered that a particle's impact 156 velocity is the same as the airflow velocity. Thus, this velocity was defined as the critical fracture 157 velocity. Fig. 7(a) shows the relationship between the critical fracture velocity and the crystallite 158 size of each particle sample. A correlation of the critical fracture velocity with the crystallite size

A C C E P T E D M A N U S C R I P T
9 can be observed. However, its R 2 value is lower than 0.95. This can be due to the differences in 160 the average particle size among the samples. To exclude the effect of particle size, the kinetic 161 energy E (J) of particles at their fracture point was calculated using the following equation, where 162 vc (m s -1 ) is the critical fracture velocity, x (m) is the average particle diameter, and ρp (kg m -1 ) is 163 the particle density: 164

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(2) 166 167 Fig. 7(b) shows the kinetic energy of a single particle at its fracture point as a function of the 168 particle's crystallite size. The kinetic energy of a single particle exhibits a good correlation with 169 the crystallite size, and its R 2 value is higher than 0.99. Using this result, a particle's fracture 170 velocity can be estimated from its crystallite size to prevent particle fracture. 171 Next, the effect of the impact angle on the critical fracture velocity was investigated. Particle B 172 was selected as a sample because its fracture stress value was approximately the average among 173 the fracture stress values of the four samples. Fig. 8 shows the relationship between the impact 174 angle and the critical fracture velocity. The solid line in Fig. 8 exhibits a trend, which can be 175 easily explained. It is observed that the particle fractured more easily at impact angles below 45°. 176 For an impact angle in the 45°-90° range, the lower the impact angle, the lower the critical 177 fracture velocity is. The single-particle fracturing under static and biaxial compression conditions

A C C E P T E D M A N U S C R I P T
10 was analyzed in (Satone et al., 2017), where it was found that the required load for particle 179 fracturing under a biaxial compression was less than that under a uniaxial compression. Under the 180 biaxial compression with equal loads applied on the two axes, the angle of the resultant force 181 formed by the two axes was 45°, and the required load for particle fracturing exhibited its lowest 182 value. This result may be attributed to the following. The particle compressed along one axis 183 deformed into a flat shape similar to that of a "Go stone" since the deformed material was able to 184 move freely from compression along the two axes. The biaxially compressed granules deformed 185 only in one free direction; however, their shape was spheroid, similar to that of a rugby ball. 186 Under the biaxial compression, the granule material exhibited fewer degrees of freedom to 187 disperse the compression load compared with the uniaxial compression case. Fracturing occurred 188 even at low forces, as the biaxial load became unbalanced. 189 When a particle impacted the wall vertically, the particle was deformed in the two axes 190 without moving direction. Its shape became flat, similar to that in the uniaxial compression. On 191 the other hand, when a particle impacted the wall diagonally, the particle could be deformed only 192 one axis. Its shape became spheroid, similar to that in the biaxial compression. This was 193 considered as the reason that the particle fractured more easily at impact angles below 45°. 194 Nevertheless, the deformation behavior of the impacted particle can only be speculated. We are in 195 the process of investigating this topic using bigger particles and a high-speed video camera.

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When the impact angle is over 45°, it is considered that the particle could not collide with the 197 wall; instead, it slid on the wall's surface. Thus, the particle could not easily fracture in this case 198 since the impact force could hardly be transmitted to the particle. In various real industrial 199 processes involving particle movement, such as a powder pneumatic transportation system, there 200 is an empirical law stating that particle fracturing occurs at the elbow of a pipe, where the airflow 201 direction changes drastically. In this case, the particle will not always impact the inner wall 202 vertically. The particle's trajectory changes because of various factors such as the elbow 203 curvature radius, the elbow angle, and the insufficient Stokes number of the particle. Among 204 these effects, the particle can impact the inner wall from various angles. This consideration is 205 qualitatively related to the above empirical law. 206 207

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In this study, the effect of terephthalic acid particle properties on particle fracture phenomena 210 was explored. Furthermore, the fracturing characteristics in real processes were determined by 211 investigating the effect of the particle impact angle on particle fracture phenomena. The results 212 indicated that 1) the crystallite size is related to the fracture stress of a particle, 2) the crystallite 213 size is related to the critical fracture velocity and the kinetic energy of the particle, and 3) a 214 particle fractures more easily at impact angles below 45°. Using these results, the occurrence of