Sedimentation of Irregular Shaped Microplastics Under Steady and Dynamic Flow Conditions

: Because of different compositions, physicochemical properties and shapes in nature of the microplastics 11 (MPs), their migration process in the environment is very different, which makes it difficult to predict the behavior 12 trajectory. This article mainly studies the sedimentation law of MPs under static and dynamic water conditions. 13 Four kinds of materials, respectively polystyrene (PS), Polyamide (PA), polyethylene terephthalate (PET) and 14 polyvinyl chloride (PVC), about 1230 MP particles with irregular shapes are selected for sedimentation 15 experiments. They are divided into three shapes: near - sphere, polygonal ellipsoid and fragment. The experimental 16 results show that the near - sphere MPs settled at the fastest rate, followed by the polygonal ellipsoid MPs, and the 17 fragmented MPs settled at the slowest rate. By the force analysis of MPs in the settlement process, and the 18 theoretical formula of MP settlement rate with their shape, particle size, density and water density are obtained, 19 which has better fitting degree.


23
Plastic pollution has now become one of the most important and obvious water 24 environmental pollutions (Kaiser et al., 2019). Over the past few decades, plastic production has 25 increased dramatically, despite government and other interventions, while a significant amount of 26 plastic waste has been released into the environment ; Barnes et al., 2009). 27 Around the world, there is growing concern about the release, distribution and environmental 28 impact of plastic waste, including particularly small pieces of plastic (Galgani et al., 2013). 29 Typically, polymer particles with a particle size of less than 5 mm are defined as MPs (Costa 30 et al., 2016). Its sources include direct emissions of larger plastic particles contained in personal 31 skincare products, toothpaste, detergents, etc., and the release of these larger plastic particles after 32 they have been shattered into small fragments through various degradation processes 33 These MPs, which are decomposed and broken into different shapes due to various natural 38 forces such as light and microorganisms in the environment, will migrate in the environment 39 through wind, runoff, and man-made wastewater discharge, ships, port activities, etc. (Derraik et  Randomly select 30 near-spheres and 30 fragments from the samples, calculate their CSF 108 index, and conduct a significance test. When the significance level was 0.05, we defined that the 109 CSF index of the near sphere was 0.9 ~ 1, the CSF index of the fragments was 0 ~ 0.7, so the CSF 110 index of the polygonal ellipsoid was 0.7 ~ 0.9. Therefore, this article discusses the three shapes of 111 MPs into nearly spherical, polygonal ellipsoid and flat fragments. 112

Preparation of water bodies of different salinity 113
In order to compare the effects of water salinity on the sedimentation rate of microplastics, 114 the salinity of seawater (the average is 36 ‰) was taken as the highest value of salinity in the 115 experimental water body. Three kinds of water solutions were prepared, and their salinities were 116 0 ‰ (980 kg/m³), 15 ‰ (1010 kg/m³) and 36 ‰ (1026 kg/m³) respectively. Take a water body 117 with a salinity of 15 ‰ as an example. The steps are as follows: 118 (1) Take deionized water and measure its water density as ρ0; 119 (2) Weigh deionized water in a beaker to measure its mass as M0, then the volume of water is 120 V=M0/ρ0; 121 (3) According to the salinity of 15 ‰, the density is ρ, and the mass of NaCl measured with a 122 balance is M=(ρ*V)-M0; 123 (4) Pour NaCl into a beaker and stir with a glass rod until it is colorless and transparent, 124 which is an aqueous solution with a salinity of 15 ‰. 125

Experimental equipment 126
This experiment mainly studies the settlement process of MPs in the water environment, 127 which is different under different hydrodynamic conditions. Therefore, there are two kinds of 128 water environment conditions, respectively static and dynamic water, to be designed in this paper. 129 The former is to study the sedimentation laws of MPs in semi-closed water bodies such as lakes 130 and reservoirs without water flow conditions. The second is to study the sedimentation laws of 131 MPs under flowing water conditions such as rivers and channels. Therefore, the following 132 equipment was set up in this experiment. 133

Static water sedimentation test equipment 134
The static water sedimentation test was carried out in a water column container with a height 135 of about 40 cm and a diameter of 6.45 cm. Because the surface roughness and water absorption of 136 MPs also had an effect on the sedimentation process, three materials of MPs, that is PA, PET and 137 PVC, were selected as the research objects, and each material was subjected to sedimentation 138 experiments at three salinity conditions of 0 ‰, 15 ‰ and 36 ‰. Thus, a total of 9 combinations 139 of experiment conditions were conducted. Mark the water column container up and down (Fig. 2), 140 fill the aqueous solution to about 5 ~ 10 cm above the upper marking line, and control the test 141 temperature at about 20 °C. At the same time, for the convenience of shooting, a background 142 board with a large color difference from the MPs is added on the back of the water column 143 container. 144 In the experiment, the MP particles were dropped about 1 cm below the water surface by 145 using tweezers to avoid the effect of water surface tension on the settlement of MP particles, 146 keeping them free to settle. When the MPs particles pass through the upper marking line, the 147 timing begins, until the timing stops when they pass through the lower marking line. Therefore, 148 the sedimentation rate is the ratio of the distance between the two marking lines to the 149 sedimentation time.

Pretreatment of samples 165
Due to the irregular shape and high surface roughness of the MP sample after grinding by the 166 grinder, it is found in the preliminary experiment that even if the density is greater than that of the aqueous solution, it is often difficult to settle smoothly. Therefore, in this experiment, before the 168 formal sedimentation experiment, the MP samples were immersed in the required aqueous 169 solution in advance, and each group of samples was immersed for more than 4 hours to make the 170 aqueous solution fully infiltrate the MP samples to ensure a smooth sedimentation process. 171

Error control and verification of experimental device 172
The sedimentation process of MPs in water environment is more complicated, and the 173 observation process is prone to large errors, especially in dynamic water sedimentation 174 experiments. Therefore, in this experiment, in order to accurately determine the sedimentation 175 time of the MPs, we photographed the entire sedimentation process with a camera, followed by 176 observation and video recording 3 times, recorded the sedimentation time, and took the average of 177 the 3 times as the sedimentation time of the MPs. In the process of dynamic water sedimentation, 178 in order to make the camera record a clear picture, we fixed the camera, water column, and 179 background plate on the oscillating instrument at the same time to keep them moving 180 synchronously to reduce the error caused by experimental observation. 181 At the same time, during the sedimentation process of MPs, changes in temperature will also 182 cause changes in the density of the water body, thereby affecting the sedimentation process of 183 MPs (Kaiser et al., 2019). Therefore, during the whole experiment, we kept the air conditioner on, 184 kept the room temperature at 20 ℃, and measured the water temperature of the water column in 185 each experiment with a thermometer to ensure the accuracy of the temperature. 186 In this experiment, the sedimentation process of MPs is carried out in a water column. In a 187 bounded space, the sedimentation rate of MPs will be reduced due to the wall flow effect of the 188 container boundary (Ristow, 1997). Therefore, in order to reduce the influence of this effect, we 189 apply a wall correction factor to correct the sedimentation rate of MPs: 190 1.14 -1 (3) Where: w is the particle's bounded sedimentation rate, m/s; w ∞ is the particle's unbounded rate, 191 m/s (the sedimentation rate in the following is the unbounded sedimentation rate); d is the particle 192 diameter, where ESD, m; L is the diameter of the water column, m. 193 Whether the experimental device is reliable is also an important part of ensuring the accuracy 194 of the experiment. In order to verify the reliability of the experimental device, a method of 195 comparison with the theoretical formula is used for verification. A near-sphere with a CSF index 196 of 0.9 to 1 and a PS MP with an ESD range of 0.371 to 1.195 mm were selected, and the 197 sedimentation experiment was performed when the salinity was 0 ‰. 198 Where: Re is the particle Reynolds number, 0 ~ 1 is laminar flow, 1 ~ 10 3 is transitional flow, 10 3 199 ~ 10 5 is turbulent flow; w is particle sedimentation rate, m/s; υ is the kinematic viscosity, m²/s; and 200 others are consistent with the above formula. 201 The movement of MPs in quiescent water is related to the particle Reynolds number, and the 202 state of flow around the MPs varies with the Reynolds number (Li, 1986). By calculating the PS 203 Reynolds number, it is found that the settlement process is in the transition flow zone. Therefore, 204 the Ganchalov settlement formula, which is widely used in the transition flow zone, is selected for 205 comparison (Fig. 4).
Where: ws is the theoretical sedimentation rate, m/s; ρs is the density of solid particles, kg/m³; ρ is 207 the density of the aqueous solution, kg/m³; g is the gravitational acceleration, taking 9.8 m/s 2 ; β is 208 the factor affecting particle size and temperature; d0 is the selected diameter, which is 0.0015 m; t 209 is the fluid temperature, which is 20 ℃. Where: E is the average relative error, the smaller the E, the better the effect; n is the number of 218 measurements. 219 3. Results

220
The minimum particle size of the MPs selected for the settlement of the MPs is 0.069 mm 221 and the maximum particle size is 3.565 mm. The calculation of its particle Reynolds number 222 shows that the sedimentation process is all transitional flow. In the experiment, in order to ensure that the particle size of MPs is not too concentrated in a certain range, each group of experiments 224 selects different shapes of MPs from large to small, so that the particle size of MPs is evenly 225 distributed in all dimensions, so that the experiment can basically represent the settlement of MPs 226 with different particle sizes. Based on this idea, the experiment measured about 1230 settlement 227 rates of MPs. The specific results are below.  Table 2. ESD, which increases with the increase of ESD, and the correlation is greater than 0.7. In terms of 237 shape, when the salinity is 0 ‰, the MP deposition rate of near-sphere shape is the largest, 238 followed by polygonal ellipsoid shape, and the smallest is fragment shape (Fig. 5A). When 239 salinity is 15 ‰, ESD is less than 3 mm and the fragments settlement rate is small; when ESD is 240 more than 3 mm, the fragments settlement rate is the largest (Fig. 5B). When salinity is 36 ‰, the 241 sedimentation rate of polygonal ellipsoid shape is greater than that of fragments shape (Fig. 5C). ESD. In terms of salinity, Fig. 6 D, E, and F show that regardless of the shape, the sedimentation 258 rate gradually decreases with the increase in salinity, but when the salinity is 15 ‰ and 36 ‰, the 259 PET sedimentation rate is basically not affected. When the significance level is 0.05, there is no 260 significant difference between the two groups of data after testing. Therefore, it can be considered 261 that the increase in salinity will have a certain degree of impact on the sedimentation rate of PET 262 MPs, but the salinity will continue to increase, then this effect can be ignored. In general, the 263 effects of shape and salinity on the sedimentation rate of PET MPs are relatively small. The 264 correlation between the shape of the fragments is weak, at 0.94, which is slightly worse than the 265 correlation between the near-sphere 0.992 and the polygonal ellipsoid shape 0.964.

here] 267
It can be seen from Fig. 7 that the sedimentation rate of PVC MPs is positively correlated 268 with ESD, which increases with the increase of ESD. In terms of shape, when the salinity is 0 ‰, 269 when the ESD is less than 2.3 mm, the sedimentation rate of the near sphere is the largest, 270 followed by the polygonal ellipsoid, and the smallest is the fragments, but the difference is not 271 much. When the ESD is greater than 2.3 mm, the sedimentation rate of the fragments shape is 272 greater than that of the polygonal ellipsoid shape. When the ESD is greater than 2.4 mm, the 273 fragments sedimentation rate is the largest (Fig. 7A). When the salinity is 15 ‰, when the ESD is 274 less than 3.2 mm, the sedimentation rate of the near sphere is the largest, followed by polygonal 275 ellipsoid, and the smallest is the fragments, and the difference is large, and when the ESD is 276 greater than 3.2 mm, the fragments sedimentation rate is the largest (Fig. 7B). When the salinity is 277 36 ‰ and the ESD is less than 3.0 mm, the fragments settling rate is small, and when the ESD is 278 greater than 3.0 mm, the fragments settling rate is the largest (Fig. 7C). In terms of salinity, Fig. 7  279 D, E, F shows that the increase in salinity will reduce the sedimentation rate of the MPs, and the 280 shape of the near sphere and the polygonal ellipsoid show a good linear relationship, while the 281 shape of the fragments is nonlinear. In general, the increase in salinity will reduce the 282 sedimentation rate of PVC MPs, but the impact is weaker. The shape has a great influence on the 283 settlement rate of PVC. The relationship between the settlement rate of the fragment shape and the 284 ESD is a non-linear positive correlation with a correlation of 0.88, and the settlement rate is the 285 largest when the ESD is greater than 3 mm. The sedimentation rate of near spheres and polygonal 286 ellipsoid is linearly related to ESD, and the correlation is 0.934 and 0.917. From Fig. 8. It can be seen that when the salinity is 0 ‰, regardless of the shape of the three 289 MPs, the sedimentation rate is not arranged according to the expected density, the density of PA is 290 the smallest, and the sedimentation rate is also the smallest. The density of PET is less than that of 291 PVC, but the sedimentation rate of PET is greater than that of PVC. In addition to the impact of 292 density, the main reason is that PVC and PA have good toughness, which is a tough plastic. The 293 shape after grinding is extremely irregular, and the grinding place is extremely rough and uneven. 294 When it settles in the water, PVC and PA are in contact with water more fully, and there are 295 obvious rotation and tumbling phenomena, which will seriously hinder the settlement of PVC and 296 PA. The PET is smooth and uniform particles after grinding, and the sedimentation process is 297 smoother and more stable. Therefore, the sedimentation rate of PET is greater than that of PVC. At 298 the same time, PA has a high water absorption rate. When PA enters the water, it forms a 299 short-term bond with water through hydrogen bonds. This bonding will further hinder the 300 sedimentation of particles, so PA sedimentation rate is the slowest. When the salinity is 15 ‰ and 301 36 ‰, the sedimentation law is similar to that of 0 ‰. 302

Dynamic water settlement result 303
In this dynamic water sedimentation experiment, the sedimentation rate of about 230 MPs 304 was measured, two MPs of PS and PET were selected, and the salinity was set to 0 ‰. The two 305 types of MPs were subjected to vibration sedimentation experiments at speeds of 50 r/min, 100 306 r/min, and 150 r/min, respectively, for a total of 6 groups. The results are shown in Table 3 (The 307 sedimentation ratio is the ratio of the MPs that settle to the bottom of the water column to the total 308 experimental sample). Combine Fig. 9 and the hydrostatic sedimentation experiment. It can be 309 clearly seen that under dynamic water conditions, the sedimentation rate of MPs is lower than that under static water conditions. 311 [Insert Table 3. here] 312 It can be seen from Fig. 9 A, B, and C that the dynamic water conditions will significantly 313 reduce the sedimentation rate of PS MPs, and as the rotation speed decreases, the sedimentation 314 rate also decreases. The sedimentation rate of the near-spherical and polygonal ellipsoid shapes 315 has a linear relationship with ESD, while the shape of the fragments has a nonlinear relationship. 316 When the rotation speed is 50 r/min, when the ESD of the near-spherical MP is less than 0.6 mm, 317 the polygonal ellipsoid shape ESD is less than 0.8 mm, and the fragment shape ESD is less than 318 0.8 mm, it will not settle. The MPs will constantly fluctuate up and down with the turbulence of 319 the water flow, and some polygonal ellipsoid may even be suspended in the water column. When 320 the rotation speed is 100 r/min, the ESD of the nearly spherical shape will not settle when the ESD 321 is less than 0.6 mm, and the polygonal ellipsoid and fragments will roll and rotate regardless of 322 their size. When the rotation speed is increased to 150 r/min, the polygonal ellipsoid shape will not 323 settle, and the fragment shape will only partially settle. The correlation of the three shapes of near 324 sphere, polygonal ellipsoid and fragment are 0.93, 0.96 and 0.85, respectively, and the correlation 325 of fragments is the worst. 326 [Insert Fig. 9 here] 327 It can be seen from Fig. 9 D, E, F that the dynamic water conditions will also reduce the 328 sedimentation rate of PET MPs, but when the rotation speed is changed, the sedimentation ratio of 329 PET MPs is basically not affected. During the experiment, the sedimentation ratio of MPs of 330 various shapes under the three speed conditions was basically 100 %. As the ESD increases, the 331 sedimentation rate also increases. There is a good linear relationship between the sedimentation 332 rate of near-spherical and polygonal ellipsoid shapes and ESD, and the correlation is 0.95, 0.97, 333 but the fragment shape has a poor correlation, only 0.84. When a single MP moves in a body of water, it will be affected by many forces, including 337 gravity (G) and floatage (Ff). The orbiting resistance of water flow due to relative motion (Fu). 338 The pressure gradient force due to the pressure gradient in the migration direction of the MPs (FP). 339 The false mass force generated during the process of depositing to the stable settlement (Fd). The 340 Basset force is generated by the instantaneous change of the flow pattern of the water body (FB). 341 The Magnus force perpendicular to the relative velocity of the MPs and the fluid generated by the 342 rotation of the MPs migration process (FM), etc. (Yao, 2014). 343 The force of MPs is very complicated, and different forces have different effects on MPs. 344 Ignoring part of the forces can simplify the force calculation of the MPs settlement process. In this 345 experiment, the studied is the settlement rate of MPs under stable, and most of the MPs are free 346 settlement and only part of them rotate. So for spherical particles, the influence of FP, Fd, FB, and 347 FM can be ignored and only the influence of G, Ff and Fu forces can be considered (Fig. 10). 348 [Insert Fig. 10 here] 349 Where: CD is the drag coefficient, and others are consistent with the above formula. 350 Analyze the force situation, which can be obtained from Newton's second law, 351 During the sedimentation process, the sedimentation rate keeps increasing until the acceleration of 352 the MPs reaches zero and reaches the final sedimentation rate, which is 353 In equation (12), CD is the key parameter of the sedimentation rate of MPs. CD has a very close 354 relationship with the particle Reynolds number and the shape of the MPs. The more regular the 355 shape, the smaller the CD. In order to explore the relationship between the CD and Re of the MPs, 356 refer to the sediment dynamics, draw the relation diagram of CD and Re of all measured data in 357 this experiment. The results show that the power function has a good fitting relationship. 358 Considering the influence of shape, it is decided to fit the data in Fig. 11 with equation (13). (Fig.  359 11, Table 4). 360 [Insert Fig. 11  Where: a, b, and c are parameters. 364 Substituting equations (4) and (13) into equation (12), Calculate the sedimentation rate of MPs according to equation (14), as shown in Fig. 12 (A). The 369 model R 2 is 0.8145, and the average relative error E is 0.25. Based on the experimental data of static settlement, the influence of the density, particle size 372 and shape of the microplastics, as well as the salinity of water on the settlement rate was 373 considered. It can be seen from Fig. 12 (A) that the measured settlement rate of static water has a 374 good goodness fit with the settlement rate calculated by the model. The relative average error 375 between the measured data and the predicted data is only 0.25, and R 2 is 0.8145, indicating that 376 the interpretation rate of the model for the sedimentation rate of MPs is 81.45 %. 377 At the same time, the settlement formula fitted in this paper is compared with the previous 378 theoretical settlement formula of the transition zone (Li, 1986;Wu et al., 2000). The results are 379 shown in Fig. 12 and Table 5. Combining with the above chart, it can be seen that the various 380 errors of the fitting formula in this article are small, and it has a good degree of fit compared with 381 the previous theoretical settlement formula. It can be seen that the settlement formula in this 382 article is more accurate in describing the settlement process of MPs. 383 [Insert Fig. 12  The model in this paper is used to calculate the settlement rate under dynamic water 388 conditions, and the result is shown in Fig. 13, which is consistent with the above discussion. For 389 PS, the measured rate of settlement under dynamic water conditions is less than the predicted rate. 390 For PET, its sedimentation rate is almost unaffected under dynamic water conditions. This is 391 because under dynamic water conditions, in addition to gravity, buoyancy, and resistance, MPs 392 will also be affected by drag forces, which once again slow down the sedimentation rate of MPs. 393 The impact on the low-density PS MPs is greater, while the impact on the denser PET MPs is 394 negligible. Therefore, this formula can predict the sedimentation rate of MPs under static water 395 conditions and the sedimentation rate of high-density MPs under dynamic water conditions. 396 [Insert Fig. 14

406
This experiment mainly studies the sedimentation process of MPs under static and dynamic 407 water conditions, and comprehensively considers the influence of MPs' density, particle size, 408 shape, and water salinity on the sedimentation process. 409 From a large amount of experimental data, the factors affecting the sedimentation rate of MPs 410 mainly include the particle size, density, shape of the MPs, and the salinity and turbulence of the 411 water body. Among them, the particle size, density of MPs is positively correlated with the 412 sedimentation rate. Irregular shapes can have a great impact. For MPs with smooth surfaces, the 413 sedimentation rate of near-spheres is the largest, followed by polygonal ellipsoid, and the 414 fragments shape has the smallest sedimentation rate. For MPs with rough surfaces, the 415 sedimentation rate of the fragment shape is nonlinear with ESD. When the ESD is less than 2 ~ 3 mm, the sedimentation rate of the near sphere is the largest, followed by polygonal ellipsoid, and 417 the smallest is the fragments. And when the ESD is greater than 2 ~ 3 mm, the sedimentation rate 418 of the fragment shape is greater than the other two shapes. The salinity of the water body also has 419 a certain influence on the sedimentation rate. MPs with a density of about 1000 ~ 1250 kg/m³ have 420 a greater impact, and increasing the salinity will significantly reduce the sedimentation rate of the 421 MPs. For MPs with a density greater than 1250 kg/m³, the salinity of the water has little effect. 422 Under the condition of dynamic conditions, the sedimentation rate of MPs will be 423 significantly reduced. For near-spherical and polygonal ellipsoid shapes, the sedimentation rate 424 under dynamic water conditions has a linear relationship with ESD, while the sedimentation rate 425 of fragment shapes has a nonlinear relationship with ESD. For MPs with a density of 1000 ~ 1250 426 kg/m³, when the speed is increased, the sedimentation rate of the MPs will increase, but the 427 sedimentation ratio will decrease. Among them, the settlement proportion of the near sphere is the 428 smallest, and the settlement proportion of the fragments is the largest. For MPs larger than 1250 429 kg/m³, the dynamic water condition will slightly reduce the sedimentation rate of MPs, but 430 increasing the speed will not change the sedimentation rate significantly. Therefore, when 431 removing MPs at the bottom of lakes, the bottom can be stirred to make the water flow oscillate, 432 which can effectively reduce the sedimentation ratio of low-density MPs. 433 At the same time, according to the force analysis of the MPs, and combined with the 434 experimental data, the formula fitting of its settlement rate is carried out. Finally, considering the 435 particle size, density, shape and water salinity of the MPs, the sedimentation formula of the MPs is 436 fitted, and make adjustments on this basis to obtain the settlement formula of low-density MPs 437 under dynamic water conditions. Compared with previous formulae, it is more suitable for the sedimentation process of microplastics. 439 In general, this paper studies the sedimentation process of a large number of irregularly 440 shaped MPs, and fits the sedimentation rate formula of MPs through force analysis. However, this 441 article still has some shortcomings. The most common fiber-shaped MPs have not been considered, 442 and the surface roughness of the MPs has not been considered in the model. These issues need to 443 be considered in subsequent studies.     Settling rate of different shapes of PS and PET under dynamic water conditions. (The dots are near spheres, triangles are polygonal ellipsoid, short horizontal lines are fragments, black is rotation speed 0, blue is rotation speed 50, red is rotation speed 100, and yellow is rotation speed 150) Figure 10 Force analysis of MP settlement.

Figure 11
CD ~ Re tting curve (All measured data).

Figure 12
Comparison of the tting formula in this paper with the various theoretical settlement formulas.

Figure 13
Measured dynamic water sedimentation rate and predicted rate (static water equation).

Figure 14
Measured dynamic water sedimentation rate and predicted rate (dynamic water equation).

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download. Table5.docx