Will it float? Rising and settling velocities of common macroplastic foils

5 Plastic accumulates in the environment because of insufficient waste handling and the materials’ 6 high durability. Better understanding of plastic behaviour in the aquatic environment is needed to 7 estimate transport and accumulation, which can be used for monitoring strategies, prevention 8 measures, and plastic clean-up activities. Plastic transport models benefit from accurate 9 description of particle characteristics, such as rising and settling velocities. For macroplastics, 10 these are however still scarce. In this research, the rising and settling behaviour of three 11 different polymer types (PET, PP, and PE) was investigated, which are the most common in the 12 environment. All of the plastic particles were foils of different surface areas. A new method for 13 releasing rising plastics without interfering the flow and disturbing the column was used. Four 14 models that estimate the velocity based on the characteristics of the plastics are discussed, of 15 which three are from literature, and one is newly derived. These models are validated using the 16 data generated in this research, and data from another study on rising and settling velocities of 17 plastic. From the models that were discussed, the best results are from the newly introduced 18 velocity model for foils (R2 = 0.96 and 0.58, for both datasets). This model shows potential to 19 estimate the rising and settling velocity of plastics, and should be examined further by using 20 additional data. The results of our paper can be used to further explore the vertical distribution of 21 plastics in rivers, lakes and oceans, which is crucial to optimize future monitoring and cleanup 22 efforts. 23

kg/m 3 < ρ < 910 kg/m 3 , respectively (Hidalgo-Ruz et al., 2012)) and will therefore rise when submerged 73 in the water column. The plastics were bought in the supermarket. For PET, the lid of a mushroom box was 74 used; for PP a raisin packaging and for PE a shopping bag. These were manually cut in different shapes 75 and sizes (table 1, figure 1D). 77 The measurements were done in an acrylate column with an inside footprint of 10x10 cm and a height 78 of 70 cm (figure 1A), filled with tap water. The particle sizes were chosen, such that there would be no 79 influence of the wall of the column on the measurements (the wall was not touched by the particle during 80 the run). The average settling and rising time of the plastics was recorded over a certain vertical length. A 81 previous study, using similarly sized plastics, showed that plastics reach their terminal velocity within 15 82 cm (Waldschläger et al., 2020). To be sure, the first 20 cm of the column was used for acceleration of the 83 plastic in this research. This was done for both rising and settling velocity measurements. The particles were released in the water column completely submerged, to make sure that no air bubbles 86 were attached to the plastics and that they would not float because of the surface tension of the water. For 87 the settling velocity measurements, a basket was put at the bottom to make it easier to pick up the particles  For the rising velocity measurements, the water column was divided in six areas (from the bottom up):

Experiment set-up
97 an acceleration part of 20 cm, four measurement parts of each 10 cm, and the excess part. These four 98 measurements per particle were only done for the rising velocity measurements (figure 1B).

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Because the measurements are done in a stable water column, a release mechanism at the bottom of the 100 column is required for rise velocity measurements. Previous methods for releasing the plastics were too 101 difficult for macroplastics, or did not inquire a stagnant water column (Waldschläger and Schüttrumpf, 102 2019; Zaat, 2020). That is why, for the rising velocity, a new method for releasing the particle was made.

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The new method consists of a flexible 'claw' mounted onto an aluminium frame ( figure 1C). The claw is 104 held into a corner, making it possible to release the plastics without interfering the flow. By pushing on top 105 of the claw, the hook releases the plastic without having to disturb the water. This way, the water remains 106 as stagnant as possible.

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First, a test run was done for the plastic, to determine the position of the release mechanism and the time 108 it takes for the plastic to reach the surface. Depending on this time, the distance over which the plastic was  the range mentioned in the article, the mean was taken as a density for each polymer type.

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To get a better view on the validity of the models, two datasets are used. One is the dataset derived in this 120 research, and the other is the data from Waldschläger et al. (2020), which includes mainly microplastics of 121 different shapes.

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The Reynolds number can give an indication for the turbulence of the flow. Depending on the turbulence 123 of the flow, assumptions in the models can be made. Because some models make assumptions that are 124 based on the turbulence of the flow, the Reynolds numbers for all polymers were calculated, using equation 125 1. This can give an indication of the applicability of the models.
In equation 1, d is the equivalent diameter of the particle in m, ρ the density of water in kg/m 3 , µ the 127 dynamic viscosity of water in P a/s and v the velocity of the particle in m/s.

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A theoretical settling velocity was calculated for all plastic items, given the parameters above and the 129 plastic size and density. When these theoretical velocities and the measured data are plotted against each

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These models base their velocity on a shape factor, or on a constant that is empirically determined, in 139 which the shape of the particle plays a role. This is relevant, because the particles measured in this research 140 have a shape that is not found in natural grains often. Therefore, the value of these models for platy particles 141 and foils is researched.

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The first model for settling velocity that was reviewed, was the Stokes equation for settling velocity basis for a lot of models for settling velocity of natural grains, and is thoroughly researched. It can also be 146 used for plastic, at least in an adjusted form (Ferguson and Church, 2004;Gibbs et al., 1971).
In this equation, r is the equivalent sphere radius (ESR) of the particle in m, g is the gravitational 148 acceleration in m/s 2 , µ the dynamic viscosity of water in P a/s, and ρ p and ρ f are the density of the 149 particle and the fluid in kg/m 3 , respectively. The equivalent sphere radius was calculated using the volume 150 of the particles, and relating that volume to a sphere. The more the particle shape deviates from a sphere, 151 the worse this equivalent radius estimation gets. That is why the Stokes equation works best for perfect 152 spheres.
A different equation for settling velocity was developed by Ferguson and Church (2004): In which R = ρp−ρ f ρ f (submerged specific gravity), D is the equivalent diameter of the particle in cm, and g 155 is the gravitational acceleration in m/s 2 . For the polymers with a density lower than water, the submerged 156 specific gravity was taken absolute in the denominator, because of the power 0.5. The constants C 1 (constant 157 from Stokes' law for laminar settling) and C 2 (drag coefficient for Reynolds numbers exceeding 10 3 ) are 158 based on the shape of the particle and the properties of the fluid. The difference with the Stokes model 159 is that this model incorporates a factor for turbulent flow, and is therefore applicable at a larger range of 160 Reynolds numbers.

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For smooth spheres, C 1 and C 2 were determined to be 18 and 0.4 respectively, but for particles with other 162 shapes these values will become higher. In this research, values of 24 for C 1 and 1.2 for C 2 were assumed, 163 as these are the theoretical limit for very angular grains for this model (Ferguson and Church, 2004 Hofmann (1994). The HSE is a shape factor which describes the shape of a particle, with 1 being a perfect  The velocity model follows from the idea that when the gravity force (eq. 5), buoyancy force (eq. 6), and 182 the drag force (eq. 7) are equal, the particle reaches its terminal velocity.
It was observed that during the settling velocity experiment, the foils came down with a swaying, sideways 185 motion. Because of this, it is assumed that the thickness D can better be approximated with the ESR ('r' in 186 the equation) times the CSF, which is the shape factor defined by Corey (1949) and McNown and Malaika 187 (1950). This results in the final velocity model for foils: In equation 10, r is the equivalent radius in m, g is the gravitational acceleration in m/s 2 , ρ f and ρ p are assigning new values for the constants, the model was changed to obtain a better fit with the measured data.

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The model was validated using the data from Waldschläger et al. (2020). In this study, for 100 particles 200 collected from a fluvial environment, the rising or settling velocity is measured. This dataset ranges from 201 microplastic to small macroplastic particles of different polymer types. The plastics were -in contrary to nature -not in water for at least a few hours before the velocity was 214 measured. This has a large impact on the rising and settling velocity of microplastics (Kaiser et al., 2017), 215 however the impact on macroplastics is not yet determined. Furthermore, in the environment biofouling 216 and particle aggregation will take place, which will change the behaviour of the plastics even further 217 (Van Melkebeke et al., 2020;Michels et al., 2018).

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The Reynolds number is a measure for turbulence (Equation 1). The Reynolds regime of this experiment 219 falls in the following range: 12 < Re < 10, 000. The four models that were used in this study are valid for 220 different Reynolds regimes (table 2) (Stokes, 1851;Ferguson and Church, 2004;Le Roux, 2002

CONCLUSION
In this research, three different polymer types and five different surface area classes were tested on their 248 rising and settling behaviour. Three different models from literature and one model derived from theory 249 were used to calculate the velocity. The newly developed technique to release the polymers with a density 250 lower than water (i.e. the rising plastics) worked. This method, consisting of a claw and an aluminium 251 frame, is easy to use and establish.

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PET was found to have a relatively large settling velocity (0.029 -0.037 m/s). This could indicate that PET 253 sinks to the bottom of a fresh-water system quite fast. However, the larger the PET foil is, the slower it will 254 sink. PE and PP are found to rise relatively slow (0.0001 -0.004 m/s and 0.002 -0.006 m/s, respectively).

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This might indicate that they are part of the water column, and that they are more influenced by turbulent 256 movements in the river.

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From all four models that were introduced, only two estimated the behaviour of the platy particles compared to the data generated in this research. This is probably due to the bigger differences in shapes 264 and sizes in the data from Waldschläger et al. (2020), which are harder to estimate using models. Despite