Microplastics segregation by rise velocity at the ocean surface

Predicting the vertical distribution of microplastics in the ocean surface mixed layer is necessary for extrapolating surface measurements and comparing observations across conditions. The competing mechanisms that control the vertical distribution are particle buoyancy, which is primarily a function of particle properties and drives microplastics to accumulate at the ocean surface, and turbulent mixing, which disperses microplastics throughout the mixed layer and depends on local hydrodynamics. In this study, we focused on the physical properties of microplastics collected within one vertical profile in the North Pacific. We measured the size, shape, and rise velocity of all microplastics collected, finding that average size and rise velocity decay with depth. In addition, we demonstrate how the vertical distribution of the microplastics depends on the rise velocity of the microplastics by segregating the data into three regimes based on a ratio of microplastic rise velocity and a characteristic turbulence velocity scale. Using an individual model for each regime, we can extrapolate the vertical distribution of microplastics to the bottom of the mixed layer and find the total concentration of microplastics. The total extrapolated concentration using the combined model results in 10× the concentration of the surface net alone and 47% more than a model which does not consider the different microplastic regimes. Finally, we discuss how the vertical distribution also depends on microplastic form, finding that lines are approximately well-mixed whereas the concentration of fragments decays with depth. These observations indicate the importance of considering the appropriate rise velocity regime when predicting the vertical distribution of microplastics.


Introduction
Plastic debris is found throughout the world's oceans, atmosphere, and lands [1,2]. At the ocean surface, low-density plastics accumulate in relatively high concentrations due to their buoyancy and environmental persistence [3,4]. By number, most pieces of plastic in the ocean are microplastics [5], typically defined as particles smaller than 5 mm in length [6]. Ocean surface microplastics have been measured for decades, where they have been shown to accumulate in subtropical convergence zones, or gyres, in the open ocean [3,7]. Microplastics measurements are typically done with a surface plankton net, and the measured concentration depends both on the local concentration, typically a function of the distance to the center of a gyre, and also the local conditions at the time of collection [8]. For example, windy days result in higher turbulent mixing, which redistributes microplastics lower in the water column, thus reducing surface concentrations [9]. The vertical mixing of microplastics has been studied and modeled due to various processes: e.g. wind-driven mixing, breaking waves, Langmuir circulation, and convection [9][10][11][12][13]. However, the physical characteristics of the microplastics themselves will also control their vertical distribution.
Microplastics recovered from the surface of the ocean are derived from various unknown sources, and are therefore variable in their size, shape, and polymer type [14]. These characteristics affect the particles' response to hydrodynamic forcing: e.g. forces due to buoyancy and drag [15,16]. Thus, we do not expect all microplastic particles to behave similarly under the same ocean conditions; e.g. we expect less buoyant microplastics to be mixed deeper, as has been observed by Kooi et al [17]. To characterize the effects of buoyancy on the particles, we measure their rise velocity. Many studies have focused on predicting the rise velocity of microplastics as a function of size, shape, and density [18][19][20]. However, to our knowledge, no study has yet to measure the individual rise velocity of all microplastics recovered from a vertical profile in the ocean, even though we expect the rise velocity to be a key parameter in determining vertical distribution [9,12].
In this study, we focus on how the physical characteristics of microplastics collected from the North Pacific relate to their vertical distribution. Specifically, we analyze how the vertical distribution varies as a function of microplastic attributes such as rise velocity and form. Additionally, we observe three distinct vertical distribution regimes when conditioned on a ratio of the particle rise velocity to a characteristic turbulent mixing velocity. By measuring individual particle characteristics, including size, mass, shape, and terminal rise velocity, we find that the microplastics measured near the ocean surface are diverse, spanning multiple orders of magnitude in size and rise velocity, and therefore should not all be modelled together.

Data collection
The samples used in this study were collected on 25 October 2012, in the North Pacific Subtropical Gyre aboard the Sea Education Association (SEA) Sailing School Vessel Robert C Seamans, using a neuston net for surface samples and MOCNESS (Multiple Opening/Closing Net and Environmental Sensing System) for samples at depth, both with 335 µm mesh; samples at each depth were collected consecutively over the course of three hours starting with the bottom net; wind and wave conditions were approximately constant over the sampling period, and the boat was heading perpendicular to the prevailing winds. A flowmeter was used to measure the volume of water sampled by each net. This is part of a larger dataset that has been previously reported in Brunner et al [10]. In this study, we further analyze the physical characteristics of individual microplastics within one vertical profile. The analyzed samples included every piece of plastic available from a vertical profile consisting of five collection depths: 0 m (surface), 0.6 m, 2.8 m, 5.5 m and 9.7 m below the surface. This specific vertical profile was chosen for further analysis because it took place under the strongest wind conditions, 17 knot winds (Force 5), out of all eight profiles. After collection, samples were visually picked out from a sieve, rinsed with DI water, allowed to dry, and stored in glass vials in the dark for further analysis.
In the laboratory each of the 216 plastic particles collected was analyzed using a Raman spectrometer (Agiltron PeakSeeker Pro, Woburn, MA) with a microscope attachment (AmScope AJX Series Metallurgical microscope), fiber optic sidelight (Schott MLS LED), and microscope camera (Lumenera Infinity 2-1RC) for polymer identification and visualization of surface characteristics. Each particle was also categorized into five groups based on form: fragment, pellet, line, film, or foam. Note that 'lines' are distinct from microfibers; microfibers have a much smaller cross-sectional diameter than lines. The microplastic particles were placed on a high-resolution scanner (Epson GT-20 000) laying on their largest dimension and scanned at 2400dpi with a black background. Using image analysis software (Image Pro Premier) the microplastics were outlined in the scanned images and numerous size parameters were taken using image calibration with a traceable ruler, including longest caliper length, ℓ max , and two-dimensional surface area, hereafter referred to as area. The individual mass of each piece was measured using an analytical balance. It is not uncommon to observe a thin biofilm on microplastics upon collection, most of which is removed during initial processing (a freshwater rinse followed by an air-drying prior to storage). Because the particles were collected in the oligotrophic subtropical gyre, biofouling is limited; thus, the stored particles are expected to be as representative of freshly collected particles as feasible.

Rise velocity experiments
Particle rise velocity, RV, was determined using a custom-built Rise Velocity Chamber constructed of a clear plastic geological coring tube filled with artificial sea water (34.5 psu) with a measuring tape affixed vertically to the back of the chamber to measure distance. The rise velocity chamber is 4.5 cm in diameter and over 240 cm tall with an elevator device attached to a fishing line used to lower the microplastics and release them at the bottom of the chamber. Temperature and salinity were recorded each day of sampling, and the water was mixed regularly to ensure that no stratification occurred. The chamber was covered securely when not in use to prevent evaporation.
Each microplastic particle was slowly lowered down and released at the bottom of the chamber. Measurements for each piece began 20 cm above the release point to ensure that the particles had reached terminal velocity. At the 20 cm mark, a timer was started using a phone app to record and save each measured time interval in a .csv file. The time for a microplastic particle to rise approximately 10 cm was recorded for a total span of 210 cm. The observer maintained a horizontal eye-level orientation to each particle as it rose. This procedure was repeated for each particle, and an average RV measurement was computed over measurements from both runs.
Variability within the measurements was quantified by dividing the rise velocity data into 10 cm segments for the two trials and calculating the standard deviation and mean of the rise velocity across all segments. We found that the average coefficient of variance (standard deviation normalized by mean) of the rise velocity was less than 10%, and that the mean standard deviation was less than 0.1 cm s −1 . A plot relating the standard deviation and mean RV for all observations is included in the supplemental materials.
We were unable to run the rise velocity experiments with certain particles because they had broken apart in previous processing steps. Therefore, we only measured the RV of 172 of the 216 total particles. All quantitative RV analyses were done with the measured values only; however, for the vertical distribution analysis we used estimated RV values for the particles with missing values using a two-dimensional linear interpolation across mass and area.

Data analysis
Under wind-driven shear mixing at the ocean surface, there are two dominant mechanisms that control the vertical distribution of microplastics: particle buoyancy and turbulent mixing. We characterize buoyancy with the microplastic RV, and we characterize the turbulent mixing due to the shear stress at the ocean surface with the water friction velocity u * . We calculate the water friction velocity using the model of Edson et al [21] (their equation (22)), and we find u * = 0.97 cm s −1 for our measurements. By taking the ratio of these two velocities, we arrive at a non-dimensional mixing parameter, which is a type of Rouse number Z (or floatability parameter [12]), where For Z ≫ 1, we expect the microplastics behavior to be buoyancy-dominated with minimal entrainment below the surface, resulting in microplastics trapped at the ocean surface. For Z ≪ 1, we expect the turbulent-mixing to be much stronger than microplastic buoyancy, resulting in microplastics becoming evenly distributed within the ocean mixed layer. For Z ∼ 1, we expect both buoyancy and turbulent mixing to be important. Another appropriate turbulence velocity scale to use could be that proposed by Chor et al [12] which additionally includes the effects of Langmuir turbulence and convection. However, because the ocean conditions were constant across all collections in this study, changing the velocity would only scale Z proportionally, and therefore we choose u * for simplicity.
In the case where Z ∼ 1, where buoyancy and turbulent mixing are approximately balanced, we can use the microplastic mixing model proposed by Kukulka et al [9] to estimate the vertical distribution of microplastics. The Kukulka et al [9] model assumes that the upward flux of particles due to buoyancy is in equilibrium with the turbulent flux mixing them downwards. By approximating the turbulent mixing of particles with an eddy diffusivity model, Kukulka et al [9] predicted a vertical concentration profile that has a maximum concentration at the surface and decays exponentially with depth, giving the following expression for number concentration c: where c 0 and L m are constants. In this case, c 0 is the surface concentration and L m is the mixing lengthscale which is equal to A 0 /RV where A 0 is the eddy diffusivity of the particles in turbulence. Note that this model assumes uniform mixing and therefore a constant value of A 0 .

Observations
A total of N = 216 microplastic particles were collected during the sampling period. Table 1 summarizes the observations across all measurement depths. Of the collected particles, 189 were classified as fragments, 22 were classified as lines, and 5 were other types (pellet, foam, or film). Particle size ranged from 0.49-31 mm (based on ℓ max ), with masses spanning less than 1 mg to 0.11 g. Concentration of microplastics both by number and by mass are reported in table 1, and while both concentrations decay with depth, the mass concentration decays faster than the number concentration. This is because the microplastics collected from the deeper samples are smaller in size than those collected near the surface. In figure 1, we plot boxplots of microplastic mass, maximum caliper length ℓ max , and area as a function of depth. While the average mass and average area of the particles does decrease with depth, average ℓ max is relatively constant with depth. All characteristics vary over multiple orders of magnitude, demonstrating how varied microplastics are in their physical characteristics. Raman spectroscopy was able to identify the polymer type of 72% of the microplastics. The most common polymer type was polyethylene (N = 128). The second most common polymer type was polypropolene (N = 25). Two particles were identified as polystyrene, and the rest were not able to be identified using Raman spectroscopy. The full dataset, including specific attributes of each particles, is available in the supplementary data.   and a standard deviation of 0.9 cm s −1 . Partitioning the data by sampling depth, however, reveals that surface measurements are skewed towards higher RV values when compared to subsurface measurements. This depth dependence is illustrated in table 2 which shows how both the maximum and mean RV values decay with depth. In figure 2(b) we plot the mean and standard deviation of the RV observations at each depth, overlaid on all measurements. From this plot, we further observe that although the mean RV decayed with each depth, the sharpest decrease in RV occurred between the surface and the shallowest subsurface point.

Rise velocity
In order to rigorously examine the significance of the mean RV decay with depth, we conducted a pairwise ANOVA test. We found that the mean surface RV was larger than all subsurface values at a level of statistical significance (p ⩽ .004), however no subsurface values were significantly different from one another. Thus, we find that the surface microplastic RV values are distinct from all subsurface values.
Finally, we can quantify the Reynolds number Re of the microplastics, which measures the ratio of inertial to viscous forces on the particles and is used to predict drag coefficients and microplastic terminal rise (or settling) velocities (e.g. see Van Melkebeke et al [22]). Defining Re = ℓ max RV/ν where ν is kinematic viscosity of seawater, we find that Re values range from 2 to 300, with a mean value of 45 and a standard deviation of 53. Thus, we find that the majority of microplastics analyzed in this study fall in the intermediate Re regime, where we expect their behavior to be Reynolds number dependent [16].

Vertical distribution
Using the non-dimensional mixing parameter Z, we segregate the data into three categories which we have named surface-trapped with Z > 2, partially-mixed with 0.5 ⩽ Z ⩽ 2, and well-mixed with Z < 0.5. Despite the similar force balance, we do not expect the dynamics of this system to exactly match the classical Rouse number regimes in the sediment transport literature due to the differences in the fluid flow. For example, the Rouse number typically characterizes sediment concentration profiles in turbulent open channel flow over a sediment bed [23], whereas microplastics at the ocean surface are mixed by turbulence generated by wind and breaking waves, among other processes, at a free surface boundary layer [24]. This analysis is sensitive to the specific Z values. We have chosen values based on an initial assessment of the data, which attempted to maximize  the distance between the lower and upper Z bounds while maintaining vertical profiles aligned with our expectation; a sensitivity analysis is included in the supplemental materials. In this analysis, we have used all particles and either their measured or estimated RV value. Because the wind conditions were approximately constant across the observations, u * is a constant, and therefore these regimes correspond directly to the microplastic RV values. Figure 3(a) shows concentration profiles in number per volume (N m −3 ) over depth. We plot the profile for each Z category and the total concentration profile for reference, highlighting the different behavior in each regime. The surface-trapped category represents the most buoyant microplastics and its profile has a peak concentration at the surface with only a small non-zero concentration at the first two measurement depths; turbulent mixing is unable to entrain the microplastics far below the surface. The partially-mixed regime is our intermediate regime where both buoyancy and turbulence are important; its concentration profile decays with depth in an exponential manner. Finally, the well-mixed category represents the least buoyant microplastics and its profile is relatively constant with depth; the uniformity of the concentration suggests turbulence in the mixed layer can overcome the buoyant upward flux of these microplastics.
The data did not partition into the three categories equally: approximately 13% of the microplastics by number were surface-trapped, 70% were partiallymixed, and 17% were well-mixed. If we divide the data by mass, we find that the ordering of the regimes changes. We calculate 60%, 38%, and 1% of the observations by mass were in the surface-trapped, partiallymixed, and well-mixed regimes respectively. Thus, while only a small fraction of the particles were buoyant enough to stay surface-trapped, they collectively represented the majority of the observations by mass due to their larger size. Mass concentration profiles over depth for each regime are included in the supplemental materials.
Using these categories, we can model the microplastics concentration over the mixed layer (which had a depth of approximately 40 m at the time of observation; the depth was estimated using a CTD cast based on a 0.2 • C temperature change threshold [25]; the measured density profile is included in , partially-mixed (0.5 ⩽ Z ⩽ 2), and well-mixed microplastics (Z < 0.5). We also plot the total concentration for reference. For this data Z = RV/u * where the water friction velocity u * was estimated to be 0.97 cm s −1 during the time of sampling. (b) Modeled concentration profile for partially-mixed and well-mixed microplastics plotted over the observations. The sum of the two models is plotted in black and the modeled concentration using all of the data fit to equation (2) is shown with a dashed line. Note the vertical scale differs between panels, and that we do not model the surface-trapped regime. the supplemental materials). First, we model the well-mixed regime with a constant profile based on the average concentration. Next, we model the partially-mixed regime with an exponential profile where we fit c 0 and L m in equation (2) to the data, finding a best fit with L m = 7.0 m and c 0 = 0.16 N m −3 . We do not attempt to fit a model to the surface-trapped microplastics. Finally, we extrapolate the models for the well-mixed and partiallymixed regimes to the bottom of the mixed layer, as depicted in figure 3(b). By integrating the modelled distribution over depth, we estimate the total concentration of buoyant microplastics per area of ocean surface. This procedure results in total estimated concentrations of 1.0 N m −2 particles in the well-mixed regime and 1.1 N m −2 particles in the partially-mixed regime. If we add in the observed surface-trapped particles (only 0.03 N m −2 ), we find the total estimated concentration to be 2.2 N m −2 when integrated over the entire mixed layer. This is over 10× larger than that measured by the surface net of 0.19 N m −2 . This discrepancy further illustrates how surface measurements alone will undercount microplastics due to vertical mixing.
In Kukulka et al [9], the authors use a parametric law for the eddy diffusivity A 0 of the microplastics; yet their model underpredicts mixing given their predicted A 0 and measured average rise velocity. In a later publication, increased mixing was shown to be a result of Langmuir turbulence [10]. In this study, we can measure our effective diffusivity directly based on our partially-mixed profile given that A 0 = L m × RV. Using the average RV of the partially-mixed microplastics (1.1 cm s −1 ), we compute the effective diffusivity of the microplastics to be A 0 = 0.077 m 2 s −1 .
We can also compare our modelled vertical distribution with one that considers all the microplastics together by fitting equation (2) to all of the data, regardless of their Z value. This profile is plotted in figure 3(b) with a dashed line, where the fitted parameters are c 0 = 0.24 N m −3 and L m = 6.1 m. Integrating this profile, we find the total estimated concentration to be 1.5 N m −2 . Thus, we find that our estimation using the three separate profiles is 47% larger than the estimate which uses only one profile. This demonstrates the importance of not using only one model to estimate the vertical distribution of microplastics, because we expect different behavior depending on the local Z value.

Microplastic form and shape
The microplastic data also segregate based on particle physical characteristics. In our data, we found that the dominant forms were fragments and lines, and therefore consider only those two types in this section. We plot the distribution of RV for both forms in figure 4(a). The lines exhibit a narrower distribution of RV values when compared with the fragments. Additionally, we see that the maximum fragment RV is almost 4× higher than that of the lines, indicating  that the fragments are much more buoyant than the lines. This agrees with previous work [17], and makes physical sense: buoyancy is proportional to particle volume and the fragments are generally more voluminous than the lines.
We also plot vertical concentration profiles of the microplastics as a function of their form in figure 4(b), where we see that the observed concentration of fragments is higher than that of the lines at all depths. With respect to the shape of the profiles, we see that the concentration of the fragments decays rapidly with depth, whereas the concentration of the lines is relatively well-mixed, showing little change in concentration over depth. This is what we would expect given the microplastic RV values; if we calculate Z for the lines we find that it is less than or equal to unity, indicating that most of the lines fall within the well-mixed regime. Alternatively, the fragments have a large range of RV and Z values, spanning all three identified regimes, and the resulting profile is a combination of all three.
One of the most common ways of classifying microplastic samples is through their longest lengthscale. In figure 5(a) we plot the longest lengthscale ℓ max of each particle against RV, separated by microplastic form. We find that the RV of the lines is independent of their length (with Pearson correlation coefficient R = −0.080), despite variations in length over an order of magnitude. When considering the fragments, we find that RV is positively correlated with length (R = 0.654), suggesting that the RV of the fragments is more sensitive to size than that of the lines.
Despite the divergent behavior in figure 5(a), we can collapse the fragment and line RV data together if we plot it against a ratio of particle mass to area ( figure 5(b)). We find both fragments and lines are strongly positively correlated with this ratio (R = 0.778 for fragments and R = 0.698 for lines). Thus, the RV increases linearly with the mass-to-area ratio, with scatter in this relationship likely due to variations in microplastic density, shape, and volume that are not captured in this plot. We did not measure density or volume directly, however they could be estimated and used to predict RV from one of the many formulas that exist (see Van Melkebeke et al [22] for examples).
Finally, microplastic shape was characterized using image analysis. Specifically, we quantify shape using circularity, defined here as 4π×area divided by the perimeter squared, and where a circularity of 1 is a perfect circle and 0 is an extremely nonspherical/irregular microplastic. In figure 6, we plot the circularity as a function of microplastic size ℓ max for fragments and lines. We observe that the circularity is inversely correlated with ℓ max for all particles (R = −0.6476), lines (R = −0.521), and fragments (R = −0.335). In other words, the smaller microplastics are on average more circular in shape. This suggests that as microplastics degrade into smaller pieces they will become more spherical.

General discussion
This study provides direct observations of microplastics segregation by rise velocity under strong winds. We demonstrate that the vertical distribution of microplastics can be divided into distinct regimes based on a ratio of the microplastic rise velocity and a turbulence velocity scale, and that these regimes can be observed in data from the open ocean.
One theme of these observations is that buoyant microplastics cover a large range of scales and therefore they cannot always be modelled as a single particle type. For example, the work of de Vos et al [26] reported how in the wake of a nurdle spill and fire, burnt nurdles and unburnt nurdles exhibited different onshore transport, suggesting that physical characteristics can dictate microplastic behavior in the environment in a meaningful way. Based on our observations, we suggest that improved models of microplastics transport and dispersal in the environment will need to consider the regimes of microplastics of interest. While modelling efforts have already begun to address this [12,27,28], we provide more direct observation of their importance. With regards to vertical distribution, we recommend that the three regimes that specifically need to be considered are that of the surface-trapped, partiallymixed, and well-mixed microplastics, as we expect these to cover the range of distinct behaviors expected in the ocean mixed layer.
This study also shows how microplastic form dictates behavior. Lines and fragments showed distinct vertical distributions, which makes sense as they have different characteristic rise velocities, and we expect rise velocity to dictate vertical distribution. Lines have smaller rise velocities on average than fragments, and therefore we expect them to be more well-mixed. Indeed, this is what we observed. The concentration of lines stayed relatively constant with a peak concentration at 5.5 m depth, whereas the fragments had a peak concentration at the surface that decayed with depth. This suggests that separating microplastics observations by form alone may be enough to infer properties of their vertical distribution. However, in this study we only considered fragments and lines, and therefore it remains to be seen how well other forms (including foams, pellets, and films) segregate in their vertical distribution.
Another observation from this study is that smaller microplastics were more spherical in shape. Microplastics experience weathering in the ocean, weakening their material and resulting in fragmentation. Some studies have tried to model the fragmentation process [29,30], but the timescales of physical and chemical degradation of microplastics in the environment are still poorly defined. The correlation between shape and size observed in these data suggests that shape may be a useful indicator of microplastic age.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).