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ArticleMarch 22, 2023

Modeling Microplastic Transport in the Marine Environment: Testing Empirical Models of Particle Terminal Sinking Velocity for Irregularly Shaped Particles
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Róisín Coyle*
Róisín Coyle
Civil Engineering, School of Natural and Built Environment, Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland, U.K.
*Email: [email protected]
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https://orcid.org/0000-0002-8684-8381
Matthew Service
Matthew Service
Agri-Food and Biosciences Institute, 18a Newforge Lane, Belfast BT9 5PX, Northern Ireland, U.K.
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Ursula Witte
Ursula Witte
School of Biological Sciences, University of Aberdeen, Aberdeen AB24 3FX, U.K.
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Gary Hardiman
Gary Hardiman
School of Biological Sciences, Institute for Global Food Security (IGFS), Queen’s University Belfast, 19 Chlorine Gardens, Belfast BT9 5DL, Northern Ireland, U.K.
Department of Medicine, Medical University of South Carolina, Charleston, South Carolina 29425, United States
More by Gary Hardiman
https://orcid.org/0000-0003-4558-0400
Jennifer McKinley
Jennifer McKinley
Geography, School of Natural and Built Environment, Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland, U.K.
More by Jennifer McKinley

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ACS ES&T Water

Cite this: ACS EST Water 2023, 3, 4, 984–995

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https://doi.org/10.1021/acsestwater.2c00466

Published March 22, 2023

CC-BY 4.0 .

Abstract

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Microplastic (mP) pollution has been indicated as an area of concern in the marine environment. However, there is no consensus on their potential to cause significant ecological harm, and a comprehensive risk assessment of mP pollution is unattainable due to gaps in our understanding of their transport, uptake, and exchange processes. This research considers drag models that have been proposed to calculate the terminal settling velocity of regularly and irregularly shaped particles to assess their applicability in a mP modeling context. The evaluation indicates three models that predict the settling velocity of mPs to a high precision and suggests that an explicit model is the most appropriate for implementation in a mP transport model. This research demonstrates that the mP settling velocity does not vary significantly over time and depth relevant to the scale of an ocean model and that the terminal settling velocity is independent of the initial particle velocity. These findings contribute toward efforts to simulate the vertical transport of mPs in the ocean, which will improve our understanding of the residence time of mPs in the water column and subsequently their availability for uptake into the marine ecosystem.

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License Summary*
You are free to share(copy and redistribute) this article in any medium or format and to adapt(remix, transform, and build upon) the material for any purpose, even commercially within the parameters below:
- Creative Commons (CC): This is a Creative Commons license.
- Attribution (BY): Credit must be given to the creator.
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This summary highlights only some of the key features and terms of the actual license. It is not a license and has no legal value. Carefully review the actual license before using these materials.

Subjects

Keywords

Synopsis

Settling velocity models can be implemented in microplastic ocean transport models for irregularly shaped particles with unknown initial settling velocity.

1. Introduction

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Plastic is the overwhelmingly predominant type of litter in the environment, (1) with particle transport models suggesting that up to 51 trillion plastic particles are floating on the ocean surface. (2) Plastic particles that are less than 5 mm in size are known as microplastics (mPs) and are estimated to account for 92% of floating plastic particles in the ocean worldwide. (3) They are difficult to remove from natural water streams and persist in the marine environment for long time periods, breaking into continually smaller particles through slow degradation processes that may take hundreds of years. (4,5)

The determination of the ecological harm caused by mPs in the marine environment is a key objective within the EU Marine Strategy Framework Directive (MSFD 2008/56/EC). (6,7) However, uncertainties surrounding mP processes and a lack of consensus on their fate in the oceans, including their potential to bioaccumulate within ecosystems, prohibit a comprehensive risk assessment of mP pollution. (8) Understanding the physical transport of mPs is a key step toward elucidating their fate and impacts in the marine environment. The determination of the sinking rate of mPs is essential to modeling their vertical transport since it impacts their residence time in the water column, which in turn influences their fate and bioavailability.

Numerous models have been developed to calculate the terminal settling velocity of natural particles and, more recently, consider the wider range of morphologies exhibited by mPs, including fibers. The study by Van Melkebeke et al. (9) evaluated 11 shape-dependent drag models to calculate the settling velocity of irregularly shaped mPs and concluded that Dioguardi et al.’s model (10) was the most accurate based on its low average error. However, an erroneous version of the model by Bagheri and Bonadonna (11) was used to reach this conclusion. It has since been suggested that the model by Zhang and Choi (12) is more accurate in predicting the settling velocity of fibers. Therefore, it would be beneficial to confirm that Van Melkebeke et al.’s conclusion is still valid when the new and revised models are considered.

When comparing explicit models, the model by Francalanci et al. (13) was found to be more accurate in predicting mP settling velocity than the model by Dietrich, (14) particularly for irregular particles with low Corey shape factor (CSF) values. The newly proposed model by Yu et al. (15) has since been found to predict the settling velocity of mPs with lower error than Francalanci et al.’s (13) model. However, no direct comparison has been made between this model and Dioguardi et al.’s model. (10)

Thus, this research paper evaluates the six drag models mentioned above and a reference model for spheres (16) to make a more complete comparison of their performance in predicting the terminal settling velocity of mPs and to reach a conclusion on which model is most appropriate in a mP modeling context. A description of each of the empirical models evaluated is included in Supporting Information 1.

This evaluation reported here considers only the vertical transport of mPs under the action of gravitational, buoyant, and drag forces in a quiescent water column. Additional processes that influence the vertical transport of mPs including wind-mixing, (17) weather events, (18) biofouling, (19) and incorporation into aggregates (20) and fecal pellets (21) are not considered.

2. Methods and Data

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2.1. Approach

The approach adopted in this study followed a series of stages.

1.	The seven models selected were evaluated using the dataset in Van Melkebeke et al. (9) This dataset is described in Section 2.4 and summarized in Table 1.
2.	Yu et al.’s model (15) was re-evaluated using the dataset from Dioguardi et al. (10) This dataset is described in Section 2.4 and summarized in Table 1.
3.	The impact of the choice of initial velocity on the result of the implicit models was investigated.
4.	The variation in the terminal settling velocity over the range of density in the ocean was explored to test the impact of assuming a constant settling velocity in a mP transport model.
5.	The impact of using a constant sinking velocity on the distance traveled by the mPs was explored.

Table 1. Outline of Experimental Datasets Used to Complete the Model Evaluation in This Study

Dataset used:	Van Melkebeke et al.	Dioguardi et al.
variables included:	measured terminal settling velocity (w_meas)	measured terminal settling velocity (w_meas)
	fluid dynamic viscosity (μ_f)	fluid dynamic viscosity (μ_f)
	fluid density (ρ_f)	fluid density (ρ_f)
	volume equivalent sphere diameter (d_p)	volume equivalent sphere diameter (d_p)
	particle density (ρ_p)	particle density (ρ_p)
	longest, intermediate, and shortest particle dimensions (a, b, and c)	longest, intermediate, and shortest particle dimensions (a, b, and c)
	sphericity (Φ)	sphericity (Φ)
	Dellino shape factor (Ψ)	Dellino shape factor (Ψ)
	circularity (χ)	circularity (χ)
	powers roundness index (P)	maximum projection area (A_mp)
	particle shape category	maximum projection perimeter (P_mp)
	fluid kinematic viscosity (ν_f)
method of measuring terminal settling velocity:	traditional cylindrical settling column experiments with following setup:	traditional cylindrical settling column experiments with following set up:
	settling column: 45 cm height and 10 cm diameter	settling column: 150 cm height and 5 cm inner radius
	fluid used: deionized water or ethanol (depending on particle density)	fluid used: two glycerin solutions
	time recording: time taken to travel two times 10 cm using a high dynamic range camera at 100 frames/sec	settling velocity recording: using a high-definition video camera at 50 frames/sec
method of characterizing particle shape:	Particle size: sieve shaker	Grain size:combination of sieving and particle counting techniques
method of characterizing particle shape:	Shape parameters: High-resolution images generated using a digital microscope and analyzed using image analysis software ImageJ.	Shape parameters: Image analysis techniques on high-resolution photographs under a stereomicroscope.
rationale for using the dataset:	Dataset contains all the detailed particle shape information required to implement each of the models under evaluation	Dataset contains all the detailed particle shape information required to independently evaluate the performance of Yu et al. (15)
reference for full experimental details:	(9)	(10)

2.2. Method to Evaluate Explicit Models

Empirical models that provide an expression to directly calculate the terminal settling velocity of particles falling in a fluid are known as explicit models. These models are computationally more efficient than implicit models since they do not require an iterative calculation. For each of the explicit models tested, the particle properties from the dataset were directly substituted into the models to output a single value of the terminal sinking velocity. The specific procedure to implement each of the explicit models is outlined in Supporting Information 6–8.

2.3. Method to Evaluate Implicit Models

Implicit models give an expression for the drag coefficient C_D and require an iterative method to calculate the terminal settling velocity. The iterative method outlined in Dioguardi et al. (10) and Bagheri and Bonadonna (11) was applied to test the implicit models. First, the particle Reynolds number Re was calculated using an assumed initial settling velocity and the particle properties in the dataset. The drag coefficient C_d was calculated using Re and subsequently utilized to calculate the drag force. The gravitational and buoyant forces acting on the particle were calculated using the particle properties and used alongside the drag force to estimate the net vertical force acting on the particle. The net force was substituted into the equation ∑F =

m (\frac{\partial w}{\partial t})

to calculate the settling velocity at the next time step. The particle Reynolds number Re was then recalculated, and the process was restarted. The iterations continued until the drag force equaled the sum of the gravitational and buoyant forces, and the particle acceleration became negligible (less than 0.001 m/s²). At this point, it was assumed that the terminal settling velocity was attained. The specific procedure to implement each of the implicit models tested is outlined in Supporting Information 2–5.

This method differs from the method of model evaluation used in Van Melkebeke et al., (9) where the terminal settling velocity was already known and was used as the initial assumed velocity. The drag coefficient C_d was obtained in the same manner as outlined above but was then implemented into Newton’s impact formula (22) to calculate the terminal settling velocity. This was compared to the measured terminal settling velocity to evaluate the model performance. In a mP transport modeling context, when the terminal settling velocity of the particle is unknown, it is more useful to apply implicit models using the iterative method wherein the initial velocity is assumed, and the calculation is iterated until the terminal settling velocity is attained.

2.4. Datasets Used

The dataset in Van Melkebeke et al. (9) was used to evaluate the models under consideration. This dataset contains information on the terminal settling velocity of 140 mPs that was obtained during cylindrical settling column experiments. A summary of the experimental methods is included in Table 1, and full experimental details can be found in their paper. (9) The mPs were generated from a range of product types to encompass the array of regular and irregular particle morphologies exhibited by mPs, including three-dimensional (3D) shapes such as granules, spheres, and fragments; quasi-two-dimensional (2D) shapes such as films; and quasi-one-dimensional (1D) shapes such as fibers and lines. The particles were quantified into 3 shape categories using image analysis software and microscopy, and, in total, the dataset contains 80 fragments, 40 films, and 20 fibers. A variety of shape descriptors were also estimated, but sphericity was found to be the only descriptor that could adequately distinguish between the three distinct morphologies. This comprehensive dataset was used to evaluate the models under consideration as it contained all the detailed information on particle morphology required to successfully implement the models.

This dataset was used to fit the models by Yu et al. (15) and Zhang and Choi (12) and, we noted, could falsely overrepresent their performance. For example, Yu et al.’s model (15) revealed high-performance characteristics when using this dataset and thus warranted further testing using an independent dataset.

As Yu et al.’s model was fitted using all the data currently available on mP settling velocity, the dataset compiled for volcanic ash particles in Dioguardi and Mele (23) and revised in Dioguardi et al. (10) was instead used to retest the models. This dataset is similar to Van Melkebeke et al.’s (9) dataset in that it contains information on the terminal settling velocity of irregularly shaped particles obtained during cylindrical settling column experiments. It also contains detailed information on each particle’s morphology, which is required to successfully implement the models but was not used to fit either of the models highlighted above, making it an appropriate choice to retest Yu et al.’s (15) model. A summary of the experimental methods used to obtain this dataset is outlined in Table 1, and full experimental details can be found in the relevant paper. (10,23)

2.5. Analysis Undertaken during Model Evaluation

Several indicators of the model’s ability to reproduce the measured terminal velocity were used during the model evaluation.

Linear regression was used to fit a model in the form y = mx to understand the relationship between the calculated settling velocity (y) and the measured settling velocity (x). In this instance, an m-value close to 1 indicates that the model accurately predicts the terminal settling velocity of the particles, with m < 1 suggesting that the model underestimates the terminal settling velocity and m > 1 suggesting that the model overestimates the terminal settling velocity. The coefficient of determination r² indicates the amount of variability in the estimated velocity that can be explained by the linear regression model, with an r² value close to 1 suggesting that it adequately fits the data and can explain the variability in the estimated terminal settling velocity.

The average absolute relative error (|AE|) measures the difference between the calculated and measured velocity as a percentage of the measured velocity

| A E | = \frac{\sum_{i = 1}^{N} | \frac{w_{t, c a l c, i} - w_{t, m e a s, i}}{w_{t, m e a s, i}} | \times 100}{N}

where N is the number of data points. For an individual particle, the absolute relative error is zero when the measured and calculated velocity are equal. An absolute relative error of 50% for an individual particle indicates that the calculated velocity is either 50% smaller or 50% larger than the measured velocity. The overall average absolute relative error therefore will demonstrate the difference between the modeled terminal settling velocity and the measured terminal settling velocity but will not provide an indication of whether the model overestimates or underestimates the particle terminal settling velocity.

The root-mean-square error (RMSE) is the square root of the average of the squared error and provides an absolute measure of the model’s ability to predict the measured terminal settling velocity. For consistency, we calculate this statistic using the same expression as Van Melkebeke et al. (9) and Dioguardi et al. (10)

R M S E = \sqrt{\frac{\sum_{i = 1}^{N} {(\frac{w_{t, c a l c, i} - w_{t, m e a s, i}}{w_{t, m e a s, i}})}^{2} \times 100}{N}}

where N is the number of data points. By squaring the relative error, RMSE applies more weight to large errors, and a low RMSE indicates that the model accurately predicts the settling velocity.

3. Results and Discussion

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3.1. Model Evaluation

Considering all the mP morphologies, Dioguardi et al.’s model (10) produces the lowest m value of 1.06 (r² = 0.94), suggesting that it accurately predicts the terminal settling velocity of the mP particles in the dataset. The models by Bagheri and Bonadonna (11) and Yu et al. (15) both produce a similar m value of 1.08. However, Dioguardi et al.’s (10) model underestimates the settling velocity of fibrous particles (Figure 1), and as a result, it has a higher absolute average relative error (|AE| = 15.82%) than both Bagheri and Bonadonna (11) (|AE| = 13.95%) and Yu et al. (15) (|AE| = 14.81%) (Table 3). It should be noted that these errors are generated relative to the measured terminal settling velocity. Furthermore, they are obtained using distinct models with m-value and r² metrics which provide a confidence measure in the data. These models also have the highest overall coefficient of determination (r² = 0.96) (Table 2), indicating that the linear regression model y = mx is a better fit to their output.

Figure 1. Output for each model evaluated showing the model-estimated terminal settling velocity against the measured terminal settling velocity from the dataset in Van Melkebeke et al. (9) The solid line indicates the ideal fit where the estimated terminal settling velocity equals the measured terminal settling velocity, and the dotted lines indicate the estimated terminal settling velocity equals ±30% of the measured terminal settling velocity. The dashed line indicates the best fit line in the form y = mx that was obtained using linear regression. The labels A–H distinguish between the results of the models evaluated. (A) Yu et al.’s model. (15) (B) Dioguardi et al.’s model (10) using the particle projection area as the particle effective area. (C) Bagheri and Bonadonna’s model (11) using the particle projection area as the particle effective area. (D) Francalanci et al’s model. (13) (E) Zhang and Choi’s model (12) using the maximum cross-sectional area as the particle effective area. (F) Zhang and Choi’s model (12) using the particle surface area as the particle effective area. (G) Dietrich’s model. (14) (H) Stokes model (16) using the particle surface area as the particle effective area.

Table 2. Summary of Output from Regression Analysis Undertaken during Model Evaluation

	overall		fragments only		films only		fibers only
model	m	r²	m	r²	m	r²	m	r²
Dioguardi et al. (2018)^a	1.06	0.94	1.09	0.95	0.97	0.94	0.66	0.40
Bagheri and Bonadonna (2016)^a	1.08	0.96	1.07	0.97	1.05	0.90	1.30	0.58
Yu et al. (2022)	1.08	0.96	1.08	0.96	0.95	0.71	1.27	0.47
Dietrich (1982)	0.92	0.80	N/A	N/A	N/A	N/A	N/A	N/A
Zhang and Choi (2021)^b	0.86	0.89	0.86	0.86	0.88	0.79	0.87	0.60
Zhang and Choi (2021)^c	1.55	0.90	1.56	0.88	1.31	0.79	1.37	0.64
Francalanci et al. (2021)	1.88	0.89	1.83	0.93	2.38	–0.06	2.58	–0.02
Stokes (1851)^b	2.02	0.81	2.10	0.80	0.49	0.64	1.42	0.51

^{^a}

Indicates that the projected area of the volume equivalent sphere was used as the effective area in the calculation of the drag force.

^{^b}

Indicates that the particle surface area was used as the effective area in the calculation of the drag force and.

^{^c}

Indicates that the maximum cross-sectional area was used as the effective area in the calculation of the drag force.

The m-value of the regression model fitted to the output using Dietrich’s model (14) (m = 0.92) (Table 2) deviated from 1 to the same degree as Bagheri and Bonadonna (11) and Yu et al.’s (15) model. However, Dietrich’s (14) model produced a lower r² value (0.80) (Figure 1) and a higher |AE| (|AE| = 19.43%) (Table 3) when all particles were considered, indicating that it is less accurate in reproducing the measured terminal settling velocity, and the regression model is less appropriate in explaining the variation in the calculated terminal settling velocity. This is evident in Figure 1. Furthermore, as Dietrich’s model (14) is not recommended for use when CSF < 0.2 and is invalid when CSF < 0.15, it was only applicable to one fibrous particle and none of the film particles. Therefore, this model will not be useful in a modeling context for irregularly shaped mPs.

Table 3. Summary of Errors in the Estimated Terminal Settling Velocity for Each Model Evaluated Compared to the Measured Terminal Settling Velocity for All Particles from the Dataset by Van Melkebeke et al. (9)^, ^a

	overall
model	AE	\|AE\|	RMSE
Bagheri and Bonadonna (2016)^b	8.97	13.95	20.56
Yu et al. (2022)	6.21	14.81	22.67
Dioguardi et al. (2018)^b	–1.47	15.82	21.28
Dietrich (1982)	–14.70	19.43	28.46
Zhang and Choi (2021)^c	–18.60	23.48	27.75
Zhang and Choi (2021)^d	28.44	33.80	43.81
Stokes (1851)^c	11.18	59.88	73.43
Francalanci et al. (2021)	128.31	128.31	151.07

^{^a}

AE = Average relative error (%), |AE| = average absolute relative error (%), and RMSE = root-mean-square error (%).

^{^b}

Indicates that the projected area of the volume equivalent sphere was used as the effective area in the calculation of drag force.

^{^c}

Indicates that the particle surface area was used as the effective area in the calculation of drag force.

^{^d}

Indicates that the maximum cross-sectional area was used as the effective area in the calculation of drag force.

The model by Zhang and Choi (12) provides the next best estimate of the measured terminal settling velocity when all morphologies are considered. The output of this model is improved when the particle surface area is used as the effective area (|AE| = 23.48%) in the drag force calculation rather than using the projection area as outlined in the paper (|AE| = 33.80%) (Figure 2).

Figure 2. Absolute average relative error of model-estimated terminal settling velocity for each model evaluated compared to the measured terminal settling velocity from the dataset by Van Melkebeke et al.. (9) The main figure illustrates the absolute average relative error for the entire dataset, while the lower figure shows the error when each morphology within the dataset is considered separately. The key for the models evaluated is Stokes = Stokes model (16) using the particle surface area as the particle effective area, Bagheri = Bagheri and Bonadonna’s model (11) using the particle projection area as the particle effective area, Dioguardi = Dioguardi et al.’s model (10) using the particle projection area as the particle effective area, Zhang:SA = Zhang and Choi’s model (12) using the particle surface area as the particle effective area, Zhang:Proj = Zhang and Choi’s model (12) using the maximum cross-sectional area as the particle effective area, Dietrich = Dietrich’s model, (14) Francalanci = Francalanci’s model, (13) and Yu = Yu et al.’s model. (15)

The models by Francalanci et al. (13) and Stokes’ (16) are less accurate, and their calculated terminal settling velocity deviates from the measured terminal settling velocity by an average of 128.31 and 59.88%, respectively, when all morphologies are considered (Table 3). As Stokes’ model (16) is a reference law for spherical particles and irregularly shaped particles in the dataset experience more drag, it is expected that it will overestimate their settling velocity. Francalanci et al.’s model (13) overestimates the terminal settling velocity of all morphologies considered, with an overall |AE| of 95.48, 170.05, and 176.13% for fragments, films, and fibers, respectively (Table 4). Similar results were obtained when Francalanci et al. (13) validated their model using the same dataset.

Table 4. Summary of Errors in the Estimated Terminal Settling Velocity for Each Model Evaluated Compared to the Measured Terminal Settling Velocity for mP Particles in the Dataset by Van Melkebeke et al. (9) Separated by Particle Morphology^a

	fragments only			films only			fibers only
model	AE	\|AE\|	RMSE	AE	\|AE\|	RMSE	AE	\|AE\|	RMSE
Bagheri and Bonadonna (2016)^b	3.21	10.51	13.27	8.60	10.51	15.02	32.75	34.59	42.47
Yu et al. (2022)	3.54	11.55	14.95	–0.68	12.14	20.42	30.63	33.18	43.23
Dioguardi et al. (2018)^b	7.27	13.87	16.69	–2.07	9.41	11.05	–35.23	36.45	42.56
Dietrich (1982)	N/A	N/A	N/A	N/A	N/A	N/A	N/A	N/A	N/A
Zhang and Choi (2021)^c	–21.13	26.11	30.20	–15.68	20.40	24.22	–14.33	19.14	23.89
Zhang and Choi (2021)^d	28.42	35.00	46.49	25.24	28.66	37.16	34.90	39.26	45.06
Stokes (1851)^c	43.78	61.24	79.87	–64.08	64.08	66.25	31.30	31.36	58.75
Francalanci et al. (2021)	95.48	95.48	102.56	170.05	170.05	200.36	176.13	176.13	193.36

^{^a}

AE = average relative error (%), |AE| = average absolute relative error (%), RMSE = root-mean-square error (%).

^{^b}

Indicates that the projected area of the volume equivalent sphere was used as the effective area in the calculation of drag force.

^{^c}

Indicates that the particle surface area was used as the effective area in the calculation of drag force.

^{^d}

Indicates that the maximum cross-sectional area was used as the effective area in the calculation of drag force.

The terminal settling velocity of the fragment particles is most accurately reproduced using Bagheri and Bonadonna’s model, (11) which has an m value of 1.07, an r² value of 0.97 (Table 2), and the lowest |AE| at 10.51% (Table 4). This occurred since the model was derived using mainly volcanic particles and ellipsoids which are analogous in morphology to fragment mPs. Comparable results are obtained for fragments when Yu et al.’s explicit model (15) is used, with an m value of 1.08, an r² value of 0.96 (Table 2), and an |AE| of 11.55% (Table 4) and also when Dioguardi et al.’s implicit model (10) is used, with an m value of 1.09, an r² value of 0.95 (Table 2), and an |AE| of 13.87% (Table 4).

Dioguardi et al.’s model (10) provides the closest estimate of the measured terminal settling velocity of film particles, with an m value of 0.97, an r² value of 0.94 (Table 2), and an |AE| of 9.41% (Table 4). Bagheri and Bonadonna (11) and Yu et al.’s (15) model both provide similarly accurate results with m values of 1.05 and 0.95, respectively (Table 2). However, Yu et al.’s model (15) produces a lower coefficient of determination (r² = 0.71) (Table 2) and higher |AE| (|AE| = 12.14%) than Bagheri and Bonadonna’s model (11) (r² = 0.90 and |AE| = 10.51%) (Tables 2 and 4), indicating that it is less accurate in reproducing the terminal settling velocity of films. This is unexpected since film mPs were included in the derivation of Yu et al.’s model, (15) and so it should provide a better prediction of their terminal settling velocity than the models by Bagheri and Bonadonna (11) and Dioguardi et al. (10) which did not take into account film particles.

All of the models evaluated were less accurate in reproducing the settling velocity of fibrous particles compared to film and fragment particles with the exception of Francalanci et al. (13) and Stokes (16) (Figures 2 and 3). Zhang and Choi’s (12) model most closely predicts the terminal settling velocity of fibrous particles with an m value of 0.87 (Table 2) and |AE| of 19.14% (Table 4). This model was derived primarily to predict the terminal settling velocity of fibrous particles, and so it is expected that it is more suitable for this purpose. It also produces relatively consistent results for all morphologies considered, with m values of 0.86 and 0.88 (Table 2) and |AE|s of 26.11 and 20.40% (Table 4) for fragments and films, respectively.

Figure 3. RMSE of the estimated terminal settling velocity for each model evaluated compared to the measured terminal settling velocity from the dataset by Van Melkebeke et al. (9) The main figure illustrates the absolute average relative error for the entire dataset, while the lower figure shows the error when each morphology within the dataset is considered separately. The key for the models evaluated is Stokes = Stokes model (16) using the particle surface area as the particle effective area, Bagheri = Bagheri and Bonadonna’s model (11) using the particle projection area as the particle effective area, Dioguardi = Dioguardi et al.’s model (10) using the particle projection area as the particle effective area, Zhang:SA = Zhang and Choi’s model (12) using the particle surface area as the particle effective area, Zhang:Proj = Zhang and Choi’s model (12) using the maximum cross-sectional area as the particle effective area, Dietrich = Dietrich’s model, (14) Francalanci = Francalanci’s model, (13) and Yu = Yu et al.’s model. (15)

Dioguardi et al. (10) and Bagheri and Bonadonna’s (11) models are noticeably less accurate in predicting the terminal settling velocity of fibers and produce an |AE| almost 3 times higher than the |AE| obtained when only fragments were considered at 36.45 and 34.59%, respectively (Table 4). This may have occurred since the dataset used during the derivation of these models did not contain particles that are analogous to fibrous particles. For example, the dataset used to derive Dioguardi et al.’s (10) model contained natural particles with Dellino shape factors from 0.335 to 0.943, while the Dellino shape factor of the fibrous particles in the dataset used in this model evaluation ranged from 0.012 to 0.187. Yu et al.’s model (15) which does take into account fibrous particles more accurately reproduces their measured terminal settling velocity, with an m value of 1.27 (Table 2) and an absolute average error of 33.18% (Table 4).

In addition, the approximated projected area of fibers used during the model evaluation is lower than their actual projected area since the most stable orientation of fibrous particles sinking in a fluid is the horizontal orientation with their maximum projection area normal to the direction of motion. The approximation used may therefore have contributed toward the reduced performance of the implicit models for fibrous particles.

Overall, the model evaluation shows that the drag models proposed by Dioguardi et al., (10) Bagheri and Bonadonna, (11) and Yu et al. (15) have a similarly high precision in predicting the terminal settling velocity of fragment and film particles but are less accurate for fibrous particles. As an explicit model, Yu et al.’s (15) model is more computationally efficient than the implicit models that require an iterative method to calculate the terminal settling velocity and therefore may be most appropriate for implementation in an mP transport model. To further verify this, the performance of Yu et al.’s (15) model was re-tested using an independent dataset.

3.2. Re-evaluation of Yu’s Model

The re-evaluation of Yu et al.’s model (15) using the independent dataset from Dioguardi et al. (10) demonstrates that the model closely estimates the terminal settling velocity of the particles, with m = 0.97 and r² = 0.96 (Figure 4). The |AE| and the RMSE were also very low, at 3.11 and 16.03%, respectively (Table 5), indicating that the model is adequate at predicting the terminal settling velocity of irregularly shaped particles in a fluid.

Figure 4. Output of the re-evaluation of the model by Yu et al. (15) showing the model-estimated terminal settling velocity against the measured terminal settling velocity from the dataset in Dioguardi et al (10) The solid line indicates the ideal fit where the modeled terminal settling velocity equals the measured terminal settling velocity, and the dotted lines indicate the modeled terminal settling velocity equals ±30% of the measured terminal settling velocity. The dashed line indicates the best fit line in the form y = mx that was obtained using linear regression.

Table 5. Results of Linear Regression and Error Analysis Undertaken during Re-evaluation of Yu et al.’s (15) Model Using the Dataset from Dioguardi et al. (10)^, ^a

model	shape	\|AE\| (%)	RMSE (%)	m	r²
Yu et al. (2022)	All	10.27	16.03	0.97	0.96

^{^a}

m is the gradient and r² is the coefficient of determination of the fitted line of the form y = mx obtained using linear regression. |AE| is the average absolute relative error (%) and RMSE is the root-mean-square error (%).

3.3. Further Analysis

While Stokes law (16) can be applied to calculate the terminal settling velocity of spherical particles, difficulties arise when estimating the terminal settling velocity of mP particles due to the wide range of morphologies they exhibit, including 3D shapes such as fragments, 2D shapes such as films, and 1D shapes such as fibers and lines. Obtaining an appropriate expression for the drag coefficient C_d and defining the effective area used to calculate the drag force of irregular particles are not straightforward tasks.

The effective area can either be taken as the particle surface area, which lends itself to understanding the drag force as friction acting on the body, or as the particle projection area, which would suggest that the drag force acts as resistance to the flow. (24) The projection area is commonly used as the effective area for irregular particles as it is often more straightforward to measure than the surface area. (25) The implicit models were tested using both the particle surface area and the projection area. The particle surface area was calculated by multiplying the particle sphericity, given in the dataset in Van Melkebeke et al., (9) by the surface area of the volume equivalent sphere. The projection area of the irregularly shaped particles was approximated using the projection area of the volume equivalent sphere as the dataset contained insufficient information for an accurate calculation.

The particle projection area is explicitly stipulated as the effective area during the derivation of Dioguardi et al. (10) and Bagheri and Bonadonna’s (11) models, and as a result, they produced less accurate results when implemented using the particle surface area. These results are not presented in this paper but are included in Supporting Information 9 for reference.

The accuracy of Stokes’ (16) model was reduced when the projection area was used as the effective area, with an overall absolute average error of 1171% compared to an error of 59.88% when the particle surface area was used. This may have occurred since the particle surface area is an order of magnitude higher than the approximated projection area, meaning that the drag force will be lower and the estimated terminal settling velocity will be higher when the projection area is used. These results are excluded from the analysis in this paper due to their low accuracy but are included in Supporting Information 9 for reference.

3.4. Impact of the Choice of Initial Velocity on the Result of the Implicit Models

When using an implicit model to calculate the terminal settling velocity, an initial value of the settling velocity must be specified to initiate the iterative calculation. To explore the impact of the choice of initial velocity on the modeled terminal settling velocity, the implicit models were run using six different initial velocity values ranging from 5 × 10^–6 to 1 × 10^–3 m/s. These values were chosen to ensure that the initial velocity was always less than the expected terminal settling velocity while also encompassing a wide range of values.

The modeled settling velocity converged to the same terminal value during these tests, regardless of the initial velocity specified, indicating that the choice of initial velocity has no impact on the result of the implicit models. The main difference observed when varying the initial velocity was that the time taken to attain the terminal settling velocity decreased as the specified initial velocity approached the terminal settling velocity since less calculation iterations were required. This is illustrated in Figure 5 which presents the results from conducting this test on six randomly selected particles using the model by Bagheri and Bonadonna. (11) The results for the other implicit models are included in Supporting Information 11.

Figure 5. Impact of the choice of initial velocity on the modeled settling velocity when using Bagheri and Bonadonna’s model (11) with the particle projection area as the effective area for six particles that were randomly extracted from the dataset by Van Melkebeke et al. (9) The output from the remaining implicit models is included in Supporting Information 11.

Therefore, when implementing these models in a mP transport model, the choice of initial velocity will not be a critical factor provided that a realistic value is chosen.

3.5. Variation in the Terminal Settling Velocity over the Range of Density in the Ocean and the Impact on the Models of Assuming a Constant Terminal Settling Velocity

Seawater density is an input variable in all the models tested. Within the ocean, there is a vertical gradient of density, with lower density seawater at the surface and higher density seawater at depth in a stable water column. The density of 99% of seawater is within ±2% of the average value (26) of 1030 kg/m³. To explore the influence of seawater density on the calculated terminal settling velocity, the models were tested using six fluid density values ranging from 1019 to 1050 kg/m³ to reflect the range of density encountered in the ocean.

The results of the test illustrate that the terminal settling velocity does not vary significantly over the expected range of seawater density for all models tested. However, when the ratio of seawater density to particle density approaches 1, the terminal settling velocity approaches zero. This occurs since there is zero net gravitational force acting on the mP when its density equals the seawater density and the mP is said to be neutrally buoyant.

For example, when Yu et al.’s model (15) was implemented at various seawater densities, the terminal settling velocity varied from 0.0004 to 0.002 m/s, excluding the particles which approached neutral buoyancy (Figures 6 and 7). This is equivalent to the particle traveling an additional 34–172 m per day at the lowest seawater density compared to the highest seawater density tested, which is a negligible distance compared to the overall depth of the ocean and spatial and temporal resolution of an ocean model.

Figure 6. Output obtained when investigating the influence of fluid density on the terminal settling velocity of six random particles using the model by Yu et al. (15) The output from the remaining implicit models is included in Supporting Information 12.

Figure 7. Range of settling velocity obtained for each of six random particles using the model by Yu et al. (15) when the fluid density varied from 1019 to 1050 kg/m³. The output from the remaining implicit models is included in Supporting Information 12.

Overall, the results of this test indicate that in a mP transport model, it is suitable to assume a constant terminal settling velocity regardless of the seawater density, provided that the model accounts for mPs attaining neutral buoyancy.

3.6. Exploring the Impact of Using a Constant Terminal Sinking Velocity on the Distance Traveled by the mPs

To further examine the impact of assuming a constant settling velocity over time on the results of an mP model, the distance traveled by the mP while attaining terminal settling velocity was compared to the distance traveled at the constant velocity during the same period. This exercise was only carried out for the implicit models as the explicit models do not provide information on particle behavior before the terminal settling velocity is attained.

As the particle accelerates until the terminal settling velocity is attained, the distance traveled at a constant velocity will always be slightly higher than the actual distance traveled. This is illustrated in the output for each of the models, which show that the distance traveled at a constant settling velocity is 14–18% higher than the actual distance traveled (Supporting Information 13). For example, when Bagheri and Bonadonna’s model (11) was tested, the distance traveled at a constant velocity was 17.55% higher than the actual distance traveled (

Figure 8). However, since the terminal settling velocity was attained in a relatively short space of time for all models considered, the distance traveled by the particles was very small. For example, the terminal settling velocity was attained after 0.07 sec on average when using Bagheri and Bonadonna’s model, (11) and the distance traveled during this time ranged from 0.07 mm to 3 cm.

Figure 8. Comparison of the distance traveled in attaining the terminal settling velocity to the distance traveled if the particle sank constantly at the terminal settling velocity in the equivalent period of time when using the model by Bagheri and Bonadonna. (11) The solid line indicates the ideal fit where there is no difference in the distance traveled, and the dotted lines indicate that the distance traveled at a constant velocity is ±30% of the distance traveled while attaining the terminal settling velocity. The dashed line indicates the best fit line in the form y = mx that was obtained using linear regression. The output from the remaining implicit models is included in Supporting Information 13 for reference.

Overall, the time taken to attain terminal settling velocity and the distance traveled during this time are negligible compared to the timestep required in an mP transport model and the overall depth of the ocean. This suggests that in the context of models of mP transport in the marine environment which consider vertical transport due only to the sum of the gravitational, buoyant, and drag forces, it is suitable to assume that the particle settling velocity is constant over time and equal to the calculated terminal settling velocity. Therefore, in the absence of more accurate data on mP vertical transport in the marine environment, it may be appropriate to use the terminal settling velocity in realistic models of mP transport, provided that this is highlighted as a simplification and a model limitation.

3.7. Limitations to This Research

There are several limitations to this study. The models evaluated during the research were empirical, and it is not recommended that they are applied beyond the limits of the experimental data used in their derivation. However, during the evaluation, the models were at times tested beyond their limits, which may impact the accuracy of their results. This occurred primarily for the models that were derived for natural particles since they did not account for the wider range of mP morphologies such as films and fibers.

As noted in Section 2.3, an iterative method was used to calculate the terminal settling velocity in this research and evaluate the appropriateness of implicit settling velocity models in an mP modeling context where the terminal settling velocity of the particle is unknown. When Van Melkebeke et al. (9) evaluated the models using the same dataset but by applying the non-iterative method which is outlined in Section 2.3, the evaluation produced different results. For example, Dioguardi et al.’s model (10) produced better results during the non-iterative tests, with m = 0.99, |AE| = 13.20, and RMSE = 19.09. Dioguardi et al. (27) also observed a very small change in the performance of the models evaluated, both positively and negatively, when they evaluated the performance of models using an iterative method compared to the non-iterative method. Therefore, while our study used the same dataset as in the study by Van Melkebeke et al., (9) it is likely that we would obtain different results when evaluating the same implicit models due to the difference in the method used to calculate the terminal settling velocity.

Finally, it is important to note that the evaluation in this paper considers only mP sinking in a quiescent water column due to the sum of the gravitational, buoyant, and drag forces. Consequently, the assumptions that were described to simplify the simulation of mP vertical transport in a modeling context are only valid in a model which does not consider any additional processes that impact the vertical transport of mPs, such as biofouling, weather events, and incorporation into biological aggregates.

4. Conclusions

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Overall, the results indicate that the models by Bagheri and Bonadonna, (11) Dioguardi et al., (10) and Yu et al. (15) most accurately reproduce the measured terminal settling velocity of fragment and film particles. The model by Zhang and Choi, (12) which was derived explicitly for fibrous particles, is most accurate in reproducing the terminal settling velocity of fibers. We recommend that Yu et al.’s explicit model (15) is the most appropriate settling velocity model in the context of a mP transport model since it provided comparably accurate results to the best performing but more computationally expensive implicit models.

The additional tests identified that, when implementing the drag models in a mP transport model, the choice of initial velocity is not a critical factor, provided that a realistic initial velocity value is chosen. Furthermore, it is suitable to assume that the mP particles have a constant settling velocity over time since the terminal settling velocity is attained in a very short space of time. Finally, an evaluation of the influence of fluid density on the estimated terminal settling velocity demonstrated that the variation in mP terminal settling velocity across the expected seawater density range is negligible. Therefore, in an mP modeling context, it is suitable to assume a constant terminal settling velocity regardless of the seawater density, provided that the model will consider the impact of mPs attaining neutral buoyancy.

These findings improve our understanding on the implementation of drag models to determine the settling velocity of irregular particles in the context of mP transport models. However, additional processes which may be important in the vertical transport of mPs should also be considered in efforts to model mP transport, including wind-mixing, (17) weather events, (18) and the influence of biofouling. (19) The settling velocity of mPs is a key parameter within mP transport models that influences their fate and bioavailability to organisms by controlling the residence time of mPs in the water column. Therefore, understanding the vertical transport of mPs is an important prerequisite to the completion of a comprehensive risk assessment of mPs in the ocean and the determination of their potential to cause significant ecological harm.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsestwater.2c00466.

Additional model descriptions, experimental details, and results of tests on individual models as mentioned in the text (pdf)

ew2c00466_si_001.pdf (15.6 MB)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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Corresponding Author
- Róisín Coyle - Civil Engineering, School of Natural and Built Environment, Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland, U.K.; https://orcid.org/0000-0002-8684-8381; Email: [email protected]
Authors
- Matthew Service - Agri-Food and Biosciences Institute, 18a Newforge Lane, Belfast BT9 5PX, Northern Ireland, U.K.
- Ursula Witte - School of Biological Sciences, University of Aberdeen, Aberdeen AB24 3FX, U.K.
- Gary Hardiman - School of Biological Sciences, Institute for Global Food Security (IGFS), Queen’s University Belfast, 19 Chlorine Gardens, Belfast BT9 5DL, Northern Ireland, U.K.; Department of Medicine, Medical University of South Carolina, Charleston, South Carolina 29425, United States; https://orcid.org/0000-0003-4558-0400
- Jennifer McKinley - Geography, School of Natural and Built Environment, Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland, U.K.
Funding
This work was supported by the Natural Environment Research Council under the Queen’s University Belfast and the University of Aberdeen Doctoral Research and Training Doctoral Training Partnership (QUADRAT DTP).
Notes
The authors declare no competing financial interest.

References

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This article references 27 other publications.

1
Morales-Caselles, C.; Viejo, J.; Martí, E.; González-Fernández, D.; Pragnell-Raasch, H.; González-Gordillo, J. I.; Montero, E.; Arroyo, G. M.; Hanke, G.; Salvo, V. S.; Basurko, O. C.; Mallos, N.; Lebreton, L.; Echevarría, F.; van Emmerik, T.; Duarte, C. M.; Gálvez, J. A.; van Sebille, E.; Galgani, F.; García, C. M.; Ross, P. S.; Bartual, A.; Ioakeimidis, C.; Markalain, G.; Isobe, A.; Cózar, A. An inshore–offshore sorting system revealed from global classification of ocean litter. Nature Sustainability 2021, 4, 484– 493, DOI: 10.1038/s41893-021-00720-8
Google Scholar
There is no corresponding record for this reference.
2
van Sebille, E.; Wilcox, C.; Lebreton, L.; Maximenko, N.; Hardesty, B. D.; van Franeker, J. A.; Eriksen, M.; Siegel, D.; Galgani, F.; Law, K. L. A global inventory of small floating plastic debris. Environ. Res. Lett. 2015, 10, 124006, DOI: 10.1088/1748-9326/10/12/124006
Google Scholar
There is no corresponding record for this reference.
3
Eriksen, M.; Lebreton, L. C. M.; Carson, H. S.; Thiel, M.; Moore, C. J.; Borerro, J. C.; Galgani, F.; Ryan, P. G.; Reisser, J. Plastic Pollution in the World’s Oceans: More than 5 Trillion Plastic Pieces Weighing over 250,000 Tons Afloat at Sea. PLOS ONE 2014, 9, e111913 DOI: 10.1371/journal.pone.0111913
Google Scholar
3
Plastic pollution in the world's oceans: more than 5 trillion plastic pieces weighing over 250,000 tons afloat at sea
Eriksen, Marcus; Labreton, Laurent C. M.; Carson, Henry S.; Thiel, Martin; Moore, Charles J.; Borerro, Jose C.; Galgani, Francois; Ryan, Peter G.; Reisser, Julia
PLoS One (2014), 9 (12), e111913/1-e111913/15, 15 pp.CODEN: POLNCL; ISSN:1932-6203. (Public Library of Science)
Plastic pollution is ubiquitous throughout the marine environment, yet ests. of the global abundance and wt. of floating plastics have lacked data, particularly from the Southern Hemisphere and remote regions. Here we report an est. of the total no. of plastic particles and their wt. floating in the world's oceans from 24 expeditions (2007-2013) across all five sub-tropical gyres, costal Australia, Bay of Bengal and the Mediterranean Sea conducting surface net tows (N = 680) and visual survey transects of large plastic debris (N = 891). Using an oceanog. model of floating debris dispersal calibrated by our data, and correcting for wind-driven vertical mixing, we est. a min. of 5.25 trillion particles weighing 268,940 tons. When comparing between four size classes, two microplastic <4.75 mm and meso- and macroplastic >4.75 mm, a tremendous loss of microplastics is obsd. from the sea surface compared to expected rates of fragmentation, suggesting there are mechanisms at play that remove <4.75 mm plastic particles from the ocean surface.
>> More from SciFinder ^®
https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXitFyjs7jP&md5=310e6b97d1ab0c3cf4a2718352ade775
4
Rezania, S.; Park, J.; Md Din, M. F. M.; Mat Taib, S. M.; Talaiekhozani, A.; Kumar Yadav, K. K.; Kamyab, H. Microplastics pollution in different aquatic environments and biota: A review of recent studies. Mar. Pollut. Bull. 2018, 133, 191– 208, DOI: 10.1016/j.marpolbul.2018.05.022
Google Scholar
4
Microplastics pollution in different aquatic environments and biota: A review of recent studies
Rezania, Shahabaldin; Park, Junboum; Md. Din, Mohd. Fadhil; Mat Taib, Shazwin; Talaiekhozani, Amirreza; Kumar Yadav, Krishna; Kamyab, Hesam
Marine Pollution Bulletin (2018), 133 (), 191-208CODEN: MPNBAZ; ISSN:0025-326X. (Elsevier Ltd.)
Microplastics (MPs) are generated from plastic and have neg. impact to our environment due to high level of fragmentation. They can be originated from various sources in different forms such as fragment, fiber, foam and so on. For detection of MPs, many techniques have been developed with different functions such as microscopic observation, d. sepn., Raman and FTIR anal. Besides, due to ingestion of MPs by wide range of marine species, research on the effect of this pollution on biota as well as human is vital. Therefore, we comprehensively reviewed the occurrence and distribution of MPs pollution in both marine and freshwater environments, including rivers, lakes and wastewater treatment plants (WWTPs). For future studies, we propose the development of new techniques for sampling MPs in aquatic environments and biota and recommend more research regarding MPs release by WWTPs.
>> More from SciFinder ^®
https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhtVWksrbJ&md5=8f3edd88c293640a8ef0bb89f7cb4796
5
Abreu, A.; Pedrotti, M. L. Microplastics in the Oceans: The Solutions Lie on Land. Field Actions Science Reports 2019, 62– 67
Google Scholar
There is no corresponding record for this reference.
6
Bakir, A.; Rowland, S. J.; Thompson, R. C. Marine Pollution Bulletin 2012, 64, 2782– 2789, DOI: 10.1016/j.marpolbul.2012.09.010
Google Scholar
6
Competitive sorption of persistent organic pollutants onto microplastics in the marine environment
Bakir, Adil; Rowland, Steven J.; Thompson, Richard C.
Marine Pollution Bulletin (2012), 64 (12), 2782-2789CODEN: MPNBAZ; ISSN:0025-326X. (Elsevier Ltd.)
Plastics are known to sorb persistent org. pollutants from seawater. However, studies to quantify sorption rates have only considered the affinity of chems. in isolation, unlike the conditions in the environment where contaminants are present as complex mixts. Here we examine whether phenanthrene and 4,4'-DDT, in a mixt., compete for sorption sites onto PVC with no added additives (unplasticized PVC or uPVC) and ultra-high mol. wt. polyethylene. Interactions were investigated by exposing particles of uPVC and UHMW PE to mixts. of 3H and 14C radiolabeled Phe and DDT. Changes in sorption capacity were modelled by applying a Freundlich binding sorption isotherms. An extended Langmuir model and an interaction factor model were also applied to predict equil. concns. of pollutants onto plastic. This study showed that in a bi-solute system, DDT exhibited no significantly different sorption behavior than in single solute systems. However, DDT did appear to interfere with the sorption of Phe onto plastic, indicating an antagonistic effect.
>> More from SciFinder ^®
https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38Xhslagtr%252FI&md5=6d939f83b3b805d7159bde4eda1b9161
7
Lusher, A. Microplastics in the Marine Environment: Distribution, Interactions and Effects. In Marine Anthropogenic Litter; Bergmann, M., Gutow, L., Klages, M., Eds.; Springer International Publishing: Cham, 2015, pp 245– 307.
Google Scholar
There is no corresponding record for this reference.
8
Zhao, S.; Danley, M.; Ward, J. E.; Li, D.; Mincer, T. J. An approach for extraction, characterization and quantitation of microplastic in natural marine snow using Raman microscopy. Anal. Methods 2017, 9, 1470– 1478, DOI: 10.1039/c6ay02302a
Google Scholar
8
An approach for extraction, characterization and quantitation of microplastic in natural marine snow using Raman microscopy
Zhao, Shiye; Danley, Meghan; Ward, J. Evan; Li, Daoji; Mincer, Tracy J.
Analytical Methods (2017), 9 (9), 1470-1478CODEN: AMNEGX; ISSN:1759-9679. (Royal Society of Chemistry)
Marine snow is a predominant form of sinking particulate carbon in the marine water column and represents a mechanism for transporting microplastics to the sea floor. We present a new dual d. sepn. method employing sodium iodide extn. followed by methanol pptn., specifically designed for microplastic isolation and identification in natural marine snow samples. A total of 59 microscopic particles from eight marine snow samples collected at Avery Point, CT were confirmed as plastics and/or substances contg. typical plastic manufg. additives. Extn. efficiency of this method was detd. using polyethylene microspheres of varying sizes (63-75 μm, 212-250 μm and 500-600 μm) yielding 90%, 93% and 98% recoveries, resp. Residual org. matter which can cause interference in downstream Raman spectroscopic analyses was eliminated by employing a 15% hydrogen peroxide (H2O2) digestion step, which caused negligible chem. modifications to the polymer samples. Extensive precautions such as combusted glassware, a microfiltration air hood, and incorporation of process blank samples ensured that airborne microplastic contamination was avoided. A phase contrast microscope equipped with a Raman spectrophotometer system using a 785 nm laser excitation source efficiently identified anthropogenic polymer materials. Unexpectedly, plastic additives such as pigments complicated the identification of polymers but their spectra were successfully interpreted through spectral subtraction and comparison to a database and authentic stds. The protocol described can be applied to detect microplastic in marine snow samples and improve our understanding of the fate of microplastic in the ocean.
>> More from SciFinder ^®
https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhslKmsrrK&md5=2e842742ae8f555a8390eec14e92e0ac
9
Van Melkebeke, M.; Janssen, C.; De Meester, S. Characteristics and Sinking Behavior of Typical Microplastics Including the Potential Effect of Biofouling: Implications for Remediation. Environ. Sci. Technol. 2020, 54, 8668– 8680, DOI: 10.1021/acs.est.9b07378
Google Scholar
9
Characteristics and sinking behavior of typical microplastics including the potential effect of biofouling: implications for remediation
Van Melkebeke, Michiel; Janssen, Colin; De Meester, Steven
Environmental Science & Technology (2020), 54 (14), 8668-8680CODEN: ESTHAG; ISSN:0013-936X. (American Chemical Society)
Microplastics are ubiquitous pollutants within the marine environment, predominantly (>90%) accumulating in sediments worldwide. Despite the increasing global concern regarding these anthropogenic pollutants, research into the remediation of microplastics is lacking. Here, we examine those characteristics of microplastics that are essential to adequately evaluate potential remediation techniques such as sedimentation and (air) flotation techniques. We analyzed the sinking behavior of typical microplastics originating from real plastic waste samples and identified the best-available drag model to quant. describe their sinking behavior. Particle shape is confirmed to be an important parameter strongly affecting the sinking behavior of microplastics. Various common shape descriptors were exptl. evaluated on their ability to appropriately characterize frequently occurring particle shapes of typical microplastics such as spheres, films, and fibers. This study is the first in this field to include film particles in its exptl. design, which were found to make up a considerable fraction of marine pollution and are shown to significantly affect the evaluation of shape-dependent drag models. Circularity χ and sphericity Φ are found to be appropriate shape descriptors in this context. We also investigated the effect of biofouling on the polarity of marine plastics and estd. its potential contribution to the settling motion of initially floating microplastics based on d.-modification. It is found that biofouling alters the polarity of plastics significantly; this is from (near) hydrophobic (i.e., water contact angles from 70 to 100°) to strong hydrophilic (i.e., water contact angles from 30 to 40°) surfaces, rendering them more difficult to sep. from sediment based on polarity as a primary sepn. factor. Thus, besides providing a better understanding of the fate and behavior of typical marine microplastics, these findings serve as a fundamental stepping-stone to the development of the first large-scale sediment remediation technique for microplastics to address the global microplastic accumulation issue.
>> More from SciFinder ^®
https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhtFymu7bM&md5=091038995f95c9d02fd91ed6d0b96826
10
Dioguardi, F.; Mele, D.; Dellino, P. A New One-Equation Model of Fluid Drag for Irregularly Shaped Particles Valid Over a Wide Range of Reynolds Number. J. Geophys. Res.: Solid Earth 2018, 123, 144– 156, DOI: 10.1002/2017jb014926
Google Scholar
There is no corresponding record for this reference.
11
Bagheri, G.; Bonadonna, C. On the drag of freely falling non-spherical particles. Powder Technol. 2016, 301, 526– 544, DOI: 10.1016/j.powtec.2016.06.015
Google Scholar
11
On the drag of freely falling non-spherical particles
Bagheri, Gholamhossein; Bonadonna, Costanza
Powder Technology (2016), 301 (), 526-544CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
We present a new general model for the prediction of the drag coeff. of non-spherical solid particles of regular and irregular shapes falling in gas or liq. valid for sub-crit. particle Reynolds nos. (i.e. Re < 3 × 105). Results are obtained from exptl. measurements on 300 regular and irregular particles in the air and anal. solns. for ellipsoids. Depending on their size, irregular particles are accurately characterized with a 3D laser scanner or SEM micro-CT method. The expts. are carried out in settling columns with height of 0.45 to 3.60 m and in a 4 m-high vertical wind tunnel. In addn., 881 addnl. exptl. data points are also considered that are compiled from the literature for particles of regular shapes falling in liqs. New correlation is based on the particle Reynolds no. and two new shape descriptors defined as a function of particle flatness, elongation and diam. New shape descriptors are easy-to-measure and can be more easily characterized than sphericity. The new correlation has an av. error of ∼ 10%, which is significantly lower than errors assocd. with existing correlations. Addnl. aspects of particle sedimentation are also investigated. First, it is found that particles falling in dense liqs., in particular at Re > 1000, tend to fall with their max. projection area perpendicular to their falling direction, whereas in gases their orientation is random. Second, effects of small-scale surface vesicularity and roughness on the drag coeff. of non-spherical particles found to be < 10%. Finally, the effect of particle orientation on the drag coeff. is discussed and addnl. correlations are presented to predict the end members of drag coeff. due to change in the particle orientation.
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12
Zhang, J.; Choi, C. E. Improved Settling Velocity for Microplastic Fibers: A New Shape-dependent Drag Model; Environmental Science & Technology, 2021.
Google Scholar
There is no corresponding record for this reference.
13
Francalanci, S.; Paris, E.; Solari, L. On the prediction of settling velocity for plastic particles of different shapes. Environ. Pollut. 2021, 290, 118068, DOI: 10.1016/j.envpol.2021.118068
Google Scholar
13
On the prediction of settling velocity for plastic particles of different shapes
Francalanci, Simona; Paris, Enio; Solari, Luca
Environmental Pollution (Oxford, United Kingdom) (2021), 290 (), 118068CODEN: ENPOEK; ISSN:0269-7491. (Elsevier Ltd.)
Transport processes of plastic particles in freshwater and marine environments are one of the relevant advances of knowledge in predicting the fate of plastic in the environment. Here, we investigated the effect of different shapes on the settling velocity, finding a representative ref. diam. which encompasses three-dimensional shapes like pellets or spherules, two-dimensional shapes like fragments or disks, and one-dimensional shapes like filaments or fibers. The new method is able to predict the settling velocity of plastic and natural particles given the representative size and the Corey shape factor coeff., over the entire range of viscous to turbulent flow regime. The calibration of the method with exptl. data, and the validation with an independent dataset, support its application in a wide range of hydraulic conditions.
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14
Dietrich, W. E. Settling velocity of natural particles. Water Resour. Res. 1982, 18, 1615– 1626, DOI: 10.1029/wr018i006p01615
Google Scholar
There is no corresponding record for this reference.
15
Yu, Z.; Yang, G.; Zhang, W. A new model for the terminal settling velocity of microplastics. Mar. Pollut. Bull. 2022, 176, 113449, DOI: 10.1016/j.marpolbul.2022.113449
Google Scholar
15
A new model for the terminal settling velocity of microplastics
Yu, Zijian; Yang, Ge; Zhang, Wenming
Marine Pollution Bulletin (2022), 176 (), 113449CODEN: MPNBAZ; ISSN:0025-326X. (Elsevier Ltd.)
Microplastic (MP) settling process is important for the transport of microplastic particles (MPs, <5 mm) in water bodies. However, for the control parameter of the drag coeff. (Cd), no generalized formula has been proposed for MPs of different shapes and materials. In this study, a total of 1343 MP settling data were collected from the literature. It was found that the drag law for perfect spheres cannot reasonably predict Cd for MPs with particle Reynolds no. of 1-103. A new formula for Cd was developed by introducing the dimensionless particle diam. (d*) and two shape descriptors. The abs. error of the new formula is 15.2%, smaller than those (42.5-72.8%) of other existing formulas. Moreover, an explicit model was developed for MP settling velocity by correlating Cd, d*, and shape descriptors, with lower abs. error (8.8%) than those (15.4-77.2%) of existing models.
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16
Stokes, G. G. On the Effect of the Internal Friction of Fluids on the Motion of Pendulums. Trans. Cambridge Philos. Soc. 1851, 9, 8
Google Scholar
There is no corresponding record for this reference.
17
Kukulka, T.; Proskurowski, G.; Morét-Ferguson, S.; Meyer, D. W.; Law, K. L. The effect of wind mixing on the vertical distribution of buoyant plastic debris. Geophys. Res. Lett. 2012, 39, 116, DOI: 10.1029/2012gl051116
Google Scholar
There is no corresponding record for this reference.
18
van Sebille, E.; Aliani, S.; Law, K. L.; Maximenko, N.; Alsina, J. M.; Bagaev, A.; Bergmann, M.; Chapron, B.; Chubarenko, I.; Cózar, A.; Delandmeter, P.; Egger, M.; Fox-Kemper, B.; Garaba, S. P.; Goddijn-Murphy, L.; Hardesty, B. D.; Hoffman, M. J.; Isobe, A.; Jongedijk, C. E.; Kaandorp, M. L. A.; Khatmullina, L.; Koelmans, A. A.; Kukulka, T.; Laufkötter, C.; Lebreton, L.; Lobelle, D.; Maes, C.; Martinez-Vicente, V.; Morales Maqueda, M. A.; Poulain-Zarcos, M.; Rodríguez, E.; Ryan, P. G.; Shanks, A. L.; Shim, W. J.; Suaria, G.; Thiel, M.; van den Bremer, T. S.; Wichmann, D. The physical oceanography of the transport of floating marine debris. Environ. Res. Lett. 2020, 15, 023003, DOI: 10.1088/1748-9326/ab6d7d
Google Scholar
There is no corresponding record for this reference.
19
Kooi, M.; Nes, E. H. v.; Scheffer, M.; Koelmans, A. A. Ups and Downs in the Ocean: Effects of Biofouling on Vertical Transport of Microplastics. Environ. Sci. Technol. 2017, 51, 7963– 7971, DOI: 10.1021/acs.est.6b04702
Google Scholar
19
Ups and Downs in the Ocean: Effects of Biofouling on Vertical Transport of Microplastics
Kooi, Merel; Nes, Egbert H. van; Scheffer, Marten; Koelmans, Albert A.
Environmental Science & Technology (2017), 51 (14), 7963-7971CODEN: ESTHAG; ISSN:0013-936X. (American Chemical Society)
Recent studies suggest size-selective removal of small plastic particles from the ocean surface, an observation that remains unexplained. We studied one of the hypotheses regarding this size-selective removal: the formation of a biofilm on the microplastics (biofouling). We developed the first theor. model that is capable of simulating the effect of biofouling on the fate of microplastic. The model is based on settling, biofilm growth, and ocean depth profiles for light, water d., temp., salinity, and viscosity. Using realistic parameters, the model simulates the vertical transport of small microplastic particles over time, and predicts that the particles either float, sink to the ocean floor, or oscillate vertically, depending on the size and d. of the particle. The predicted size-dependent vertical movement of microplastic particles results in a max. concn. at intermediate depths. Consequently, relatively low abundances of small particles are predicted at the ocean surface, while at the same time these small particles may never reach the ocean floor. Our results hint at the fate of "lost" plastic in the ocean, and provide a start for predicting risks of exposure to microplastics for potentially vulnerable species living at these depths.
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20
Long, M.; Moriceau, B.; Gallinari, M.; Lambert, C.; Huvet, A.; Raffray, J.; Soudant, P. Interactions between microplastics and phytoplankton aggregates: Impact on their respective fates. Mar. Chem. 2015, 175, 39– 46, DOI: 10.1016/j.marchem.2015.04.003
Google Scholar
20
Interactions between microplastics and phytoplankton aggregates: Impact on their respective fates
Long, Marc; Moriceau, Brivaela; Gallinari, Morgane; Lambert, Christophe; Huvet, Arnaud; Raffray, Jean; Soudant, Philippe
Marine Chemistry (2015), 175 (), 39-46CODEN: MRCHBD; ISSN:0304-4203. (Elsevier B.V.)
Plastic debris are resistant to degrdn., and therefore tend to accumulate in marine environment. Nevertheless recent estns. of plastic concns. at the surface of the ocean were lower than expected leading the communities to seek new sinks. Among the different processes suggested we chose to focus on the transport of microplastics from the surface to deeper layers of the ocean via phytoplankton aggregates that constitute most of the sinking flux. Interactions between microplastics and aggregates were studied by building a new device: the flow-through roller tank that mimics the behavior of lab. made aggregates sinking through a dense layer of microplastics. Three types of aggregates formed from two different algae species (the diatom Chaetoceros neogracile, the cryptophyte Rhodomonas salina and a mix) were used as model. With their frustule made of biogenic silica which is denser than the org. matter, diatom aggregates sunk faster than R. salina aggregates. Diatom aggregates were on av. bigger and stickier while aggregates from R. salina were smaller and more fragile. With higher concns. measured in R. salina aggregates, all model-aggregates incorporated and concd. microplastics, substantially increasing the microplastic sinking rates from tenths to hundreds of metres per day. Our results clearly show that marine aggregates can be an efficient sink for microplastics by influencing their vertical distribution in the water column. Furthermore, despite the high plastic concns. tested, our study opens new questions regarding the impact of plastics on sedimentation fluxes in oceans. As an effect of microplastic incorporation, the sinking rates of diatom aggregates strongly decreased meanwhile the sinking rates of cryptophyte aggregates increased.
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21
Cole, M.; Lindeque, P. K.; Fileman, E.; Clark, J.; Lewis, C.; Halsband, C.; Galloway, T. S. Microplastics Alter the Properties and Sinking Rates of Zooplankton Faecal Pellets. Environ. Sci. Technol. 2016, 50, 3239– 3246, DOI: 10.1021/acs.est.5b05905
Google Scholar
21
Microplastics Alter the Properties and Sinking Rates of Zooplankton Fecal Pellets
Cole, Matthew; Lindeque, Penelope K.; Fileman, Elaine; Clark, James; Lewis, Ceri; Halsband, Claudia; Galloway, Tamara S.
Environmental Science & Technology (2016), 50 (6), 3239-3246CODEN: ESTHAG; ISSN:0013-936X. (American Chemical Society)
Plastic debris is a widespread contaminant, prevalent in aquatic ecosystems across the globe. Zooplankton readily ingest microscopic plastic (microplastic, <1 mm), which are later egested within their fecal pellets. These pellets are a source of food for marine organisms, and contribute to the oceanic vertical flux of particulate org. matter as part of the biol. pump. The effects of microplastics on fecal pellet properties are currently unknown. We test the hypotheses that (1) fecal pellets are a vector for transport of microplastics, (2) polystyrene microplastics can alter the properties and sinking rates of zooplankton egests and, (3) fecal pellets can facilitate the transfer of plastics to coprophagous biota. Following exposure to 20.6 μm polystyrene microplastics (1000 microplastics/mL) and natural prey (∼1650 algae/mL) the copepod Calanus helgolandicus egested fecal pellets with significantly (p <0.001) reduced densities, a 2.25-fold redn. in sinking rates, and a higher propensity for fragmentation. We further show that microplastics, encapsulated within egests of the copepod Centropages typicus, could be transferred to C. helgolandicus via coprophagy. Our results support the proposal that sinking fecal matter represents a mechanism by which floating plastics can be vertically transported away from surface waters.
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22
Dellino, P.; Mele, D.; Bonasia, R.; Braia, G.; La Volpe, L.; Sulpizio, R. The analysis of the influence of pumice shape on its terminal velocity. Geophys. Res. Lett. 2005, 32(). DOI: 10.1029/2005gl023954
Google Scholar
There is no corresponding record for this reference.
23
Dioguardi, F.; Mele, D. A new shape dependent drag correlation formula for non-spherical rough particles. Experiments and results. Powder Technol. 2015, 277, 222– 230, DOI: 10.1016/j.powtec.2015.02.062
Google Scholar
23
A new shape dependent drag correlation formula for non-spherical rough particles. Experiments and results
Dioguardi, Fabio; Mele, Daniela
Powder Technology (2015), 277 (), 222-230CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
The drag of non-spherical rough particles has been investigated in a wide range of Reynolds nos. (0.03-10,000). The study is based on exptl. measurements of the terminal velocities of irregular particles falling in fluids of different densities and viscosities. The particle shape is described by a shape factor that takes into account both sphericity and circularity, which are measured via image particle anal. techniques. This shape factor is particularly suitable for non-spherical and highly irregular particles. The drag coeff. has been correlated to the particle Reynolds no. and the shape factor and a new correlation law has been found; the correlation has the functional form of a power law. Due to the mutual dependency of the particle terminal velocity on the drag coeff., which in turn depends on the particle shape and Reynolds no., an iterative procedure needs to be designed for calcg. the terminal velocity of particles of a specific size and shape. Such a procedure is adopted herein and a spreadsheet and a Fortran 90 code allowing the iterative calcn. are provided in the Supplementary Material. The fitting of exptl. measurements with our model calcns. show that our new law predicts the drag coeffs. and the terminal velocity of irregularly shaped particles, as volcanic ash, more accurately than other shape-dependent drag laws.
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24
Glenn Research Centre. NASA the Drag Equation, 2022. (accessed 28 April, 2022). https://www.grc.nasa.gov/www/k-12/airplane/drageq.html.
Google Scholar
There is no corresponding record for this reference.
25
Gregory, J., Particles in Water: Properties and Processes. 1st ed; CRC Press: 2005.
Google Scholar
There is no corresponding record for this reference.
26
Wright, J.; Colling, A.; Open University Oceanography Course Team Seawater: Its Composition, Properties, and Behaviour; Butterworth Heinemann: Oxford; Milton Keynes, 2007. in association with the.Open UniversityP
Google Scholar
There is no corresponding record for this reference.
27
Dioguardi, F.; Mele, D.; Dellino, P. Reply to Comment by G. Bagheri and C. Bonadonna on “A New One-Equation Model of Fluid Drag for Irregularly Shaped Particles Valid Over a Wide Range of Reynolds Number”. J. Geophys. Res.: Solid Earth 2019, 124, 10265– 10269, DOI: 10.1029/2019jb018035
Google Scholar
There is no corresponding record for this reference.

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Stefan Dittmar, Aki S. Ruhl, Korinna Altmann, Martin Jekel. Settling Velocities of Small Microplastic Fragments and Fibers. Environmental Science & Technology 2024, 58 (14) , 6359-6369. https://doi.org/10.1021/acs.est.3c09602
Daria Tatsii, Silvia Bucci, Taraprasad Bhowmick, Johannes Guettler, Lucie Bakels, Gholamhossein Bagheri, Andreas Stohl. Shape Matters: Long-Range Transport of Microplastic Fibers in the Atmosphere. Environmental Science & Technology 2024, 58 (1) , 671-682. https://doi.org/10.1021/acs.est.3c08209
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Jiaqi Zhang, Clarence Edward Choi. Towards A universal settling model for microplastics with diverse shapes: Machine learning breaking morphological barriers. Water Research 2025, 272 , 122961. https://doi.org/10.1016/j.watres.2024.122961
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Abstract
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Figure 1
Figure 1. Output for each model evaluated showing the model-estimated terminal settling velocity against the measured terminal settling velocity from the dataset in Van Melkebeke et al. (9) The solid line indicates the ideal fit where the estimated terminal settling velocity equals the measured terminal settling velocity, and the dotted lines indicate the estimated terminal settling velocity equals ±30% of the measured terminal settling velocity. The dashed line indicates the best fit line in the form y = mx that was obtained using linear regression. The labels A–H distinguish between the results of the models evaluated. (A) Yu et al.’s model. (15) (B) Dioguardi et al.’s model (10) using the particle projection area as the particle effective area. (C) Bagheri and Bonadonna’s model (11) using the particle projection area as the particle effective area. (D) Francalanci et al’s model. (13) (E) Zhang and Choi’s model (12) using the maximum cross-sectional area as the particle effective area. (F) Zhang and Choi’s model (12) using the particle surface area as the particle effective area. (G) Dietrich’s model. (14) (H) Stokes model (16) using the particle surface area as the particle effective area.
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Figure 2
Figure 2. Absolute average relative error of model-estimated terminal settling velocity for each model evaluated compared to the measured terminal settling velocity from the dataset by Van Melkebeke et al.. (9) The main figure illustrates the absolute average relative error for the entire dataset, while the lower figure shows the error when each morphology within the dataset is considered separately. The key for the models evaluated is Stokes = Stokes model (16) using the particle surface area as the particle effective area, Bagheri = Bagheri and Bonadonna’s model (11) using the particle projection area as the particle effective area, Dioguardi = Dioguardi et al.’s model (10) using the particle projection area as the particle effective area, Zhang:SA = Zhang and Choi’s model (12) using the particle surface area as the particle effective area, Zhang:Proj = Zhang and Choi’s model (12) using the maximum cross-sectional area as the particle effective area, Dietrich = Dietrich’s model, (14) Francalanci = Francalanci’s model, (13) and Yu = Yu et al.’s model. (15)
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Figure 3
Figure 3. RMSE of the estimated terminal settling velocity for each model evaluated compared to the measured terminal settling velocity from the dataset by Van Melkebeke et al. (9) The main figure illustrates the absolute average relative error for the entire dataset, while the lower figure shows the error when each morphology within the dataset is considered separately. The key for the models evaluated is Stokes = Stokes model (16) using the particle surface area as the particle effective area, Bagheri = Bagheri and Bonadonna’s model (11) using the particle projection area as the particle effective area, Dioguardi = Dioguardi et al.’s model (10) using the particle projection area as the particle effective area, Zhang:SA = Zhang and Choi’s model (12) using the particle surface area as the particle effective area, Zhang:Proj = Zhang and Choi’s model (12) using the maximum cross-sectional area as the particle effective area, Dietrich = Dietrich’s model, (14) Francalanci = Francalanci’s model, (13) and Yu = Yu et al.’s model. (15)
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Figure 4
Figure 4. Output of the re-evaluation of the model by Yu et al. (15) showing the model-estimated terminal settling velocity against the measured terminal settling velocity from the dataset in Dioguardi et al (10) The solid line indicates the ideal fit where the modeled terminal settling velocity equals the measured terminal settling velocity, and the dotted lines indicate the modeled terminal settling velocity equals ±30% of the measured terminal settling velocity. The dashed line indicates the best fit line in the form y = mx that was obtained using linear regression.
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Figure 5
Figure 5. Impact of the choice of initial velocity on the modeled settling velocity when using Bagheri and Bonadonna’s model (11) with the particle projection area as the effective area for six particles that were randomly extracted from the dataset by Van Melkebeke et al. (9) The output from the remaining implicit models is included in Supporting Information 11.
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Figure 6
Figure 6. Output obtained when investigating the influence of fluid density on the terminal settling velocity of six random particles using the model by Yu et al. (15) The output from the remaining implicit models is included in Supporting Information 12.
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Figure 7
Figure 7. Range of settling velocity obtained for each of six random particles using the model by Yu et al. (15) when the fluid density varied from 1019 to 1050 kg/m³. The output from the remaining implicit models is included in Supporting Information 12.
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Figure 8
Figure 8. Comparison of the distance traveled in attaining the terminal settling velocity to the distance traveled if the particle sank constantly at the terminal settling velocity in the equivalent period of time when using the model by Bagheri and Bonadonna. (11) The solid line indicates the ideal fit where there is no difference in the distance traveled, and the dotted lines indicate that the distance traveled at a constant velocity is ±30% of the distance traveled while attaining the terminal settling velocity. The dashed line indicates the best fit line in the form y = mx that was obtained using linear regression. The output from the remaining implicit models is included in Supporting Information 13 for reference.
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References
This article references 27 other publications.
1. 1
  Morales-Caselles, C.; Viejo, J.; Martí, E.; González-Fernández, D.; Pragnell-Raasch, H.; González-Gordillo, J. I.; Montero, E.; Arroyo, G. M.; Hanke, G.; Salvo, V. S.; Basurko, O. C.; Mallos, N.; Lebreton, L.; Echevarría, F.; van Emmerik, T.; Duarte, C. M.; Gálvez, J. A.; van Sebille, E.; Galgani, F.; García, C. M.; Ross, P. S.; Bartual, A.; Ioakeimidis, C.; Markalain, G.; Isobe, A.; Cózar, A. An inshore–offshore sorting system revealed from global classification of ocean litter. Nature Sustainability 2021, 4, 484– 493, DOI: 10.1038/s41893-021-00720-8
  There is no corresponding record for this reference.
2. 2
  van Sebille, E.; Wilcox, C.; Lebreton, L.; Maximenko, N.; Hardesty, B. D.; van Franeker, J. A.; Eriksen, M.; Siegel, D.; Galgani, F.; Law, K. L. A global inventory of small floating plastic debris. Environ. Res. Lett. 2015, 10, 124006, DOI: 10.1088/1748-9326/10/12/124006
  There is no corresponding record for this reference.
3. 3
  Eriksen, M.; Lebreton, L. C. M.; Carson, H. S.; Thiel, M.; Moore, C. J.; Borerro, J. C.; Galgani, F.; Ryan, P. G.; Reisser, J. Plastic Pollution in the World’s Oceans: More than 5 Trillion Plastic Pieces Weighing over 250,000 Tons Afloat at Sea. PLOS ONE 2014, 9, e111913 DOI: 10.1371/journal.pone.0111913
  3
  Plastic pollution in the world's oceans: more than 5 trillion plastic pieces weighing over 250,000 tons afloat at sea
  Eriksen, Marcus; Labreton, Laurent C. M.; Carson, Henry S.; Thiel, Martin; Moore, Charles J.; Borerro, Jose C.; Galgani, Francois; Ryan, Peter G.; Reisser, Julia
  PLoS One (2014), 9 (12), e111913/1-e111913/15, 15 pp.CODEN: POLNCL; ISSN:1932-6203. (Public Library of Science)
  Plastic pollution is ubiquitous throughout the marine environment, yet ests. of the global abundance and wt. of floating plastics have lacked data, particularly from the Southern Hemisphere and remote regions. Here we report an est. of the total no. of plastic particles and their wt. floating in the world's oceans from 24 expeditions (2007-2013) across all five sub-tropical gyres, costal Australia, Bay of Bengal and the Mediterranean Sea conducting surface net tows (N = 680) and visual survey transects of large plastic debris (N = 891). Using an oceanog. model of floating debris dispersal calibrated by our data, and correcting for wind-driven vertical mixing, we est. a min. of 5.25 trillion particles weighing 268,940 tons. When comparing between four size classes, two microplastic <4.75 mm and meso- and macroplastic >4.75 mm, a tremendous loss of microplastics is obsd. from the sea surface compared to expected rates of fragmentation, suggesting there are mechanisms at play that remove <4.75 mm plastic particles from the ocean surface.
  >> More from SciFinder ^®
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4. 4
  Rezania, S.; Park, J.; Md Din, M. F. M.; Mat Taib, S. M.; Talaiekhozani, A.; Kumar Yadav, K. K.; Kamyab, H. Microplastics pollution in different aquatic environments and biota: A review of recent studies. Mar. Pollut. Bull. 2018, 133, 191– 208, DOI: 10.1016/j.marpolbul.2018.05.022
  4
  Microplastics pollution in different aquatic environments and biota: A review of recent studies
  Rezania, Shahabaldin; Park, Junboum; Md. Din, Mohd. Fadhil; Mat Taib, Shazwin; Talaiekhozani, Amirreza; Kumar Yadav, Krishna; Kamyab, Hesam
  Marine Pollution Bulletin (2018), 133 (), 191-208CODEN: MPNBAZ; ISSN:0025-326X. (Elsevier Ltd.)
  Microplastics (MPs) are generated from plastic and have neg. impact to our environment due to high level of fragmentation. They can be originated from various sources in different forms such as fragment, fiber, foam and so on. For detection of MPs, many techniques have been developed with different functions such as microscopic observation, d. sepn., Raman and FTIR anal. Besides, due to ingestion of MPs by wide range of marine species, research on the effect of this pollution on biota as well as human is vital. Therefore, we comprehensively reviewed the occurrence and distribution of MPs pollution in both marine and freshwater environments, including rivers, lakes and wastewater treatment plants (WWTPs). For future studies, we propose the development of new techniques for sampling MPs in aquatic environments and biota and recommend more research regarding MPs release by WWTPs.
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5. 5
  Abreu, A.; Pedrotti, M. L. Microplastics in the Oceans: The Solutions Lie on Land. Field Actions Science Reports 2019, 62– 67
  There is no corresponding record for this reference.
6. 6
  Bakir, A.; Rowland, S. J.; Thompson, R. C. Marine Pollution Bulletin 2012, 64, 2782– 2789, DOI: 10.1016/j.marpolbul.2012.09.010
  6
  Competitive sorption of persistent organic pollutants onto microplastics in the marine environment
  Bakir, Adil; Rowland, Steven J.; Thompson, Richard C.
  Marine Pollution Bulletin (2012), 64 (12), 2782-2789CODEN: MPNBAZ; ISSN:0025-326X. (Elsevier Ltd.)
  Plastics are known to sorb persistent org. pollutants from seawater. However, studies to quantify sorption rates have only considered the affinity of chems. in isolation, unlike the conditions in the environment where contaminants are present as complex mixts. Here we examine whether phenanthrene and 4,4'-DDT, in a mixt., compete for sorption sites onto PVC with no added additives (unplasticized PVC or uPVC) and ultra-high mol. wt. polyethylene. Interactions were investigated by exposing particles of uPVC and UHMW PE to mixts. of 3H and 14C radiolabeled Phe and DDT. Changes in sorption capacity were modelled by applying a Freundlich binding sorption isotherms. An extended Langmuir model and an interaction factor model were also applied to predict equil. concns. of pollutants onto plastic. This study showed that in a bi-solute system, DDT exhibited no significantly different sorption behavior than in single solute systems. However, DDT did appear to interfere with the sorption of Phe onto plastic, indicating an antagonistic effect.
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7. 7
  Lusher, A. Microplastics in the Marine Environment: Distribution, Interactions and Effects. In Marine Anthropogenic Litter; Bergmann, M., Gutow, L., Klages, M., Eds.; Springer International Publishing: Cham, 2015, pp 245– 307.
  There is no corresponding record for this reference.
8. 8
  Zhao, S.; Danley, M.; Ward, J. E.; Li, D.; Mincer, T. J. An approach for extraction, characterization and quantitation of microplastic in natural marine snow using Raman microscopy. Anal. Methods 2017, 9, 1470– 1478, DOI: 10.1039/c6ay02302a
  8
  An approach for extraction, characterization and quantitation of microplastic in natural marine snow using Raman microscopy
  Zhao, Shiye; Danley, Meghan; Ward, J. Evan; Li, Daoji; Mincer, Tracy J.
  Analytical Methods (2017), 9 (9), 1470-1478CODEN: AMNEGX; ISSN:1759-9679. (Royal Society of Chemistry)
  Marine snow is a predominant form of sinking particulate carbon in the marine water column and represents a mechanism for transporting microplastics to the sea floor. We present a new dual d. sepn. method employing sodium iodide extn. followed by methanol pptn., specifically designed for microplastic isolation and identification in natural marine snow samples. A total of 59 microscopic particles from eight marine snow samples collected at Avery Point, CT were confirmed as plastics and/or substances contg. typical plastic manufg. additives. Extn. efficiency of this method was detd. using polyethylene microspheres of varying sizes (63-75 μm, 212-250 μm and 500-600 μm) yielding 90%, 93% and 98% recoveries, resp. Residual org. matter which can cause interference in downstream Raman spectroscopic analyses was eliminated by employing a 15% hydrogen peroxide (H2O2) digestion step, which caused negligible chem. modifications to the polymer samples. Extensive precautions such as combusted glassware, a microfiltration air hood, and incorporation of process blank samples ensured that airborne microplastic contamination was avoided. A phase contrast microscope equipped with a Raman spectrophotometer system using a 785 nm laser excitation source efficiently identified anthropogenic polymer materials. Unexpectedly, plastic additives such as pigments complicated the identification of polymers but their spectra were successfully interpreted through spectral subtraction and comparison to a database and authentic stds. The protocol described can be applied to detect microplastic in marine snow samples and improve our understanding of the fate of microplastic in the ocean.
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9. 9
  Van Melkebeke, M.; Janssen, C.; De Meester, S. Characteristics and Sinking Behavior of Typical Microplastics Including the Potential Effect of Biofouling: Implications for Remediation. Environ. Sci. Technol. 2020, 54, 8668– 8680, DOI: 10.1021/acs.est.9b07378
  9
  Characteristics and sinking behavior of typical microplastics including the potential effect of biofouling: implications for remediation
  Van Melkebeke, Michiel; Janssen, Colin; De Meester, Steven
  Environmental Science & Technology (2020), 54 (14), 8668-8680CODEN: ESTHAG; ISSN:0013-936X. (American Chemical Society)
  Microplastics are ubiquitous pollutants within the marine environment, predominantly (>90%) accumulating in sediments worldwide. Despite the increasing global concern regarding these anthropogenic pollutants, research into the remediation of microplastics is lacking. Here, we examine those characteristics of microplastics that are essential to adequately evaluate potential remediation techniques such as sedimentation and (air) flotation techniques. We analyzed the sinking behavior of typical microplastics originating from real plastic waste samples and identified the best-available drag model to quant. describe their sinking behavior. Particle shape is confirmed to be an important parameter strongly affecting the sinking behavior of microplastics. Various common shape descriptors were exptl. evaluated on their ability to appropriately characterize frequently occurring particle shapes of typical microplastics such as spheres, films, and fibers. This study is the first in this field to include film particles in its exptl. design, which were found to make up a considerable fraction of marine pollution and are shown to significantly affect the evaluation of shape-dependent drag models. Circularity χ and sphericity Φ are found to be appropriate shape descriptors in this context. We also investigated the effect of biofouling on the polarity of marine plastics and estd. its potential contribution to the settling motion of initially floating microplastics based on d.-modification. It is found that biofouling alters the polarity of plastics significantly; this is from (near) hydrophobic (i.e., water contact angles from 70 to 100°) to strong hydrophilic (i.e., water contact angles from 30 to 40°) surfaces, rendering them more difficult to sep. from sediment based on polarity as a primary sepn. factor. Thus, besides providing a better understanding of the fate and behavior of typical marine microplastics, these findings serve as a fundamental stepping-stone to the development of the first large-scale sediment remediation technique for microplastics to address the global microplastic accumulation issue.
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10. 10
  Dioguardi, F.; Mele, D.; Dellino, P. A New One-Equation Model of Fluid Drag for Irregularly Shaped Particles Valid Over a Wide Range of Reynolds Number. J. Geophys. Res.: Solid Earth 2018, 123, 144– 156, DOI: 10.1002/2017jb014926
  There is no corresponding record for this reference.
11. 11
  Bagheri, G.; Bonadonna, C. On the drag of freely falling non-spherical particles. Powder Technol. 2016, 301, 526– 544, DOI: 10.1016/j.powtec.2016.06.015
  11
  On the drag of freely falling non-spherical particles
  Bagheri, Gholamhossein; Bonadonna, Costanza
  Powder Technology (2016), 301 (), 526-544CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
  We present a new general model for the prediction of the drag coeff. of non-spherical solid particles of regular and irregular shapes falling in gas or liq. valid for sub-crit. particle Reynolds nos. (i.e. Re < 3 × 105). Results are obtained from exptl. measurements on 300 regular and irregular particles in the air and anal. solns. for ellipsoids. Depending on their size, irregular particles are accurately characterized with a 3D laser scanner or SEM micro-CT method. The expts. are carried out in settling columns with height of 0.45 to 3.60 m and in a 4 m-high vertical wind tunnel. In addn., 881 addnl. exptl. data points are also considered that are compiled from the literature for particles of regular shapes falling in liqs. New correlation is based on the particle Reynolds no. and two new shape descriptors defined as a function of particle flatness, elongation and diam. New shape descriptors are easy-to-measure and can be more easily characterized than sphericity. The new correlation has an av. error of ∼ 10%, which is significantly lower than errors assocd. with existing correlations. Addnl. aspects of particle sedimentation are also investigated. First, it is found that particles falling in dense liqs., in particular at Re > 1000, tend to fall with their max. projection area perpendicular to their falling direction, whereas in gases their orientation is random. Second, effects of small-scale surface vesicularity and roughness on the drag coeff. of non-spherical particles found to be < 10%. Finally, the effect of particle orientation on the drag coeff. is discussed and addnl. correlations are presented to predict the end members of drag coeff. due to change in the particle orientation.
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12. 12
  Zhang, J.; Choi, C. E. Improved Settling Velocity for Microplastic Fibers: A New Shape-dependent Drag Model; Environmental Science & Technology, 2021.
  There is no corresponding record for this reference.
13. 13
  Francalanci, S.; Paris, E.; Solari, L. On the prediction of settling velocity for plastic particles of different shapes. Environ. Pollut. 2021, 290, 118068, DOI: 10.1016/j.envpol.2021.118068
  13
  On the prediction of settling velocity for plastic particles of different shapes
  Francalanci, Simona; Paris, Enio; Solari, Luca
  Environmental Pollution (Oxford, United Kingdom) (2021), 290 (), 118068CODEN: ENPOEK; ISSN:0269-7491. (Elsevier Ltd.)
  Transport processes of plastic particles in freshwater and marine environments are one of the relevant advances of knowledge in predicting the fate of plastic in the environment. Here, we investigated the effect of different shapes on the settling velocity, finding a representative ref. diam. which encompasses three-dimensional shapes like pellets or spherules, two-dimensional shapes like fragments or disks, and one-dimensional shapes like filaments or fibers. The new method is able to predict the settling velocity of plastic and natural particles given the representative size and the Corey shape factor coeff., over the entire range of viscous to turbulent flow regime. The calibration of the method with exptl. data, and the validation with an independent dataset, support its application in a wide range of hydraulic conditions.
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14. 14
  Dietrich, W. E. Settling velocity of natural particles. Water Resour. Res. 1982, 18, 1615– 1626, DOI: 10.1029/wr018i006p01615
  There is no corresponding record for this reference.
15. 15
  Yu, Z.; Yang, G.; Zhang, W. A new model for the terminal settling velocity of microplastics. Mar. Pollut. Bull. 2022, 176, 113449, DOI: 10.1016/j.marpolbul.2022.113449
  15
  A new model for the terminal settling velocity of microplastics
  Yu, Zijian; Yang, Ge; Zhang, Wenming
  Marine Pollution Bulletin (2022), 176 (), 113449CODEN: MPNBAZ; ISSN:0025-326X. (Elsevier Ltd.)
  Microplastic (MP) settling process is important for the transport of microplastic particles (MPs, <5 mm) in water bodies. However, for the control parameter of the drag coeff. (Cd), no generalized formula has been proposed for MPs of different shapes and materials. In this study, a total of 1343 MP settling data were collected from the literature. It was found that the drag law for perfect spheres cannot reasonably predict Cd for MPs with particle Reynolds no. of 1-103. A new formula for Cd was developed by introducing the dimensionless particle diam. (d*) and two shape descriptors. The abs. error of the new formula is 15.2%, smaller than those (42.5-72.8%) of other existing formulas. Moreover, an explicit model was developed for MP settling velocity by correlating Cd, d*, and shape descriptors, with lower abs. error (8.8%) than those (15.4-77.2%) of existing models.
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16. 16
  Stokes, G. G. On the Effect of the Internal Friction of Fluids on the Motion of Pendulums. Trans. Cambridge Philos. Soc. 1851, 9, 8
  There is no corresponding record for this reference.
17. 17
  Kukulka, T.; Proskurowski, G.; Morét-Ferguson, S.; Meyer, D. W.; Law, K. L. The effect of wind mixing on the vertical distribution of buoyant plastic debris. Geophys. Res. Lett. 2012, 39, 116, DOI: 10.1029/2012gl051116
  There is no corresponding record for this reference.
18. 18
  van Sebille, E.; Aliani, S.; Law, K. L.; Maximenko, N.; Alsina, J. M.; Bagaev, A.; Bergmann, M.; Chapron, B.; Chubarenko, I.; Cózar, A.; Delandmeter, P.; Egger, M.; Fox-Kemper, B.; Garaba, S. P.; Goddijn-Murphy, L.; Hardesty, B. D.; Hoffman, M. J.; Isobe, A.; Jongedijk, C. E.; Kaandorp, M. L. A.; Khatmullina, L.; Koelmans, A. A.; Kukulka, T.; Laufkötter, C.; Lebreton, L.; Lobelle, D.; Maes, C.; Martinez-Vicente, V.; Morales Maqueda, M. A.; Poulain-Zarcos, M.; Rodríguez, E.; Ryan, P. G.; Shanks, A. L.; Shim, W. J.; Suaria, G.; Thiel, M.; van den Bremer, T. S.; Wichmann, D. The physical oceanography of the transport of floating marine debris. Environ. Res. Lett. 2020, 15, 023003, DOI: 10.1088/1748-9326/ab6d7d
  There is no corresponding record for this reference.
19. 19
  Kooi, M.; Nes, E. H. v.; Scheffer, M.; Koelmans, A. A. Ups and Downs in the Ocean: Effects of Biofouling on Vertical Transport of Microplastics. Environ. Sci. Technol. 2017, 51, 7963– 7971, DOI: 10.1021/acs.est.6b04702
  19
  Ups and Downs in the Ocean: Effects of Biofouling on Vertical Transport of Microplastics
  Kooi, Merel; Nes, Egbert H. van; Scheffer, Marten; Koelmans, Albert A.
  Environmental Science & Technology (2017), 51 (14), 7963-7971CODEN: ESTHAG; ISSN:0013-936X. (American Chemical Society)
  Recent studies suggest size-selective removal of small plastic particles from the ocean surface, an observation that remains unexplained. We studied one of the hypotheses regarding this size-selective removal: the formation of a biofilm on the microplastics (biofouling). We developed the first theor. model that is capable of simulating the effect of biofouling on the fate of microplastic. The model is based on settling, biofilm growth, and ocean depth profiles for light, water d., temp., salinity, and viscosity. Using realistic parameters, the model simulates the vertical transport of small microplastic particles over time, and predicts that the particles either float, sink to the ocean floor, or oscillate vertically, depending on the size and d. of the particle. The predicted size-dependent vertical movement of microplastic particles results in a max. concn. at intermediate depths. Consequently, relatively low abundances of small particles are predicted at the ocean surface, while at the same time these small particles may never reach the ocean floor. Our results hint at the fate of "lost" plastic in the ocean, and provide a start for predicting risks of exposure to microplastics for potentially vulnerable species living at these depths.
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20. 20
  Long, M.; Moriceau, B.; Gallinari, M.; Lambert, C.; Huvet, A.; Raffray, J.; Soudant, P. Interactions between microplastics and phytoplankton aggregates: Impact on their respective fates. Mar. Chem. 2015, 175, 39– 46, DOI: 10.1016/j.marchem.2015.04.003
  20
  Interactions between microplastics and phytoplankton aggregates: Impact on their respective fates
  Long, Marc; Moriceau, Brivaela; Gallinari, Morgane; Lambert, Christophe; Huvet, Arnaud; Raffray, Jean; Soudant, Philippe
  Marine Chemistry (2015), 175 (), 39-46CODEN: MRCHBD; ISSN:0304-4203. (Elsevier B.V.)
  Plastic debris are resistant to degrdn., and therefore tend to accumulate in marine environment. Nevertheless recent estns. of plastic concns. at the surface of the ocean were lower than expected leading the communities to seek new sinks. Among the different processes suggested we chose to focus on the transport of microplastics from the surface to deeper layers of the ocean via phytoplankton aggregates that constitute most of the sinking flux. Interactions between microplastics and aggregates were studied by building a new device: the flow-through roller tank that mimics the behavior of lab. made aggregates sinking through a dense layer of microplastics. Three types of aggregates formed from two different algae species (the diatom Chaetoceros neogracile, the cryptophyte Rhodomonas salina and a mix) were used as model. With their frustule made of biogenic silica which is denser than the org. matter, diatom aggregates sunk faster than R. salina aggregates. Diatom aggregates were on av. bigger and stickier while aggregates from R. salina were smaller and more fragile. With higher concns. measured in R. salina aggregates, all model-aggregates incorporated and concd. microplastics, substantially increasing the microplastic sinking rates from tenths to hundreds of metres per day. Our results clearly show that marine aggregates can be an efficient sink for microplastics by influencing their vertical distribution in the water column. Furthermore, despite the high plastic concns. tested, our study opens new questions regarding the impact of plastics on sedimentation fluxes in oceans. As an effect of microplastic incorporation, the sinking rates of diatom aggregates strongly decreased meanwhile the sinking rates of cryptophyte aggregates increased.
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21. 21
  Cole, M.; Lindeque, P. K.; Fileman, E.; Clark, J.; Lewis, C.; Halsband, C.; Galloway, T. S. Microplastics Alter the Properties and Sinking Rates of Zooplankton Faecal Pellets. Environ. Sci. Technol. 2016, 50, 3239– 3246, DOI: 10.1021/acs.est.5b05905
  21
  Microplastics Alter the Properties and Sinking Rates of Zooplankton Fecal Pellets
  Cole, Matthew; Lindeque, Penelope K.; Fileman, Elaine; Clark, James; Lewis, Ceri; Halsband, Claudia; Galloway, Tamara S.
  Environmental Science & Technology (2016), 50 (6), 3239-3246CODEN: ESTHAG; ISSN:0013-936X. (American Chemical Society)
  Plastic debris is a widespread contaminant, prevalent in aquatic ecosystems across the globe. Zooplankton readily ingest microscopic plastic (microplastic, <1 mm), which are later egested within their fecal pellets. These pellets are a source of food for marine organisms, and contribute to the oceanic vertical flux of particulate org. matter as part of the biol. pump. The effects of microplastics on fecal pellet properties are currently unknown. We test the hypotheses that (1) fecal pellets are a vector for transport of microplastics, (2) polystyrene microplastics can alter the properties and sinking rates of zooplankton egests and, (3) fecal pellets can facilitate the transfer of plastics to coprophagous biota. Following exposure to 20.6 μm polystyrene microplastics (1000 microplastics/mL) and natural prey (∼1650 algae/mL) the copepod Calanus helgolandicus egested fecal pellets with significantly (p <0.001) reduced densities, a 2.25-fold redn. in sinking rates, and a higher propensity for fragmentation. We further show that microplastics, encapsulated within egests of the copepod Centropages typicus, could be transferred to C. helgolandicus via coprophagy. Our results support the proposal that sinking fecal matter represents a mechanism by which floating plastics can be vertically transported away from surface waters.
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22. 22
  Dellino, P.; Mele, D.; Bonasia, R.; Braia, G.; La Volpe, L.; Sulpizio, R. The analysis of the influence of pumice shape on its terminal velocity. Geophys. Res. Lett. 2005, 32(). DOI: 10.1029/2005gl023954
  There is no corresponding record for this reference.
23. 23
  Dioguardi, F.; Mele, D. A new shape dependent drag correlation formula for non-spherical rough particles. Experiments and results. Powder Technol. 2015, 277, 222– 230, DOI: 10.1016/j.powtec.2015.02.062
  23
  A new shape dependent drag correlation formula for non-spherical rough particles. Experiments and results
  Dioguardi, Fabio; Mele, Daniela
  Powder Technology (2015), 277 (), 222-230CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
  The drag of non-spherical rough particles has been investigated in a wide range of Reynolds nos. (0.03-10,000). The study is based on exptl. measurements of the terminal velocities of irregular particles falling in fluids of different densities and viscosities. The particle shape is described by a shape factor that takes into account both sphericity and circularity, which are measured via image particle anal. techniques. This shape factor is particularly suitable for non-spherical and highly irregular particles. The drag coeff. has been correlated to the particle Reynolds no. and the shape factor and a new correlation law has been found; the correlation has the functional form of a power law. Due to the mutual dependency of the particle terminal velocity on the drag coeff., which in turn depends on the particle shape and Reynolds no., an iterative procedure needs to be designed for calcg. the terminal velocity of particles of a specific size and shape. Such a procedure is adopted herein and a spreadsheet and a Fortran 90 code allowing the iterative calcn. are provided in the Supplementary Material. The fitting of exptl. measurements with our model calcns. show that our new law predicts the drag coeffs. and the terminal velocity of irregularly shaped particles, as volcanic ash, more accurately than other shape-dependent drag laws.
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24. 24
  Glenn Research Centre. NASA the Drag Equation, 2022. (accessed 28 April, 2022). https://www.grc.nasa.gov/www/k-12/airplane/drageq.html.
  There is no corresponding record for this reference.
25. 25
  Gregory, J., Particles in Water: Properties and Processes. 1st ed; CRC Press: 2005.
  There is no corresponding record for this reference.
26. 26
  Wright, J.; Colling, A.; Open University Oceanography Course Team Seawater: Its Composition, Properties, and Behaviour; Butterworth Heinemann: Oxford; Milton Keynes, 2007. in association with the.Open UniversityP
  There is no corresponding record for this reference.
27. 27
  Dioguardi, F.; Mele, D.; Dellino, P. Reply to Comment by G. Bagheri and C. Bonadonna on “A New One-Equation Model of Fluid Drag for Irregularly Shaped Particles Valid Over a Wide Range of Reynolds Number”. J. Geophys. Res.: Solid Earth 2019, 124, 10265– 10269, DOI: 10.1029/2019jb018035
  There is no corresponding record for this reference.
Supporting Information
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsestwater.2c00466.
- Additional model descriptions, experimental details, and results of tests on individual models as mentioned in the text (pdf)
- ew2c00466_si_001.pdf (15.6 MB)
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Modeling Microplastic Transport in the Marine Environment: Testing Empirical Models of Particle Terminal Sinking Velocity for Irregularly Shaped ParticlesClick to copy article linkArticle link copied!

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1. Introduction

2. Methods and Data

2.1. Approach

2.2. Method to Evaluate Explicit Models

2.3. Method to Evaluate Implicit Models

2.4. Datasets Used

2.5. Analysis Undertaken during Model Evaluation

3. Results and Discussion

3.1. Model Evaluation

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3.2. Re-evaluation of Yu’s Model

Figure 4

3.3. Further Analysis

3.4. Impact of the Choice of Initial Velocity on the Result of the Implicit Models

Figure 5

3.5. Variation in the Terminal Settling Velocity over the Range of Density in the Ocean and the Impact on the Models of Assuming a Constant Terminal Settling Velocity

Figure 6

Figure 7

3.6. Exploring the Impact of Using a Constant Terminal Sinking Velocity on the Distance Traveled by the mPs

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3.7. Limitations to This Research

4. Conclusions

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Modeling Microplastic Transport in the Marine Environment: Testing Empirical Models of Particle Terminal Sinking Velocity for Irregularly Shaped Particles
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