Alberto Baudena
email: alberto.baudena@gmail.com.

Rainer Kiko

Isabel Jalón-Rojas

Maria Luiza Pedrotti

Low-Density Plastic Debris Dispersion beneath the Mediterranean Sea Surface

Keywords: low-density plastic, marine pollution, water column, seafloor, transport, sinking speed

Introduction

Plastic pollution represents a major threat to the oceans, causing socio-economic damage and impacting tourism, fishing, and marine ecosystems [START_REF] David | Accumulation and fragmentation of plastic debris in global environments[END_REF][START_REF] Beaumont | Global ecological, social and economic impacts of marine plastic[END_REF]. More than 914 marine species have been reported to accidentally ingest or be entangled by plastic, a number expected to increase in the near future [START_REF] Kühn | Quantitative overview of marine debris ingested by marine megafauna[END_REF]. In addition, plastic debris is a vector for invasive species and persistent organic pollutants [START_REF] José | Plastic as a vector of dispersion for marine species with invasive potential. a review[END_REF][START_REF] Obinwanne Okoye | Toxic chemicals and persistent organic pollutants associated with micro-and nanoplastics pollution[END_REF][START_REF] Andrady | Microplastics in the marine environment[END_REF]. Around 300,000 metric tons of plastic have been estimated to float at the sea surface [START_REF] Isobe | A multilevel dataset of microplastic abundance in the world's upper ocean and the Laurentian Great Lakes[END_REF]. However, they only represent a tiny portion of the plastic expected to enter the marine environment each year [START_REF] Jambeck | Plastic waste inputs from land into the ocean[END_REF][START_REF] Van Sebille | A global inventory of small floating plastic debris[END_REF][START_REF] Lau | Evaluating scenarios toward zero plastic pollution[END_REF], suggesting that plastic may be even more present in other ocean compartments. Even if the amount of plastic entering the oceans (e.g., via rivers) and the plastic budget are still open questions [START_REF] Lau | Evaluating scenarios toward zero plastic pollution[END_REF][START_REF] Borrelle | Predicted growth in plastic waste exceeds efforts to mitigate plastic pollution[END_REF][START_REF] Weiss | The missing ocean plastic sink: Gone with the rivers[END_REF], a growing body of evidence suggests that plastic debris is present not only at the sea surface, but in the whole water column and sea bottom (e.g. refs. [START_REF] Choy | The vertical distribution and biological transport of marine microplastics across the epipelagic and mesopelagic water column[END_REF][START_REF] Egger | First evidence of plastic fallout from the North Pacific Garbage Patch[END_REF][START_REF] Lefebvre | Microplastics ftir characterisation and distribution in the water column and digestive tracts of small pelagic fish in the gulf of lions[END_REF][START_REF] Kane | Seafloor microplastic hotspots controlled by deep-sea circulation[END_REF][START_REF] Pierdomenico | Massive benthic litter funnelled to deep sea by flash-flood generated hyperpycnal flows[END_REF][START_REF] Galgani | Litter on the Sea Floor Along European Coasts[END_REF]. Surprisingly, observations reported plastic debris composed of polymers lighter than seawater in the water column, down to at least 1000 m depth [START_REF] Egger | First evidence of plastic fallout from the North Pacific Garbage Patch[END_REF].

Several processes are responsible for the removal of plastic debris from the sea surface, the most studied being biofouling [START_REF] Chubarenko | On some physical and dynamical properties of microplastic particles in marine environment[END_REF][START_REF] Kooi | Ups and downs in the ocean: Effects of biofouling on vertical transport of microplastics[END_REF] -the colonisation of plastic debris by bacteria, algae or invertebrates -which increases its relative density. This process continues until, eventually, the debris leaves the surface, and has been documented by laboratory and, recently, by in situ studies [START_REF] Francesca | Biofouling on buoyant marine plastics: An experimental study into the effect of size on surface longevity[END_REF][START_REF] Kaiser | Effects of biofouling on the sinking behavior of microplastics[END_REF][START_REF] Gerritse | Fragmentation of plastic objects in a laboratory seawater microcosm[END_REF][START_REF] Karkanorachaki | Sinking characteristics of microplastics in the marine environment[END_REF].

Other processes that could lead to the removal of surface plastic debris are aggregation in marine snow and faecal pellet formation after ingestion [START_REF] Cole | Microplastics alter the properties and sinking rates of zooplankton faecal pellets[END_REF][START_REF] Porter | Role of marine snows in microplastic fate and bioavailability[END_REF].

However, information about the pathways and fate of settling plastic debris is lacking. A common assumption is that plastic debris reaches the seafloor where it has left the surface [START_REF] Liubartseva | Tracking plastics in the Mediterranean: 2D Lagrangian model[END_REF]. This assumption has also been used to estimate the seafloor plastic concentration [START_REF] Kane | Seafloor microplastic hotspots controlled by deep-sea circulation[END_REF].

The aim of this study is to assess the validity of this assumption and to improve the understanding of plastic transport from the sea surface to the sea bottom. This information is essential to solve the plastic budget problem, to understand plastic fate, and for mitigation strategies. For that purpose, we use a Lagrangian plastic-tracking model to analyse (i) the potential pathways of plastic debris from the surface to the seafloor, (ii) its distribution once it reaches the seafloor, and (iii) its potential sources. We focus on plastic whose absolute density is lighter than seawater (referred to as low-density plastic, LDP), usually smaller than 5 mm in size [START_REF] Luiza Pedrotti | An integrative assessment of the plastic debris load in the mediterranean sea[END_REF]. This includes low-and high-density polyethylene and polypropylene, which represent 88% of the LDP debris floating at the surface of the Mediterranean Sea [START_REF] Kedzierski | Chemical composition of microplastics floating on the surface of the Mediterranean Sea[END_REF], and about half of the produced plastic globally [START_REF] Geyer | Production, use, and fate of all plastics ever made[END_REF][START_REF] Andrady | Microplastics in the marine environment[END_REF]. We only focus on the sinking phase of LDP debris, as multiple works already studied its cycle from the moment it is released at sea until it starts sinking (e.g. [START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF][START_REF] Liubartseva | Tracking plastics in the Mediterranean: 2D Lagrangian model[END_REF][START_REF] Lobelle | Global modeled sinking characteristics of biofouled microplastic[END_REF]). We do not consider high density plastic debris, which is expected to sink directly to the seafloor [START_REF] Pierdomenico | Massive benthic litter funnelled to deep sea by flash-flood generated hyperpycnal flows[END_REF][START_REF] Jalón-Rojas | Effects of biofilms and particle physical properties on the rising and settling velocities of microplastic fibers and sheets[END_REF] and about which there is little information, nor extremely light items which mainly float at the air-sea interface. Lagrangian methods are widely used to describe the transport of particles in the ocean and are suited to describe the transport of LDP debris.

These models can cover areas wider than observations and can describe forward and backward trajectories useful to identify sources and pathways.

This study is a first modeling effort to evaluate the transport dynamics and fate of LDP in the Mediterranean Sea, which is an ideal case study for two main reasons: (i) globally, it is one of the most plastic polluted seas [START_REF] Luiza Pedrotti | An integrative assessment of the plastic debris load in the mediterranean sea[END_REF][START_REF] Cózar | Plastic accumulation in the Mediterranean Sea[END_REF]; (ii) its plastic pollution at the sea surface has been intensively studied, allowing us to estimate key physical parameters such as plastic debris sinking speed and to set initial conditions. In particular, we combine recent observations of plastic concentration in the water column, the largest Mediterranean Sea database of floating LDP debris to date, one of the best performing drag models, and esti-mates of the location and amount of LDP leaving the sea surface. The latter metric was obtained from the first Lagrangian model quantitatively validated in the Mediterranean Sea [START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF], by assuming that the probability of a LDP leaving the surface increases with the time it spent in water according to a prescribed function. With this information, we are also able to calibrate the model and perform a detailed sensitivity test. We then provide an assessment of the paths and fate of LDP sinking in the Mediterranean sea as well as an estimation of the contribution of the different countries to the coastal seafloor pollution. Finally, we consider the implications of the calculated density differences between generic sinking LDP debris and seawater to assess the role of biological transport throughout the water column, consistent with recent studies.

Materials and Methods

The numerical Lagrangian model: velocity field and trajectory computation

Here, we simulate the path of LDP debris once they start sinking from the surface (due to biofouling or other processes) down to 1000 m. We do not analyse what occurs to debris prior to that (i.e., from the moment it was released at sea to when it left the sea surface), as several studies already investigated this question (e.g. [START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF][START_REF] Liubartseva | Tracking plastics in the Mediterranean: 2D Lagrangian model[END_REF][START_REF] Mansui | Predicting marine litter accumulation patterns in the mediterranean basin: Spatio-temporal variability and comparison with empirical data[END_REF]). Hence, this study can be seen as a continuation of those works. To this aim, we used the TrackMPD model [START_REF] Jalón-Rojas | A 3D numerical model to Track Marine Plastic Debris (TrackMPD): Sensitivity of microplastic trajectories and fates to particle dynamical properties and physical processes[END_REF], an advanced 3D Lagrangian model recently developed to simulate the fate of plastic debris at sea. The TrackMPD model reads the velocity field offline, and computes the trajectories with a Runge-Kutta scheme of order 4-5 both in time and space. Time steps were set to 3 hours. Model initialisation and simulated scenarios are reported in Subsec. 2.3.

The velocity field used to simulate the virtual particle trajectories was a high resolution configuration of the NEMO model (NemoMed36; 1/36 • ×1/36 • ) provided at daily intervals, with 50 stretched vertical levels (sigma coordinate system), developed by Arsouze et al. (37). This circulation model was initialised with sea surface temperature and salinity fields and took into account riverine freshwater runoff. It included the vertical component of the velocity field w as well. This product has already been used to simulate 3D virtual plastic trajectories in the Mediterranean Sea [START_REF] Soto-Navarro | 3d hotspots of marine litter in the mediterranean: A modeling study[END_REF].

A Stokes component was added to the NemoMed36 velocity field. The Stokes product (MEDSEA HINDCAST WAV 006 012), with a spatial resolution of 1/24 • , was spatially interpolated over the grid of NemoMed36, and was summed to its upper layer. This allowed us to take into account Stokes drift due to waves at the surface, which affects particles in the first meters of their sinking. Stokes effect indirectly includes windage and is known to affect plastic fate (39).

Constraining the model settings

A key parameter to study the fate of (biofouled) sinking LDP debris in the water column is its settling speed. In situ observations of LDP settling speed are not available to date. A few studies have measured the settling velocity of biofouled plastic particles under laboratory conditions and found that a large number of parameters, both physical (e.g. particle polymer, shape and size;

water temperature and salinity) and biological (e.g. biofilm growth and density) can impact the sinking speed [START_REF] Jalón-Rojas | Effects of biofilms and particle physical properties on the rising and settling velocities of microplastic fibers and sheets[END_REF][START_REF] Karkanorachaki | Sinking characteristics of microplastics in the marine environment[END_REF][START_REF] Chubarenko | On some physical and dynamical properties of microplastic particles in marine environment[END_REF]. The large spectrum of sinking LDP and environmental conditions in the ocean make difficult the definition of settling speed in numerical simulations. For these reasons, we calculated a (maximum) representative sinking speed value to calibrate our model, ensuring that mean simulated and observed LDP concentrations in the water column have the same order of magnitude. We assumed that the water column LDP concentration is the result of a linear fall of LDP debris from the sea surface.

The larger the LDP sinking speed, the lower the water column LDP concentration for a given rate of plastic submergence from surface (Fig. 1 14) also when considering the mass (µg/m 3 ). This is also corroborated by the fact that the Mediterranean is one of the seas most affected by plastic pollution, with surface LDP concentrations comparable to those found in the North Pacific Garbage Patch (NPGP) [START_REF] Luiza Pedrotti | An integrative assessment of the plastic debris load in the mediterranean sea[END_REF][START_REF] Cózar | Plastic accumulation in the Mediterranean Sea[END_REF][START_REF] Baini | Abundance and characterization of microplastics in the coastal waters of tuscany (italy): The application of the msfd monitoring protocol in the mediterranean sea[END_REF]. Biofouling was predicted to be larger in several regions of the Mediterranean Sea than in the oligotrophic NPGP area [START_REF] Lobelle | Global modeled sinking characteristics of biofouled microplastic[END_REF], suggesting that more LDP particles might leave the surface in the Mediterranean. However Mediterranean Sea studies [START_REF] Baini | Abundance and characterization of microplastics in the coastal waters of tuscany (italy): The application of the msfd monitoring protocol in the mediterranean sea[END_REF][START_REF] Lefebvre | Microplastics ftir characterisation and distribution in the water column and digestive tracts of small pelagic fish in the gulf of lions[END_REF][START_REF] Vasilopoulou | Microplastics investigation using zooplankton samples from the coasts of Cyprus (Eastern Mediterranean)[END_REF] sampled lower water volumes, inducing possible biases towards higher concentrations [START_REF] Liu | A novel method enabling the accurate quantification of microplastics in the water column of deep ocean[END_REF][START_REF] Liu | Elucidating the vertical transport of microplastics in the water column: A review of sampling methodologies and distributions[END_REF][START_REF] Li | Profiling the vertical transport of microplastics in the West Pacific Ocean and the East Indian Ocean with a novel in situ filtration technique[END_REF]. Therefore, we considered a minimum water column LDP concentration 199

C O M IN = 1.60 µg/m 3
Table 1: Literature on Mediterranean water column plastic concentration (adapted with permission from Liu et al., [START_REF] Liu | Elucidating the vertical transport of microplastics in the water column: A review of sampling methodologies and distributions[END_REF], Copyright 2020 Elsevier).

Annual estimates of LDP plastic entering the Mediterranean

Sea.

We defined N T BY as the number of tons of LDP leaving the Mediterranean surface every year due to biofouling or other processes. N T BY was obtained assuming that ∼11.5% of the amount of floating plastic debris entering the Mediterranean Sea every year from coastal sources or vessel discards (N LDP Y ) left the sea surface during that period due to biofouling or other processes. This percentage was based on the study by Baudena et al., [START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF], and was similar to the value obtained in a previous study (9.2 %, 27). Thus:

N T BY = 0.115 • N LDP Y . (1)
N LDP Y was estimated using the findings of ref. [START_REF] Jambeck | Plastic waste inputs from land into the ocean[END_REF]. The authors calculated the number of tons of plastic debris entering the global ocean in 2010. Considering that ∼50% of plastic is LDP (mainly low-and high-density polyethylene and polypropylene, 30, 6), about 100,000 tons of LDP debris were estimated to enter the Mediterranean Sea in 2010. This quantity includes also extremely light and large LDP not considered here. However, these constitute less than 1% of items collected in the Mediterranean Sea [START_REF] Luiza Pedrotti | An integrative assessment of the plastic debris load in the mediterranean sea[END_REF]. Overall, the assumed quantity represents a compromise between recent estimates, both lower (58, 59) and higher [START_REF] Borrelle | Predicted growth in plastic waste exceeds efforts to mitigate plastic pollution[END_REF][START_REF] Lau | Evaluating scenarios toward zero plastic pollution[END_REF]. Furthermore, we stress that this value was adopted in recent studies modelling plastic-debris dispersion in this basin [START_REF] Liubartseva | Tracking plastics in the Mediterranean: 2D Lagrangian model[END_REF][START_REF] Soto-Navarro | 3d hotspots of marine litter in the mediterranean: A modeling study[END_REF][START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF]. The sensitivity of the results with respect to this parameter is studied by simulating a further scenario (Subsec. 2.3).

Estimation of the maximum sinking speed of LDP debris SS M AX

N T BY can be converted into a flux F of LDP mass leaving each m 2 of sea surface every day by considering the Mediterranean surface ( 2.5×10 12 m 2 ):

F = N T BY • 10 6 365 • 2.5 • 10 12 g d m 2 = 1.10 • 10 -9 N T BY g d m 2
(2)

The predicted concentration of the falling particles in the water column C P (expressed as g/m 3 ) depends on their vertical sinking velocity SS. We stress that the flux of particles sinking from the sea surface is a release of individual particles (the LDP debris) at discrete intervals (Fig. 1), similar to a rain effect.

Thus, the concentration C P was considered as the ratio between F (Expr. 2)

and SS (expressed in m/d, Fig. 1):

C P = F SS = N T BY SS 1.10 • 10 -9 g m 3 (3)
Expr.

(3) implies that the more slowly LDP debris sinks, the greater the resulting water column plastic concentration is, and vice versa (Fig. 1, panels B.1 and B.2). If N T BY increases (and we assume the same sinking speed), so does the water column plastic concentration. Here, C P was derived considering the same sinking speed and mass for all the particles. We also derived an expression for the predicted concentration by considering individual sinking speed and mass, and showed that these did not affect C P , nor the conclusions of our paper (Supporting Information S.1).

By inverting Expr. (3), we could obtain an expression for the sinking speed of the LDP debris, SS:

SS = N T BY C P 1.10 • 10 -9 , (4)
from which it was possible to obtain a maximum estimate of the settling speed SS M AX in the Mediterranean Sea. To do so, we considered the estimate of

N T
SS M AX = N T BY C O M IN 1.10 • 10 -9 , (5)
By substituting these values in Expr. ( 5

Model initialisation and simulated scenarios

The simulated particles were considered representative of LDP debris of all sizes, with the exception of extremely light foamed plastics (such as polystyrene foam)

or air filled objects which tend to stay suspended at the air-sea interface. The latter represent less than 1% of plastic debris collected in the Mediterranean Sea [START_REF] Luiza Pedrotti | An integrative assessment of the plastic debris load in the mediterranean sea[END_REF]. In general, 95% of LDP debris collected in the Mediterranean Sea are less than 5 mm in size [START_REF] Luiza Pedrotti | An integrative assessment of the plastic debris load in the mediterranean sea[END_REF]. LDP debris were considered to sink, assuming that biofouling, weathering or other processes decrease the buoyancy of these particles. Virtual LDP particles were released at the surface at daily intervals between January 1, and December 31, 2010. This time interval is consistent with the residence time of plastic debris at the Mediterranean surface [START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF][START_REF] Liubartseva | Tracking plastics in the Mediterranean: 2D Lagrangian model[END_REF].

To initialise the particle starting positions, we used the results of Baudena et al., [START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF], which simulated the path of LDP debris from their release at sea (by coastal cities, river mouths, and vessels) to the moment they started sinking.

In that work, the authors assumed that the probability of a simulated LDP particle leaving the sea surface (due to e.g. biofouling, etc.) increases with the time spent in water. This probability peaked in correspondence with the biofouling time (the period of time necessary to induce sinking, see Supplementary Fig. 2 particles were advected for 1000 days. At the end of the simulation, 90% of particles reached 1000 m depth or were deposited. The 10 % left were at an average depth of 900±100 m, thus very close to reaching 1000 m depth. Thus, we use their final position to calculate the seafloor concentration (Subsec. 2.4).

The particles were considered as non-inertial passive tracers with a constant sinking velocity, which were transported by currents and by isotropic horizontal and vertical diffusion (diffusivity coefficient K h and K v , respectively).

We used K h =10 m 2 /s and K v =5•10 -5 m 2 /s, in line with the values used in previous plastic studies [START_REF] Liubartseva | Tracking plastics in the Mediterranean: 2D Lagrangian model[END_REF][START_REF] Jalón-Rojas | A 3D numerical model to Track Marine Plastic Debris (TrackMPD): Sensitivity of microplastic trajectories and fates to particle dynamical properties and physical processes[END_REF][START_REF] Mikael | Closing the Mediterranean marine floating plastic mass budget: Inverse modeling of sources and sinks[END_REF][START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF]. In order to test the sensitivity of the results to the choice of the diffusivity coefficients, different K h and K v values were used (Scenarios 5-8, Table 2). In order to evaluate the role of the vertical component of the current field w on the simulated LDP concentration, w was set to zero in scenario 9 (Table 2). Scenarios 5-9 were run with the same sinking speed of Scenario 1, namely 7.8 m/d. In order to evaluate the sensitivity of the results with respect to a potentially larger SS M AX (which could be due to a larger flux of LDP leaving the surface, Subsec. 2.2.3), in Scenario 10 we used a sinking speed of 15.6 m/d. Finally, in Scenario 11 we evaluated the sensitivity of the results with respect to the release conditions: to do so, the surface sinking rate of Baudena et al. [START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF] was varied at each location of ±10% randomly. This new sinking rate was used to initialise the particle release locations of that scenario.

Model output analyses

One of the limitations in simulating particle trajectories from the surface to the seafloor in a deep basin such as the Mediterranean Sea is the elevated computational cost. To overcome this issue, we calculated the concentration of the simulated particles on a virtual layer at 1000 m depth. In the regions with a seafloor shallower than 1000 m, we kept the original depth (provided by the velocity field domain [START_REF] Arsouze | Sensibility analysis of the Western Mediterranean Transition inferred by four companion simulations[END_REF]). 1000 m was chosen as the reference depth because it is usually considered as the upper boundary of the deep sea. Thus, LDP reaching this layer are therefore considered as sequestered in the deep sea. Furthermore, this assumption allowed us to simulate sinking speeds down to 1.0 m/d, which

would not have been possible for further depths due to computational costs.

The concentration on a deeper virtual seafloor, at 2000 m depth, was calculated for scenarios 1-3 only, and is reported in Supporting Information S.2.

Further, we calculated the concentration of particles deposited less than 20 km from the coast (hereafter the coastal strip). We chose this distance because it is associated with the inner average continental shelf, exploited by industrial and recreational fishery and essential for tourism activity [START_REF] Drius | Tackling challenges for Mediterranean sustainable coastal tourism: An ecosystem service perspective[END_REF][START_REF] Morales-Nin | Managing coastal zone fisheries: A Mediterranean case study[END_REF]. This concentration was calculated for each Mediterranean country. For each deposited particle we identified if it was released by a land (coastal city or river mouth) or a sea (vessel discard) source. To this aim, we tracked each particle backward in time from the seafloor to the surface (using our trajectories) and from the surface to its release source (using the trajectories calculated by Baudena et al.,[START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF]. If the original release source was land based, we determined the corresponding source country as well. The plastic sources considered were those used in Baudena et al., [START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF], coastal cities (62), river mouths [START_REF] Laurent | River plastic emissions to the world's oceans[END_REF], and vessel discards [START_REF] Wu | Mapping global shipping density from AIS Data[END_REF].

We analysed the connectivity between Mediterranean surface and seafloor by considering the starting and final position of each particle and by calculating a connectivity matrix (65) at two different resolutions. Further details are reported in Supporting Information S.3.

To understand the pathways of the LDP particles reaching a zone of high LDP concentration, located north-east of the Balearic archipelago (Fig. 3A), we calculated their crossroadness [START_REF] Baudena | Crossroads of the mesoscale circulation[END_REF][START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF]. This metric provides, for a given point, the percent of the trajectories that passed in its neighborhood (defined as a circle of radius 0.1 • ). Further details are reported in Supporting Information S.4.

Density of sinking LDP debris from a drag model

In Subsec.

SS DM = 4gd p ∆ρ 3C d ρ SW , ( 6
)
where g is the gravity acceleration (9.81 m/s 2 ), d p is the particle size, ∆ρ is the difference between the particle density and that of seawater, ρ SW . C d is the particle drag coefficient, which the authors expressed as follows:

C d = 24
Re p = ρ SW SS DM d p µ f ,
with µ f being the water dynamic viscosity. The range of validity of Eq. ( 6) is 0.03< Re p <10 4 , which was respected with the parameters used. Ψ is the shape factor, defined as the ratio between the particle sphericity Φ and cir- calculate 75,030 SS values, which were then averaged together. We found that SS DM matched SS M AX for ∆ρ 0.025 kg/m 3 (Fig. 2). The ∆ρ obtained did not change considerably when the predicted water column plastic concentration C P was calculated considering also the individual mass of each of the 75,030 LDP debris (Supporting Information S.1). We also performed a sensitivity test to analyse the robustness of the mean SS DM while varying the three other parameters d p , ρ SW , and µ f . These calculations indicated that they did not affect the mean SS DM value (Supporting Information S.5) significantly.

Overall, above considerations show that only a minor excess density of 0.025 kg/m 3 compared to seawater is required to reach a maximum sinking speed of 7.8 m/d. Smaller ∆ρ are related to lower sinking speeds.

3 Results

Concentration of deposited LDP debris and distance travelled during its sinking

The spatial distribution of particles deposited on the 1000 m depth virtual layer (Fig. 3B, C, D, andE;) was consistently different from the distribution of particles leaving the surface (Fig. 3A) for all the sinking speeds considered.

When reducing the sinking speed, the difference increased (Fig. 3B to Fig. 3E).

This result was particularly visible in the western Mediterranean: while large amounts of virtual particles were predicted to leave the surface north of the Balearic archipelago, the concentration at 1000 m depth in this same region was relatively low for all the scenarios considered. Conversely, the 1000 m concentration was greater north-east of the Balearic archipelago, in a region where the surface sinking rate was lower (cyan rectangle in Fig. 3A). This region, covering 1.63% of the Mediterranean surface, contained 1.36% of the virtual LDP particles leaving the Mediterranean surface. Notably, at 1000 m depth, it accumulated the 3.07 %, 4.68%, 6.66%, and 7.36% of the virtual LDP particles for scenarios 1-4, respectively. The LDP particles deposited there were mostly from the south and the east of this region, as supported by supplementary analyses (Supporting Information S.4)

The connectivity analysis between the locations where particles left the surface and where they reached the seafloor indicated that between 90-95% of the particles (scenarios 1-4) deposited at a certain location (defined by a ∼111 km size square) started to sink in other regions (Supporting Information S.3). In the Southern Adriatic Sea, where a hotspot of enhanced LDP accumulation was identified, between 32-50% of the particles were from adjacent regions. Other LDP accumulation regions were detected across the basin, such as in the Tyrrhenian and Ionian Seas, in the Strait of Sicily, or in the Eastern Mediterranean.

The spatial variability between the concentration of virtual LDP particles leaving the surface and reaching the 1000 m virtual seafloor was confirmed also by the cumulative pdf of the lateral transport distance (Fig. 3F). This was defined as the distance between the locations at which particles left the surface and those where they reached 1000 m depth. The mean lateral transport distance for scenario 1 was 119±99 km; for scenario 2: 172±136 km; for scenario 3: 232±177 km; and for scenario 4: 282±218 km. The percentage of virtual LDP particles with a lateral transport distance larger than 100 km was 30%

for scenario 1, increasing to more than 60% for scenario 4. This conclusion was robust to changes in the horizontal and vertical diffusivity, to the exclusion of the vertical component of the velocity field, to the increase of the sinking speed of the LDP particles up to the double of SS M AX , and to changes of the surface sinking rate used to initialise the particle starting locations (Supporting Information S.6).

In situ observations of seafloor plastic concentration in the Mediterranean are sparse in space and time and differ in methodology. In addition, these collected all types of plastic, while here we focus on LDP only. Hence, a quantitative comparison with our model results is currently not possible. Despite these constraints, our model predictions qualitatively agree with in situ measurements (databases and their references in Supporting Information S.7). Largest seafloor concentrations are reported in the Central Adriatic Sea, close to the Turkiye shore, and in the Balearic archipelago, where our model predicts the largest LDP concentrations. Conversely, the lowest concentrations were measured on the Eastern Sardinia shelf, in the Northern Tyrrhenian Sea, and close to Alicante (Spain), in agreement with our model predictions (further details in Supporting Information S.7).

LDP concentration on the coastal strip of Mediterranean countries

The concentration of particles deposited on the coastal strip (i.e. in this study within 20 km from the coast, Subsec. 2.4) ranged between 5.5-8.9 kg/km 2 (scenarios 1-4), which was between 11-69% larger than the concentration of particles sinking from the sea surface above (i.e., less than 20 km from the coast; 5.2 kg/km 2 ). The bottom coastal strips of Algeria and Turkiye showed the largest particle concentrations (15.6 and 13.9 kg/km 2 , respectively, obtained from an ensemble average of scenarios 1-4; Fig. 4).

We tracked the particles deposited on the bottom coastal strip backward in time (based on Baudena et al., [START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF], Methods), and we found that ∼60% were from vessel discards, while ∼40% were released from land sources. On average, ∼20%

of the particles deposited on the coastal strip of a given country were from the land sources of the same country, while ∼20% were from other countries, with some variability. For example, 53% of particles deposited on the coastal strip of Cyprus were from neighbouring countries. The corresponding values for Croatia and Syria were 47 and 46%, respectively. Conversely, 73% of particles deposited on the coastal strip of Turkiye were from Turkish coastal sources. Finally, 83% of the particles deposited on the coastal strip of Egypt were from vessel discards. This proportion was similar for particles deposited on the coastal strip of Malta and Libya (84 and 83%, respectively). Results obtained for scenarios 1-4 separately (Supporting Information S.8) were consistent with this pattern. The study of the pathways of sinking LDP debris has highlighted that the locations where LDP debris left the surface did not coincide with the locations where it was found at depth, as assumed by recent studies [START_REF] Liubartseva | Tracking plastics in the Mediterranean: 2D Lagrangian model[END_REF][START_REF] Kane | Seafloor microplastic hotspots controlled by deep-sea circulation[END_REF]. This stressed the importance of a three dimensional approach to study plastic dispersion [START_REF] Jalón-Rojas | Technical note: On the importance of a three-dimensional approach for modelling the transport of neustic microplastics[END_REF].

When neglecting the vertical component of the currents, the accumulation of virtual LDP particles in specific regions slightly decreased, e. Even if further information is needed to quantitatively validate our model outputs, our results were in general agreement with in situ observations of seafloor plastic concentration (Supporting Information S.7), corroborating our findings.

In addition, our results were robust with respect to horizontal and vertical diffusivity changes, removal of the vertical velocity current component, variation of the LDP debris sinking speed, and changes of starting sinking locations (Supporting Information S.6).

Bottom coastal LDP pollution.

The estimated LDP concentration on the bottom coastal strip increased for decreasing sinking speeds (from 5.6 kg/km 2 for 7.8 m/d sinking speed to 8.9 kg/km 2 for 1 m/d). This concentration was 11-69% higher than the concentration of LDP particles leaving the sea surface in the same region (5.2 kg/km 2 ).

This indicated that currents at depth tend to propel debris towards coastal regions. This agrees with the pattern of surface currents, which are expected to retain LDP debris in the majority of Mediterranean coastal regions [START_REF] Liubartseva | Tracking plastics in the Mediterranean: 2D Lagrangian model[END_REF][START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF].

Notably, ∼ 20% of the particles deposited in the coastal region of a given country were from neighbouring countries, while∼ 60% were from maritime sources.

The high percentage of deposited LDP debris originating from maritime sources (60%) is due to the fact that these particles spend more time at the surface than particles released from land sources, which tend to strand quickly and are therefore less biofouled. In general, while previous studies suggested that each country is the primary responsible for the plastic pollution of its own beaches [START_REF] Liubartseva | Tracking plastics in the Mediterranean: 2D Lagrangian model[END_REF][START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF], LDP debris on the bottom coastal strip seems to be from multiple Mediterranean countries and especially from shipping lanes. For instance, Egypt has been reported to have large rates of beaching plastic debris, mostly released from its own land sources [START_REF] Liubartseva | Tracking plastics in the Mediterranean: 2D Lagrangian model[END_REF][START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF]: however, we suggest that its coastal strip pollution is mainly due to LDP particles released at sea or from other countries.

Overall, LDP pollution emerges as a shared problem in the Mediterranean basin, as particles polluting the bottom coastal strip were mostly released at sea or from distant countries. [START_REF] Tsiaras | Modeling the pathways and accumulation patterns of micro-and macro-plastics in the Mediterranean[END_REF]. Other biological activities can occur below the euphotic zone, such as the biofilm formation via heterotrophic organisms that do not necessarily require light to grow [START_REF] Fischer | Modeling submerged biofouled microplastics and their vertical trajectories[END_REF]. Aggregation in marine snow and consumption by zooplankton may cause plastic debris to sink, whereas remineralization at depth would remove organic mass from plastic debris, making it rise again [START_REF] Kvale | A critical examination of the role of marine snow and zooplankton fecal pellets in removing ocean surface microplastic[END_REF][START_REF] Kvale | The global biological microplastic particle sink[END_REF]. Zooplankton faecal pellets usually do not reach the seafloor due to coprophagy (see a review in 77), potentially releasing buoyant plastic debris. In addition, faecal pellets containing plastic debris are more subject to fragmentation [START_REF] Cole | Microplastics alter the properties and sinking rates of zooplankton faecal pellets[END_REF], potentially enhancing resuspension. Chemical processes can affect the buoyancy of LDP debris as well, especially in regions where biological activities are limited, such as in the NPGP. For example, weathering of debris causes hydrogen abstraction with oxygen substitution penetrating deeper into the polymeric matrix, altering its absolute density [START_REF] Jahnke | Reducing uncertainty and confronting ignorance about the possible impacts of weathering plastic in the marine environment[END_REF]. Crystallinity also increases over time during degradative attack of the amorphous regions leading to an increase in density [START_REF] Jenkins | The effect of crystalline morphology on the degradation of polycaprolactone in a solution of phosphate buffer and lipase[END_REF].

However, these processes, potentially responsible for the sinking of LDP debris, have been observed only in laboratory studies or, in situ, uniquely at the sea surface [START_REF] Francesca | Biofouling on buoyant marine plastics: An experimental study into the effect of size on surface longevity[END_REF][START_REF] Kaiser | Effects of biofouling on the sinking behavior of microplastics[END_REF][START_REF] Gerritse | Fragmentation of plastic objects in a laboratory seawater microcosm[END_REF][START_REF] Karkanorachaki | Sinking characteristics of microplastics in the marine environment[END_REF], with the exception of the recent observation of LDP in marine snow [START_REF] Galgani | Hitchhiking into the Deep: How Microplastic Particles are Exported through the Biological Carbon Pump in the North Atlantic Ocean[END_REF]. The presence of LDP at depth is hence poorly understood.

To investigate this question, we used a drag model and the largest collection of Mediterranean LDP debris to date. We calculated the difference of density be- This conclusion is corroborated by the fact that currents, in the Mediterranean Sea, seems unable to transport LDP debris at great depths. Indeed, Soto-Navarro et al., [START_REF] Soto-Navarro | 3d hotspots of marine litter in the mediterranean: A modeling study[END_REF] have shown that vertical currents redistribute plastic debris mainly in the first 100 meters of the water column. Onink et al., [START_REF] Onink | Influence of Particle Size and Fragmentation on Large-Scale Microplastic Transport in the Mediterranean Sea[END_REF] predicted a transport to greater depths primarily due to internal tides, but only for a small proportion of LDP debris (<1%). Tsiaras et al., [START_REF] Tsiaras | Modeling the pathways and accumulation patterns of micro-and macro-plastics in the Mediterranean[END_REF] studied the water column plastic concentration in some regions of the Mediterranean Sea, and found that model predictions were orders of magnitude lower than observations. In addition, de la Fuente et al., [START_REF] De La Fuente | Sinking microplastics in the water column: simulations in the Mediterranean Sea[END_REF] argued that neither the vertical nor horizontal currents affect the water column debris concentration in the Mediterranean Sea significantly (see in particular their Figure 5). All in all, our results point to the fact that LDP debris may persist in the water column for time windows larger than previously suspected (e.g. [START_REF] Liubartseva | Tracking plastics in the Mediterranean: 2D Lagrangian model[END_REF][START_REF] Kane | Seafloor microplastic hotspots controlled by deep-sea circulation[END_REF] and travels for hundreds of kilometers. This can increase their bioavailability and their potential negative impact for marine biota [START_REF] Kühn | Quantitative overview of marine debris ingested by marine megafauna[END_REF][START_REF] Fabri-Ruiz | Mistaking plastic for zooplankton: Risk assessment of plastic ingestion in the mediterranean sea[END_REF]. This study provides an upper limit for the LDP sinking speed that can be used to constrain future plastic-tracking studies. Further information on concentration of LDP in the water column and on the seafloor, as well as observations of in situ sinking speeds are urgently needed, given the potential damage of plastic debris on pelagic and benthic ecosystems.

Limits and perspectives

The Lagrangian simulations were subject to approximations. We used a constant sinking velocity of LDP particles from the surface to 1000 m depth, while this can vary, due to seawater density variation or biochemical processes. The sinking speed was considered equal for all the particles, while this may not be the case (Subsec. 2.5). We focused on the 1000 m (and 2000 m, Supporting Information S.2) depth layer, while several Mediterranean areas are deeper than 3000 m. Particles were released for one year only, and land based and maritime plastic sources used to calculate the surface sinking rate (our initial condition)

were subject to high uncertainties [START_REF] Weiss | The missing ocean plastic sink: Gone with the rivers[END_REF][START_REF] Liubartseva | Tracking plastics in the Mediterranean: 2D Lagrangian model[END_REF][START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF]. The surface sinking rate needs further refinement, including processes such as fragmentation, seasonality and spatial variability (e.g. 82). The horizontal and vertical diffusivity were considered as homogeneous through the basin and constant in time, while they can have both spatial and temporal variability. These choices were due to the fact that information about concrete ways of parameterising these dynamics (e.g.

the change in time of the sinking speed) were not available or not validated by observations to date.

Therefore, while the concentration of LDPs on the seafloor is affected by high uncertainties, our results represent a first step forward in the modelisation of sinking LDP debris, as evidenced also by the agreement with in situ seafloor observations. The hotspots of plastic debris accumulation on the seafloor as well as its transport pathways may be used to design optimal sampling or removal strategies (e.g. 31). These could be focused both at large or regional scales, and may benefit from future improvements of TrackMPD simulated processes.

The previous considerations advocate for further research efforts, as additional information is essential to deepen the knowledge on the biological processes affecting the vertical path of plastic debris (e.g. refs. [START_REF] Lobelle | Global modeled sinking characteristics of biofouled microplastic[END_REF][START_REF] Fischer | Modeling submerged biofouled microplastics and their vertical trajectories[END_REF][START_REF] Tsiaras | Modeling the pathways and accumulation patterns of micro-and macro-plastics in the Mediterranean[END_REF][START_REF] Kvale | The global biological microplastic particle sink[END_REF]), and to implement the characterisation of the hydrodynamical field transporting it (for instance, by increasing its spatio-temporal resolution). Also, resuspension from the seafloor or funnelling effects (for instance due to canyons) should be investigated [START_REF] Kane | Seafloor microplastic hotspots controlled by deep-sea circulation[END_REF][START_REF] Pierdomenico | Massive benthic litter funnelled to deep sea by flash-flood generated hyperpycnal flows[END_REF][START_REF] Ballent | Modelled transport of benthic marine microplastic pollution in the Nazaré Canyon[END_REF]. This information is needed to improve plastic-tracking models and, more generally, to mitigate plastic pollution.

Supporting Information

Use of individual sinking velocities and particle mass; LDP seafloor concentra-

Figure 1 :

 1 Figure 1: Illustrative scheme of the paradigm used to calculate the sinking speed of LDP debris. The predicted water column LDP concentration C P decreases when LDP sinking speed increases (panels B.1 and B.2). In order to have C P equal or greater to a given value observed C O (panel A), the LDP sinking speed must not be larger than a given value. In this case panel B.1 represents the maximum possible sinking speed of LDP debris. Panel B.2 shows that, if a larger sinking speed is considered, then C P is lower than C O .

  size of net used in the reference. b: mesh size of filter or sieve used in filtering process. c: only size range of MPs was presented in the literature. d: N/A represented no available information.

cularity χ .

 . The vertical sinking velocity SS DM depends therefore on the six parameters, d p , ∆ρ, ρ SW , µ f , Φ, and χ. We considered a seawater density ρ SW =1027 kg/m 3 and a viscosity µ f =0.00109 Pa•s; the latter is representative of a seawater temperature of 20 • (https://www.engineeringtoolbox.com/seawater-properties-d 840.html), which is the mean Mediterranean surface temperature. As d p , Φ, and χ we used the d p , Φ, and χ of each of the 75,030 debris collected during the Tara expedition (Subsec.

2 . 5 )

 25 . Therefore, ∆ρ represents the only unknown parameter in Expr. 6. Different ∆ρ values were tested in Expr. (6), ranging from 0.001 to 0.1 kg/m 3 . The Matlab function provided in Dioguardi et al., (67) was used to

Figure 2 :

 2 Figure 2: Mean theoretical sinking speed SS DM of 75,030 LDP debris (y-axis, subsec. 2.5) as a function of the difference between the density of the biofouled LDP debris and the seawater ∆ρ (x-axis). SS DM are reported as mean values (red dots) with standard deviation (errorbar). The blue horizontal line identifies the SS M AX value calculated in Subsec. 2.2.3 (7.8 m/d).

Figure 3 :

 3 Figure 3: (A): amount of virtual LDP particles that left the Mediterranean surface in 2010 (the surface sinking rate integrated between January 1, and December 31, 2010; kg/km 2 ; adapted with permission from Baudena et al., (31), Copyright 2022 Nature). (B-E): concentration of virtual LDP particles released in 2010 deposited on a virtual seafloor at 1000 m depth, for scenario 1, 2, 3, and 4, respectively. The virtual 1000 m seafloor was built by considering all the seafloor locations deeper than 1000 m as 1000 m deep. The blue lines in panel A-E indicate the 1000 m isobath. (F): cumulative pdf of the lateral transport distance (the distance between the location in which the particle left the surface and the location in which it reached the virtual 1000 m seafloor) of the 7,652,197 virtual particles released in 2010, for scenario 1 (blue line), 2 (red line), 3 (cyan line), and 4 (green line). The cyan rectangle in panel (A) shows the region considered for the statistical analyses.

Figure 4 : 4 Discussion 4 . 1

 4441 Figure4: Concentration of particles released in 2010 which deposited on the coastal strip (defined as the region less than 20 km from the coast) of the different Mediterranean countries, obtained from the ensemble average of scenarios 1-4. For each country, the red rectangle represents the amount of particles deposited on its coastal strip which were released from its own land sources, the yellow rectangle represents those released from other countries, and the blue rectangle those directly released at sea.

  g. for the area north-east of the Balearic archipelago (last panel in Fig. S.6). When considering a virtual seafloor down to 2000 m (Supporting Information S.2), the accumulation slightly decreased as well. This indicated an important role played by vertical current shear and by horizontal stirring on the accumulation of LDP particles, in coherence with recent studies[START_REF] Fischer | Modeling submerged biofouled microplastics and their vertical trajectories[END_REF][START_REF] Soto-Navarro | 3d hotspots of marine litter in the mediterranean: A modeling study[END_REF]. For instance, we observed a region of LDP particle accumulation at 1000 m depth in the Adriatic Sea. This matched remarkably well with a recently discovered persistent bottleneck structure in the circulation of this sea[START_REF] Ser-Giacomi | Lagrangian betweenness as a measure of bottlenecks in dynamical systems with oceanographic examples[END_REF], which may be responsible for this LDP accumulation. In a specific region north-east of the Balearic archipelago, the number of LDP debris deposited increased for slower sinking speeds. Crossroadness analyses indicated a possible mechanism of particle accumulation at depth (Supporting Information S.4): particles are transported toward this area due to the regional converging circulation. At the same time, particles sinking more slowly spend more time suspended in the water column, traveling larger distances. Hence, the probability they end up in that region increases. Our simulations also pointed to the fact that a large fraction of LDP particles could potentially reach the deep sea: 48-63 % of the virtual LDP particles leaving the surface were transported to 1000 m depth, while 38-46 % reached 2000 m in Scenarios 1-3.

  Fischer et al.,[START_REF] Fischer | Modeling submerged biofouled microplastics and their vertical trajectories[END_REF] suggested a larger impact of vertical transport, but only when associated with an intense biological activity.

  BY for the Mediterranean Sea (11,500 tons/year, Subsec. 2.2.2) and imposed C

P =C O M IN (1.60 µg/m 3 , Egger et al., (14), Subsec. 2.2.1):

Table 2 )

 2 in Baudena et al.,[START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF]. In this way, the authors calculated the Mediterranean surface sinking rate (the amount of LDP debris that disappears from the surface each day in a square kilometer of sea surface). To strengthen that metric Baudena et al.,[START_REF] Baudena | The streaming of plastic in the Mediterranean Sea[END_REF] considered different biofouling times (between 50-200 days, based on literature values) and obtained similar estimates when considering 16 different parameterisations and an ensemble average. Hence, in our study, particles were released proportionally to the Mediterranean surface sinking rate, i.e. the larger the surface sinking rate in a region, the larger the number of particles released there. The choice of the dataset of Baudena et al.(31) is further motivated by the fact that it was the first Lagrangian model quantitatively validated in the Mediterranean Sea. . The choice of the maximum value used for the sinking speed (SS M AX =7.8 m/d) is motivated in Subsec. 2.2. All virtual plastic particles of a given scenario were advected for a time period (provided in Table 2) long enough to reach at least 1000 m depth. For scenario 4 (sinking speed of 1 m/d),

	7,652,197 virtual particles were released in total, using four sinking speed values
	(7.8 m/d, Scenario 1; 4 m/d, Scenario 2; 2 m/d, Scenario 3; 1 m/d, Scenario
	4;

Table 2 :

 2 Parameters used for each of the ten simulated scenarios.

	Nº Scenario	Current velocity field	Vertical component of currents included (yes/no)	Sinking speed particles (m/d)	Release period	Advective (days) period	Kh (m 2 /s) Kv (m 2 /s)	Notes
	S1	NemoMed36	yes	7,8		450
	S2	NemoMed36	yes	4,0		550
							10	5•10 -5
	S3	NemoMed36	yes	2,0		1050
	S4	NemoMed36	yes	1,0		1050
	S5	NemoMed36	yes	7,8		450	5
								5•10 -5
	S6	NemoMed36	yes	7,8	1 Jan-31	450	15
	S7	NemoMed36	yes	7,8	Dec 2010	450		1•10 -5
							10
	S8	NemoMed36	yes	7,8		450		10•10 -5
	S9	NemoMed36	no	7,8		450	10	5•10 -5
	S10	NemoMed36	yes	15,6		225	10	5•10 -5
									Surface sinking
	S11	NemoMed36	yes	7,8		450	10	5•10 -5	rate varied of
									±10%
					1

  2.2.3, we estimated a maximum sinking speed SS M AX of LDP debris equal to 7.8 m/d. Here we calculate the difference of LDP and seawater densities necessary to obtain such value. To this aim we use (i) the largest LDP debris dataset collected in the Mediterranean Sea to date and (ii) the drag model of Dioguardi et al., (67).

	Mediterranean Sea LDP debris database
	We exploited the largest LDP field dataset in the Mediterranean Sea to date,
	collected during the Tara Expedition (122 stations, ref. 28,
	https://zenodo.org/record/5538238). This dataset provided the ferret (consid-
	ered representative of the particle size d p ), sphericity Φ, and circularity χ of
	each LDP debris collected at the sea surface (75,030 items in total). We used
	these debris physical properties to estimate the velocity at which they are ex-
	pected to sink once biofouled.

Drag model to calculate the sinking velocity

Van Melkebeke et al.,

[START_REF] Van Melkebeke | Characteristics and sinking behavior of typical microplastics including the potential effect of biofouling: Implications for remediation[END_REF]

evaluated eleven drag models estimating the vertical sinking velocities of plastic particles with different characteristics, such as size, shape, and density. The best performing drag model was the one reported in (67, average error of 13.20%), which calculated the vertical sinking speed SS DM as follows:

  tion at 2000 m; surface-seafloor connectivity; crossroadness analyses; sensitivity test of SS DM ; sensitivity test of LDP seafloor concentration; in situ observations of plastic seafloor concentration; sensitivity test of coastal strip LDP concentration.

Acknowledgements

We thank the commitment of the following institutions: CNRS, Sorbonne University, LOV. The Tara Ocean Foundation and its founders and sponsors: agnès b. R , Etienne Bourgois, the Veolia Environment Foundation, Lorient Agglomeration, Serge Ferrari, the Foundation Prince Albert II of Monaco, IDEC, the "Tara" schooner, crews and teams. We thank MERCATOR-CORIOLIS and ACRI-ST for providing daily satellite data during the expedition. We are also grateful to the French Ministry of Foreign Affairs for supporting the expedition and to the countries that graciously granted sampling permission. The authors are grateful to Enrico Ser-Giacomi for his helpful advice on the design of the research. We also thank Nicolas Benoit for continuous assistance on the Mesu computational server, and Thomas Arsouze for the assistance on the hydrodynamical product used. The authors thank Inés Jambou for her help with the graphical abstract (Table of Contents graphic). This study is part of the "PlastiMed BeMed : Closing the plastic tap" project conducted by the International Union for Conservation of Nature (IUCN) with the financial support of the Prince Albert II of Monaco Foundation and EU H2020 LABPLAS project under the grant agreement (ID: 101003954), DOI: 10.3030/101003954. R.K. furthermore acknowledges support via a Make Our Planet Great Again grant from the French National Research Agency (ANR) within the Programme d'Investissements d'Avenir (reference ANR-19-MPGA-0012).

Data availability

All the data necessary to produce all the figures of the main text, including the LDP seafloor concentration, the coastal strip pollution, and the SS DM vs ∆ρ relationship, are publicly available at https://doi.org/10.5281/zenodo.7350455.

The surface sinking rate used to initialise the particle release is available at https://doi.org/10.5281/zenodo.5931213. The in situ plastic concentrations are


Renaud Ansart
email: ansart@imft.fr

Herv É Neau

Philippe Accart

Alain De Ryck

Olivier Simonin
email: simonin@imft.fr

ELUTRIATION FROM FLUIDIZED BEDS: COMPARISON BETWEEN EXPERIMENTAL MEASUREMENTS AND 3D SIMULATION RESULTS

This paper presents comparisons between experimental measurements and unsteady threedimensional numerical simulations performed by an unstructured parallelized CFD multiphase flow code of elutriation and transport of mono-dispersed glass beads type B and A/B in a fluidized bed. These comparisons show a satisfactory agreement between experimental measurements and numerical predictions. The numerical results also show a strong dependence on the mesh size, especially for fine particles. A model accounting for influences of mesoscales structures on overall bed hydrodynamics, which are not resolved by coarse mesh simulations, is applied. Results obtained with the model show improvements for the dense fluidized bed and even for a transport step.

INTRODUCTION

Gas-solid fluidized beds are used in a wide range of industrial applications such as coal combustion, catalytic polymerization and uranium fluoridation. Many of the fluidized bed industrial processes involve poly-dispersed powder and even multi-species of powders. In bubbling fluidized bed combustion and catalytic cracking, elutriation is a major cause of inefficiency, while it could be highly desirable in specific case. Whether the intention is to minimize or to promote elutriation, the involved phenomena must be properly known if the process has to be efficiently controlled.

Numerical simulation is becoming an efficient approach to study the separation and entrainment processes observed in an industrial fluidized bed. In the literature, there is a lack of experimental data to validate CFD simulations of these phenomena. Thus, a joint experimental and numerical project between RAPSODEE Centre and IMFT was initiated. The object of this paper is to present comparisons between threedimensional numerical simulation predictions and experimental data of particle gas pressure drop and entrainment in a fluidized bed.

EXPERIMENTAL SET UP

The column in the laboratory experimental set up was 10 cm in diameter and 59 cm high (Fig. 1) and was fitted with a conical outlet. The column material was stainless steel to avoid electrostatic charge (Ansart et al. ( 1)). The bronze distributor had a pressure drop of 6 kPa at a superficial gas velocity of 0.18 m • s -1 . Fluidizing air was supplied by a Brooks smart mass flow meter and controllers 5853S with an accuracy of ±0.7 % of the rate and ±0.2 % of full scale (2.32 m • s -1 ).

The process was divided into two parts: the first allowed the fluidization of particles by a homogeneous superficial gas velocity (V f 1 < V t ), in order to obtain a bubbling fluidized bed regime. According to a linear ramp-up of 5 s during the second part, the fluidization velocity was increased to entrain the particles (V f 2 > V t ). The particles entrained were collected through a vessel at the outlet of a cyclone. The mass of particles collected was continuously weighed during the process with a resolution time of 1 s and an accuracy of 0.01 g. Pressure variations along the pipe were monitored by severals sensors located every 1.5 cm. Honeywell DC pressure instrumentation was used with an accuracy of ±0.25 % of full scale. The resolution time was 0.1 s.

The measurement of gas pressure on the wall was made through an 8 mm diameter opening with a filter.

The powder was glass beads with properties described in Table 1. For 2.5 kg of solid mass, the bed at rest in the column is approximatively 21 cm. Two particle sizes called fine (Geldart type A/B) and coarse (Geldart type B) were used. The mean diameters of powder were determined using a Mastersizer 2000 with 1.5 bar of dispersion. The bulk material was sieved to ensure an almost mono-dispersed distribution. The terminal settling velocity V t of the particle was calculated by the expression of the drag coefficient, Equation [START_REF] Parmentier | A numerical study of fluidization behavior of Geldart B, A/B and A particles using an eulerian multifluid modeling approach[END_REF]. According to Re mf , an estimation of minimum fluidization velocity U mf was computed using the expression recommended by Wen and Yu:

Re mf = (33.7 2 + 0.0408 ρ g (ρ p -ρ g )d 3 p g µ 2 g ) 0.5 -33.7 U mf = Re mf µ g ρ p d p . (1)

MATHEMATICAL MODEL

Simulations were carried out using an Eulerian n-fluid modeling approach for polydispersed fluid-particle flows implemented in the NEPTUNE CFD software which was developed and implemented by IMFT (Institut de M écanique des Fluides de Toulouse). This software is a multiphase flow code developed in the framework of the NEP-TUNE project, financially supported by CEA (Commissariat à l' Énergie Atomique), EDF ( Électricit é de France), IRSN (Institut de Radioprotection et de S ûret é Nuc éaire) and AREVA.

In the proposed modeling approach, the mean transport equations (mass, momentum and fluctuant kinetic energy) are solved for each phase and coupled through interphase transfer terms. These equations are derived by phase ensemble averaging weighted by the gas density for the continuous phase and by using kinetic theory of granular flows supplemented by fluid and turbulence effects for the dispersed phase (Balzer et al. ( 2), Gobin et al. ( 3)). In the following development, subscript k = g, refers to the gas phase and k = p refers to the particle phase. The mass balance equation is:

∂ ∂t α k ρ k + ∂ ∂x i α k ρ k U k,i = 0, (2)
where α k is the k th phase volume fraction, ρ k the density and U k,i the i th component of the velocity. In equation ( 2), the right-hand-side is equal to zero without mass transfer. The mean momentum transport equation for the phase k is written:

α k ρ k ∂U k,i ∂t + U k,j ∂U k,i ∂x j = -α k ∂P g ∂x i + α k ρ k g i + I k,i + ∂ ∂x j -α k ρ k u k,i u k,j + Θ p,ij , (3)
where u k,i is the fluctuating part of the instantaneous velocity of phase k, P g is the mean gas pressure, g i the i th component of the gravity acceleration and I k,i the mean gas particle interphase momentum transfer without the mean gas pressure contribution. Finally, Θ k,ij is for k = g the molecular viscous tensor and for k = p the collisional particle stress tensor. Due to the large particle to gas density ratio, only the drag force was assumed to be acting on the particles. Hence, the mean gas-particle interphase momentum transfer can be written:

I p,i = -I g,i = -α p ρ p V r,i τ F gp with 1 τ F gp = 3 4 ρ g ρ p |v r | d p C d,WY . (4)
with C d,WY given by Wen & Yu's correlation:

C d,W Y = 24 Rep 1 + 0.15Re 0.687 p α -1.7 g Re p < 1000 Re p = α g ρg |vr| dp µg 0.44 α -1.7 g Re p ≥ 1000 (5)
The mean relative velocity V r,i between gas and particle is expressed in terms of the mean gas velocity, mean particle velocity and drift velocity. In equation ( 3), the collisional particle stress tensor is derived in the frame of the kinetic theory of granular media (Boelle et al. ( 4)).

For the gas turbulence, a standard k -ε model extended to the multiphase flows accounting for additional source terms due to the interfacial interactions was used.

For the dispersed phase, a coupled transport equation system is solved on particle fluctuating kinetic energy and fluid-particle fluctuating velocity covariance (q 2 p -q f p ). In this paper, the influence of mesh size on the numerical predictions was studied. The mesh size required to fully resolve all of the fine-scale structures decreased as a function of the mean particle relaxation timescale (Parmentier et al. ( 5)). Because of limited computational resources, a filtered approach can be used to model the drag term accurately (Agrawal ( 6)). In the framework of a filtered approach for gas-solid flows, Parmentier et al. [START_REF] Parmentier | A functional subgrid drift velocity model for filtered drag prediction in dense fluidized bed[END_REF] proposed that the filtered drag can be modeled by:

α p ρ p τ F gp V r,i = α p ρ p τ F gp (δ ij + h(α p )K ij f (∆ * G )) V r,j , (6)
where V r,j = is the resolved relative velocity.

K ij = δ ij K h + δ i3 δ j3 (K v -K h )
, the model coefficient is the same in x and y direction (K h and K v are determined by a dynamic adjustment performed by a second filter).

h(α p ) = - √ u (1 -u) 2 (1 -1.88 u + 5.16 u 2 )
, where u = α p /α m et α m = 0.64 is the maximum compacting. The forms of the h and f functions are derived from a highly-resolved simulation of mono-dispersed gas-solid flow. The function f is modeled as the following equation:

f (∆ * G ) = ∆ * G 2 a 2 + ∆ * G 2 with ∆ * G = ∆ G τ St p √ gL . (7)
where a = 0.084, ∆ * G is a dimensionless mesh size, ∆ G the cube root of the cell volume, L the bed diameter and τ st p stokes relaxation time.

NUMERICAL PARAMETERS

To study the influence of mesh refinement, we used three 3D meshes based on Ogrid technique were used. The reference mesh contained 428 451 hexahedra with approximately ∆ x = ∆ y = ∆ z = 3.7 mm. The mesh was uniformly refined by a factor of 1.5 which consisted of 1 477 060 cells. The coarse mesh was made up of 123 816 cells constructed from the reference mesh by coarsening by a factor of 1.5. The numerical simulations were performed on parallel computers with 8 cores for the coarse mesh, 64 cores for the reference mesh and 128 cores for the fine mesh, because of mesh size and physical time needed (Neau et al. ( 8)).

At the bottom (z = 0), the fluidization grid was an inlet for the gas, with an imposed superficial velocity corresponding to the fluidization velocity v f , and a wall for the particles. At the top of the fluidized bed, a free outlet for both the gas and the particles was defined. The wall-type boundary condition was friction for the gas and a no-slip for the particle. Fede et al. [START_REF] Fede | 3D numerical simulation and pept experimental investigation of pressurized gas-solid fluidized bed hydrodynamic[END_REF] have shown that the gas pressure drop predictions are improved with a no-slip boundary condition for the mean particle velocity and zero-flux condition for the mean particle agitation q p 2 .

RESULTS AND DISCUSSION

First of all, a comparison between the numerical predictions for the coarse particles and the experimental results was obtained. Then, the same comparison was carried Fig. 2: Comparison between experimental data and numerical simulation predictions for coarse particles. In the left plot the data were obtained during the bubbling step f 1 = 2.5 U mf and in the right plot during the entrainment step

V f 2 = 1.03 V t .
out for the results of fine particles. In the experiments, the particle phase was slightly poly-dispersed (span ≈ 0.4). However, the numerical simulations were carried out with a monodisperse particle distribution having a median diameter equal to d 50 .

Coarse particles

Gas pressure drop along the wall during the bubbling phase and the mass of particles collected obtained by numerical predictions, for the coarse and reference mesh sizes, were compared with the experimental measurements. To study the wall gas pressure drop during the bubbling step, the numerical simulations were carried out as follows: at t = 0 the fluidized bed was filled up with a uniform solid mass fraction according to the experimental solid mass. A transitory step takes place for t ∈ [0 s, 20 s] corresponding to the destabilization of the fluidized bed. Then, the statistics were computed for t ∈ [20 s, 60 s] insuring a statistical convergence.

As Fig. 2 shows, the mesh refinement had no effect on the bed expansion or the mass of particles entrained for the coarse particles (type B). The coarse mesh was sufficient to predict bed dynamics, and no further mesh refinement was needed. Moreover, a very good agreement between numerical predictions of the wall gas pressure drop and the experimental data during the bubbling step (V f 1 = 2.5 U mf ), Fig. 2(a), was obtained. Above the bed particles, the gradient of gas pressure was equal is negligible for the numerical results and for the experimental measurements. Inside the bed, both distributions were linear. The numerical results predicted the same bed height as the experimental data.

Fig. 2(b) shows the evolution of the mass of particles collected during the entrainment step (V f 2 = 1.03 V t ). A good agreement between the experimental measurements of the mass flow rate of coarse particles and the numerical results was obtained. Indeed, at the start of the entrainment process the flux of particles was slightly overestimated, and during the following progress of the process the numerical predictions of the flux were very close to the measurements.

Fine particles

For fine particles, the numerical simulations were performed on three mesh sizes. Fig. 3(a) shows the wall distribution of time averaged gas pressure, during the bubbling step (V f 1 = 5 U mf ), for the experimental measurements and for the numerical predictions. As shown, mesh refinement had a strong effect on the numerical results for the fine particles. For the coarse and reference mesh sizes, the bed expansion was overestimated. Only, the fine mesh case was able to predict a similar wall gas pressure as the experimental measurements, and to correctly estimate the bed height. The structures of the gas-particle fluidized bed were not able to be resolved by the coarse and reference mesh simulations and they had a drastic influence on the macroscopic flow. To account for the effect of unresolved structures on the macroscopic behavior in the coarse and reference mesh sizes, the sub-grid model described before was used to model the effective drag term.

The Fig. 3(b) shows that the wall gas pressure drop predictions are greatly improved by using the sub-grid model. With the sub-grid model, the bed height was almost independent of the mesh size. A satisfactory agreement was obtained between the numerical predictions (fine grid and large grid with sub-grid model) and experimental measurements of the bed height, Table 2. The mean bed height was defined as the height where the gas pressure distribution slope was modified.

The Fig. 4 shows the mass of fine particles collected during the entrainment step (V f 2 = 1.53 V t ). In the bubbling phase, mesh refinement had a strong effect on the mass flow rate of particles entrained. Comparisons with the fine mesh simulation results showed that the coarse and reference mesh simulations overestimated the mass flow rate of the particles entrained. With the sub-grid model, the numerical simulations were approaching to the experimental measurements. The simulation for the reference mesh with sub-grid model appeared to give similar results as with the simulation of fine mesh but with less expensive computational resources. As for the coarse particles, the flux of particles at the start of the process was slightly overestimated, and was similar to the experimental measurements for the following test duration.

CONCLUSION

An experimental test unit was designed and built to study particle separation and entrainment in a fluidized bed by measuring the gas pressure along the column and the mass of particles leaving the column. A three dimensional, unsteady numerical predictions was carried out with the unstructured parallelized CFD multiphase flow NEPTUNE CFD were compared with experimental measurements.

Comparisons were obtained for two types of particles (B and A/B). The numerical predictions for type A/B have strong dependency on the mesh size. To account for the effect of unresolved structures on the macroscopic behavior for coarse grid simulations, a sub-grid model was used to model the drag term. Accordingly, the numerical results were greatly improved and were in good agreement with the fine grid simulation. Coarse numerical simulations with the sub-grid model were hugely much less expensive from the point of view of the computational resources. The numerical predictions of the bed height and of the entrainment rate were in good agreement with experimental measurements. The next step of this study is to focus on the elutriation of a mixture of fine and coarse particles.

Fig. 1 :

 1 Fig. 1: Experimental set up.

  Mass of particles collected.

  Effect of sub-grid model for drag force.

Fig. 3 :

 3 Fig.3: Comparison between experimental data and numerical simulation predictions of wall mean gas pressure for fine particles during the bubbling step. V f 1 = 5 U mf .

Fig. 4 :

 4 Fig. 4: Mass of fine particles collected during the entrainment step. V f 2 = 1.53 V t .

  V t .

		Bed height
		(cm)
	Coarse mesh	27
	Reference mesh	26.2
	Fine mesh	24.1
	Coarse mesh + sub-grid	24.5
	Reference mesh + sub-grid	24.2
	Fine mesh + sub-grid	23.6
	Exp. data	24.2
	Table. 2: Time-averaged bed height.

ACKNOWLEDGMENTS

This work was granted access to the HPC resources of CINES under the allocation 2010-026012 made by GENCI (Grand Equipement National de Calcul Intensif) and CALMIP (Centre de Calcul Midi-Pyr én ées) under the allocation P0111.