Settling velocity of atmospheric particles in seawater: Based on hydrostatic

1. Introduction
   The deposition of atmospheric particle to the ocean has a significant impact on marine nutrient cycling and carbon sequestration (Bao et al., 2017; Mahowald et al., 2018; Ventura et al., 2021). Previous research has predominantly focused on the impact of atmospheric chemical fluxes to the ocean’s surface and upper mixed layer, a dynamic region extending from the sea surface to varying depths of several tens to hundreds of meters (Bishop et al., 2002; Troost et al., 2013; Xiu and Chai, 2021). Studies have demonstrated that atmospheric particles settling slowly, more likely to be consumed, thereby retaining essential compounds within the ocean’s upper layers and enhancing their avail- ability for phytoplankton utilization (Boyd and Trull, 2007; Quay, 2023). The residence time of atmospheric particles in the marine euphotic zone (time required for particle to settle across the euphotic zone) dictates whether phytoplankton have sufficient time to effectively utilize chemicals on the particle, which is determined primarily by settling velocity. Despite its recognized importance, there remains a significant gap in the quantitative understanding of the settling veloc- ities of atmospheric particles upon their entry into the marine envi- ronment. This deficiency limits our ability to comprehensively assess the broader implications of atmospheric deposition on marine ecosystems,

particularly in terms of nutrient cycling and carbon sequestration. Addressing this knowledge gap is essential for advancing our under- standing of the complex interactions between atmospheric processes and marine biogeochemistry, and for enhancing the accuracy of models predicting the impact of global environmental changes on oceanic systems.
The settling velocity of particles is significantly influenced by their inherent properties, with particle diameter and density being identified as primary determinants, as elucidated by the principles of Stokes’ Law and other predictive models (Ahrens, 2000; Song et al., 2008). Maggi (2013) proposed that particle density decreases with increasing organic matter in the particles and that the settling velocities of mineral, bio- mineral, and biological particles decreases in the order of their corre- sponding particle density. It has also been found that organic matter on particle, although less dense, promotes flocculation between particles thereby increasing the settling velocity (Deng et al., 2022; Mrokowska and Krzto-Maziopa, 2024). Contrarily, investigations into specific particle types, such as marine snow and phytoplankton aggregates, have revealed that their settling velocities may not be directly correlated with size and density (Ploug et al., 2008; Iversen and Lampitt, 2020). The shape of particles has also been recognized as a critical factor affecting their settling velocity; for instance, irregularly shaped microplastic

particles exhibit markedly reduced settling velocities when compared to their spherical counterparts (Kaiser et al., 2019; Goral et al., 2023). In addition to particle properties, water salinity also affects particle settling velocity. Increased density due to higher salinity increases the buoyancy force on settling particles, significantly reducing their settling velocity (Prairie et al., 2015; Mrokowska, 2020). Furthermore, several studies have shown that increasing salinity promotes the flocculation of fine particles, thereby accelerating particle settling (Portela et al., 2013; Zhang et al., 2021). The intrinsic characteristics of these particles, along with environmental factors, influence the settling process by affecting the forces acting on the particles, particularly gravity, buoyancy, and viscous resistance etc.
Experimental methodologies serve as the cornerstone for elucidating the settling dynamics of particles. Dating back to the early 1990s, pio- neering research efforts were undertaken to study the settling processes of particles within the water column in controlled laboratory settlings. A notable early study by Smayda and Boleyn (1965) involved measuring the settling velocities of phytoplankton cells utilizing an inverted mi- croscope (Smayda and Boleyn, 1965). Additionally, the SETCOL method, introduced by Bienfang (1981), has been widely adopted for investigating phytoplankton settling in marine environments, attributed to its straightforward equipment requirements and experimental pro- tocols. This method has also been extended to assess the settling ve- locities of inorganic particles, such as olivine, in marine settlings (Bienfang, 1981; Li et al., 2018a, 2018b; Wang et al., 2022). Despite their utility, concerns have been raised regarding both methodologies, especially concerning the wall effects that may arise from the configu- ration and dimensions of the experimental apparatus (Peperzak et al., 2003; Du Clos and Gemmell, 2024). Furthermore, the SETCOL method primarily provides average settling velocities for particles of varied sizes, thus limiting the depth of analysis regarding the influence of particle intrinsic properties on their settling behavior. In response to these limitations, non-invasive and minimally disruptive optical tech- niques have increasingly been utilized since 2006 for the study of par- ticle settling. The employment of laser scanners, FlowCAM, and plankton trackers has facilitated the precise measurement of settling velocities for a diverse array of particles, including phytoplankton cells and microplastics. These advanced methodologies also allow for a detailed analysis of how particle morphological characteristics impact their settling processes (Walsby and Holland, 2006; Bach et al., 2012; Durante et al., 2020; Elagami et al., 2022). For the study of atmospheric particle settle we can draw on these methods.

The settling particles analyzed through the aforementioned methods, such as phytoplankton, olivine, microplastics, etc., are generally char- acterized by their diameters exceeding 20 μm. In stark contrast, atmo- spheric particles feature intricate chemical compositions and smaller dimensions, rendering the direct application of prior research findings to sub-20 μm particles challenging. Moreover, density emerges as the paramount factor influencing the settling velocity of particles; however, accurately measuring the density of atmospheric particles poses sub- stantial difficulties. Consequently, conventional formulas designed for calculating the settling velocities of particles may not seamlessly extend to atmospheric particles with complex compositions. Further study on the settling velocity of atmospheric particle necessitates an approach grounded in the physic-chemical properties of the particles themselves, especially the shape and chemical composition.
In this study, we introduce a non-intrusive, minimally disruptive approach by using video data to quantify the settling velocity of atmo- spheric particle upon its falling into the salty water. Compared to other studies, our investigation considered not only the effects of particle diameter, shape, and water salinity but also the inorganic and organic compositions of particles on the settling velocity. As mentioned above, previous studies focused on particles above 20 μm in diameter, and the researches of particles with diameter < 20 μm is scarce. In this study, we focus on atmospheric particles within the range of 5-20 μm. Addition- ally, we developed a new formula that can be applied to assess the

settling velocities of particles. We hypothesized that the settling velocity of atmospheric particles could be predicted from particle diameter, percentage of organic matter, seawater density, etc., and that the resi- dence time of particles in the euphotic zone could be further calculated based on the thickness of the euphotic zone in different sea areas.

2. Experimental setup and apparatus
   2.1. Particle collection and processing
   For this study, total suspended particulate (TSP) samples were collected utilizing a high-volume sampler (KC-1000) equipped with quartz filters (Whatman QMA 1851-865) over a period of approxi- mately 24 h at the Atmospheric Observation Station of Ocean University of China, Laoshan Campus (36◦ 9′39″N, 120◦ 29′29″E). Prior to collection, the quartz filters were pre-treated by baking in a muffle oven at 400 ◦ C for 12 h. A portion of each collected sample was dedicated to sedi- mentation experiments, while the remainder was reserved for chemical composition analysis. In total, nineteen samples underwent collection and subsequent analysis in this research endeavor.
   The analytical focus was on the quantification of organic carbon
   (OC) and a suite of ions including Na+, NH, K+, Mg2+, Ca2+, F − , Cl − ,
   NO , NO , SO − , PO − . the quantification of Organic Carbon was per-
   formed using a Sunset OC-EC Analyzer (Model 4), and ion concentra- tions were determined through ion chromatography utilizing a Dionex ICS-6000 system. Detailed methodology is elaborated in the supple- mentary information (Text A1). To examine the impact of chemical compositions on settling velocity, the organic-inorganic ratio within the particles was estimated by comparing the organic matter (OM) content with the total ion content. Drawing on the findings of Turpin and Lim (2001), an OM to OC ratio of 1.6 ± 0.2, characteristic of urban aerosols, was adopted for calculating the OM content in particles using the for- mula OM = 1.6 × OC. As shown in previous research (Wangmian and Humin, 2001), soluble ions accounted for 40 % of the total mass con- centration in TSP, which is regarded as the main inorganic component of the particle.
   The chemical composition of the samples, depicted in Fig. 1, reveals
   that Na+, Ca2+, NH, NO , SO − , Cl − , and organic matter collectively
   comprise 88 % - 98 % of the total mass in our samples. The proportion of organic matter varied significantly, ranging from approximately 7-62
   %. Among the cations, NH, Na+, and Ca2+ were predominant, whereas

Fig. 1. Diagram of the chemical mass percentages of the particles sampled in Laoshan campus of Ocean University of China in Qingdao, China.

K+ and Mg2+ were present in low and negligible concentrations,
respectively. For anions, SO − , NO , and Cl − were the most abundant,
while PO − and F − were present in very low concentrations, and NO
was not detected.
According to Levy et al. (2013), the effective density of particles was calculated. The density of the organic component is about 1.4 g/cm3 (Dinar et al., 2006; Kostenidou et al., 2007; Levy et al., 2013). In this study, we consider that the inorganic components in atmospheric par- ticles include NaCl, CaCl2, NH4 NO3, (NH4)2SO4 (Fig. 1), with their densities of 2.16 g/cm3, 2.15 g/cm3, 1.72 g/cm3, 1.77 g/cm3 respec- tively (Yin et al., 2015; Haynes, 2016). The density of chloride is taken as 2.155 g/cm3 and the density of ammonium salt is taken as 1.745 g/ cm3.
Then the average density of the inorganic component can be esti- mated as:
ρ = (1)
m1 + m2 + … + mn
where mi and ρi denote the mass percentage (%) and density of inorganic components in each sample of atmospheric particles. The density of chloride is estimated as m1 ρ1 = (Na+% + Ca2+% + Cl − %) × 2.155,
ammonium salt in sample is estimated as m2 ρ2 = (NH% + NO% +
SO − %) × 1.745. Based on the mass percentages of inorganic compo-
nent in particles (Fig. 1) and the densities shown above, we estimated the inorganic density of each of the 19 samples according to Eq. (1), the average density of the inorganic component was calculated as ρi = 1.81 g/cm3, the mass percentage of each inorganic ion is shown in Appen- dices Table A1.
Therefore, the particle density is estimated by Eq. (2).
ρs = 1.4 × OM% + 1.81 × (1 − OM%) (2)
According to Eq. (2), the density of the sample particles was esti- mated to be 1585-1782 kg/m3 (Table A2). This estimation aligns with the documented range of atmospheric particle density in the literature (Pitz et al., 2008; Liu et al., 2015; Li et al., 2018a, 2018b).

2.2. Experiment setup of particle sedimentation
In the sedimentation experimental system (Fig. 2), a vertical slide rail was used to control the vertical movement of the camera. The recording apparatus utilized is a smartphone (iPhone 14 Pro, 1080 × 1920 pixels, 9×) camera equipped with a macro lens (Kase, China, 40-85 mm,10×), placed 1 cm outside the settling column, providing a view window of 2 × 3.5 mm. The settling column adopts a rectangular shape with di- mensions of 50 × 20 × 20 cm (height × width × length). Illumination is provided by an LED lamp positioned at the same height as the camera lens. Prior to the experiment, the settling column, camera and lamp were assembled and a leveling instrument were used to adjust them vertically to the ground.
The experimental design included varying the water salinity levels to 0, 10, 20, and 30, to simulate conditions of pure water and seawaters from different marginal sea locations. For the salinity level of 0,

Fig. 2. Structure of the settling experimental system for particles.

ultrapure water was utilized, whereas salinities of 10, 20, and 30 were achieved by diluting ultrapure water with artificial seawater salts. The settling column was filled with 18 l of water, resulting in a water depth of approximately 45 cm. To ensure uniform water temperature throughout the column and mitigate convection currents induced by temperature gradients, the water was introduced into the settling col- umn the day prior to the experiment and allowed to equilibrate in the laboratory for 12 h.
Camera was initially placed 15 cm below the surface of the water. The experimental procedure commenced with the atmospheric particles being gently washed from the sampling filter into the settling column. Concurrently, the camera was initiated to record the event. Through precise adjustments made via the vertical slide rail, the camera’s height was meticulously calibrated to capture the entire sedimentation process of the particles, tracking their journey from the moment they entered the camera view until their eventual settlement at the bottom of the column.

2.3. Measurement of particle settling velocity, particle diameter and shape
The sedimentation behavior of particles was meticulously captured at a rate of 30 frames per second. The acquired video footage was analyzed using Tracker, an open-source video analysis software avail- able at https://physlets.org/tracker. This tool facilitated the extraction of progressive data on the particles’ size, shape, and their x-y co- ordinates at each frame. The settling velocity for particles at a specific height within the column was determined by averaging the per frame velocities of individual particles across the view window. Particle diameter and shape were quantified utilizing the video recordings. Nonetheless, an aperture effect caused by light reflection under intense illumination conditions led to an overestimation of particle diameters during their descent. To address this issue, an image binarization tech- nique was employed, converting the grayscale pixel values in the images to binary (0 or 255), thereby producing clear black and white contrasts. By setting an appropriate threshold value, it was possible to mitigate the overestimation of particle diameters due to reflective artifacts, accu- rately delineating the true contours of the particles. Calibration exper- iments, under the specific experimental lighting conditions, utilized standard polystyrene spheres (Jiangsu Zhichuan Technology Co. China, 1050 kg/m3) with diameters of 10 μm and 20 μm. The geometric mean diameters of these spheres were measured, revealing that a binarization threshold value of 120 effectively eliminated the overestimation caused by light reflection, aligning the measured sizes with those of the stan- dard spheres. Consequently, a threshold value of 120 was adopted for subsequent experiments, although it is noted that this threshold is contingent upon the specific lighting conditions of this study and may vary under different circumstances.
Every frame of captured image of the particle is a two-dimensional picture, but a continual rotation of the particle during its settling pro- cess was observed. Thus, each frame of the 2D image shows the contours of the particles in different orientations. In order to reproduce as much as possible the real diameter of the 3D particles, we measured the size of the particle in horizontal, vertical and tilted 45◦ directions in different frames (Fig. A1) during its sinking processes. The lengths in each di- rection were averaged, where the longest axis was defined as a, the intermediate-length axis as b, and the shortest axis as c. The particle diameter was estimated by the geometric mean of these axes, i.e. D =
√3---. Particle shape was evaluated using the Corey shape factor (csf), i.
e. csf = (Corey et al., 1949). The value of csf closer to 1 indicated a more spherical particle. In this study, csf acts as the parameter to eval- uate the influence of shape on particle settling velocity. In order to validate the feasibility of the method, we measured the settling veloc- ities of 10 μm and 20 μm polystyrene standard spheres by performing hydrostatic settling experiments with purified water and comparisons were made with the results of the Stokes law calculations. The results are

shown in Fig. A2, and this experimental method could measure the

settling velocity of particles accurately.