The capture of crude oil droplets by filter feeders at high and low Reynolds numbers

Filter feeding is widespread across phyla, body sizes and ecosystems (Jørgensen, 1955). It consists of capturing particles of various sizes and origins that are dispersed in the water column using a filtering apparatus. Depending on the species, filter feeders select particles from the water column based on size, shape, taste, chemical cues and even texture (Gerritsen and Porter, 1982; Gonçalves et al., 2014; Hartmann and Kunkel, 1991; Tiselius et al., 2013). These particles may be debris, bacteria, algae, protists or plankton. Less appreciated is that filter feeders also feed on suspended oil droplets (Conover, 1971; Nordtug et al., 2015). These droplets may be lipids of decaying plants and animals or petroleum droplets from a spill, pipe seepage or other anthropogenic activities. The naturally occurring oils serve many beneficial functions for zooplankton, including regulating buoyancy during vertical migrations or as a lipid reserve for gametogenesis and overwintering (Thorisson, 2006; Visser and Jónasdóttir, 1999). The cyprid larva of a barnacle depends on lipid droplet provisions to locate a suitable settlement site (Franco et al., 2016). The ingestion of crude oil droplets may have detrimental and sublethal effects, including lower egg counts and hatching rates, an increase in faecal pellet production and a general decrease in feeding and swimming activity (Almeda et al., 2014; Cohen et al., 2014; Nordtug et al., 2015).

The capture of solid particles by filter feeders has been studied extensively from a theoretical (Rubenstein and Koehl, 1977) and biological perspective (Kiørboe, 2011). We do not have an experimental understanding of oil droplet capture by a feeding appendage or appendages. This subject is significant because droplet capture is how oil enters the food web. Petroleum oil ecotoxicology has been widely studied at the species and community levels (Daly et al., 2021; Lemcke et al., 2019; Yilmaz and İşinibilir, 2018). To prevent these toxic effects, we must begin with an understanding of droplet capture mechanics. We have provided a theoretical foundation to understand these mechanics (Mehrabian et al., 2018). In theory, oil droplet capture is largely determined by the same factors that regulate solid particle capture, but there are additional variables to consider.

In addition to droplet size, density and Reynolds number, the wettability of a fibre impacts the capture of an oil droplet (Mehrabian et al., 2018; Conova, 1999; Gerritsen and Porter, 1982). Wettability consists of the affinity a fluid has for a solid surface and the degree to which it will spread on it. The wetting of a surface is governed by its texture, surface chemistry and hydrophobicity. Models suggest that particle capture is enhanced when the collection surface has low wettability (Conova, 1997). The exoskeleton of Daphnia sp. has low wettability and displays hydrophobic characteristics (Dodson, 2004; Gerritsen and Porter, 1982).

Oil droplet capture mechanics are largely the same as those for particles: direct interception, inertial interaction and gravitational deposition (Rubenstein and Koehl, 1977; Mehrabian et al., 2018). Direct interception is in play when a particle reaches a minimum distance of its radius from the fibre and contacts it. Recent work by Boudina et al. (2020) estimated that, in inertia-governed systems, particle size must not be more than 70% of the fibre's boundary layer for direct interception to be considered. Otherwise, inertial interaction is likely to be the main capture mechanism. Inertial interaction occurs when forces on the particle are strong enough to make it deviate from its streamline and cause it to touch the fibre. Gravitational deposition takes place when a difference of density between the particle and fluid exists. This will cause it to move upward or downward depending upon whether the particle is more or less buoyant that the fluid. The particle can then contact the fibre and be captured.

Thus, flow velocity, particle radius and density play an important role in particle capture. Increasing the droplet size or stream velocity will result in a higher probability of capture by direct interception or inertial interaction. As with particles, all capture mechanisms can occur simultaneously, but usually one or two will predominate (Rubenstein and Koehl, 1977). Again, the dimensionless number with the highest index will determine the capturing mechanism that is the most likely to take place. Once a droplet (or particle) is captured by a fibre, it can remain in contact with the fibre, be manipulated by appendages for ingestion or detach from the fibre if external forces permit. Letendre et al. (2020) describes conditions for such detachment of oil droplets to occur. For a droplet to detach the fibre and re-enter the water column, the critical ratio of inertial to capillary forces must be achieved, which can be increased by a higher flow velocity or a lower oil/water interfacial tension.

The goals of this paper were to identify the capture mechanisms of crude oil droplets using the cladoceran Daphnia magna and two species of barnacles (Balanus glandula and Balanus crenatus) (see Fig. S2 for pictures of studied species). We also describe the wettability of the filtering appendages of these species and discuss its role in the capture and retention of oil droplets.

To ensure good visibility of the appendages and to minimize fixation artefacts, specimens were first relaxed in a solution of magnesium chloride. MgCl₂ was introduced drop by drop until D. magna had minimal appendage movement and barnacles stopped feeding. At this point, barnacles were removed from their calcareous plates and the cirri were removed. Individuals were then fixed in 2.5% glutaraldehyde buffered in a 0.2 mol l⁻¹ phosphate buffer (7.6 pH) for 3 h. The carapace of D. magna was removed for better observation of the filtering thoracic legs. Specimens were transferred in a 2% OsO₄ buffered solution for 2 h. Samples were then rinsed 3 times for a period of 5 min in the phosphate buffer. At this point, the samples went through a graded ethanol series from 30% to 90% with 10% increment, then 95% and 100%, 3 times. Each step lasted 15 min. The samples were mounted on aluminium stubs and placed in an air drying desiccator overnight, then a 15 μm layer of gold was applied to the stubs, before scanning electron microscopy (SEM) observations. The D. magna samples were observed at the École Polytechnique de Montréal using a JEOL JSM-7699F SEM. Barnacles were observed at the same location but with an environmental scanning electron microscope. SEM samples were used to accurately measure appendage morphology and to study the surface texture of the various filtering appendages.

Two species of barnacles were used to quantify oil droplet capture: the relatively large Balanus glandula Darwin 1854 and the small Balanus crenatus Bruguière 1789. Specimens were acquired by Westwind Sealabs from the south coast of Vancouver Island, Canada. Specimens were gently scraped off their substrate and placed in an 80 gallon (∼303 l) saltwater tank at 10°C. These species were chosen to observe capture events at different flow velocities and Reynolds numbers, as they have different cirrus length, width and spacing. Observations were made in a 3×4×18 inch (7.6×10.2×45.7 cm) rectangular flow tank equipped with a variable speed motor. The camera was positioned to the side of the flow tank so that the animal was filmed from the side view. The animals were individually put on modelling clay and stuck to the bottom of the flume tank. A sufficient amount of clay was used to elevate the animal where it would experience the free-stream velocity of the flume and not be affected by the flume's boundary layer. A 532 nm Aries green laser was placed above the flume and a crystal split the beam in a thin sheet parallel to the water flow. That sheet was then positioned above the barnacle. To create the crude oil-in-water emulsion, 75 μl of crude oil was pipetted in 1 litre of conditioned tap water. The crude oil used has a density of 855 kg m⁻³, a viscosity of 98 mPa s and an interfacial tension of 27.1 mN m⁻¹. The emulsion was mixed at 900 rpm for 20 min on a stirring plate using a magnetic stirrer. This guaranteed a normal distribution of oil droplet size. The emulsion was then poured into the flume. When feeding occurred, whether passive or active, 4 s of video were captured at 1057 frames s⁻¹. A schematic diagram of the experimental setup is given in Fig. S3. When studying the interactions of oil droplets with filtering appendages in water, the key parameters are flow velocity, appendage radius and droplet radius (Letendre et al., 2020). The velocity used for the Reynolds number and capture mechanism intensity calculations was the free-stream velocity of the flume tank, which was constant when the animal was placed at its centre. For these velocity measurements, a 15 cm ruler was placed at the centre of the flume and parallel to the flow. The laser sheet was positioned on the same plane as the ruler. When particles were in focus with the gradation of the ruler, they were filmed with a Chronos 1.4 v.0.3.1 high-speed camera. This footage was then analysed with the image processing software ImageJ using the TrackMate plugin to determine the free-stream velocity (Tinevez et al., 2017). Only trajectories that contained at least 50 frames were used and 1000 particle trajectories were considered for the mean velocity of each increment on the variable speed motor. Flow-stream velocity varied from 1.40 to 24 cm s⁻¹. This range of velocities was chosen for Reynolds numbers that allowed for observation of passive and active filtering of the two species and because they are in the range of previous fluid mechanics (Vo et al., 2018) and feeding studies (Eckman and Duggins, 1993; Geierman and Emlet, 2009; Nishizaki and Carrington, 2014) of B. glandula and B. crenatus.

SEM image analysis was also made using ImageJ. Rami and setae diameter were measured at the middle of the fibre and at its tip for both species of barnacles. Only the sixth pair of setae from each segment was measured as it is the longest and widest fibre. Setae spacing was measured as the distance between the centre of two setae at half-length (i.e. where the diameter was also measured). The spacing of the rami was measured from the high-speed videos of the barnacles feeding. The measurement was made when two rami were in focus, facing the lens and passively feeding in the flume.

Daphnia magna Straus 1820 specimens were purchased from Boreal Science and kept in an incubator at 21°C. They were fed every 3 days with Spirulina powder. The crude oil-in-water emulsion was mixed as described above. During mixing, a D. magna specimen was selected and its carapace was dried using a paper wipe, ensuring a dry surface. A drop of non-toxic super glue was applied to the dorsal posterior end of the animal to secure it to a 100 μm insect pin. The animal was then pinned on a silicone pad inside a Petri dish. This way, the animal could move all its appendages freely while accomplishing minimal movement, permitting ideal filming conditions. The ventral side of the animal was then positioned upwards for microscope observations. The laser sheet was projected horizontally, but positioned slightly above the ventral surface of the animal in order to see the oil droplets that were displaced by its feeding current. This setup was placed under an Olympus S2X16 dissection scope equipped with the same high-speed camera. Observations were filmed at 200 frames s⁻¹ for 20 s periods and at 1057 frames s⁻¹ for 4 s periods. We recorded when there was metachronal movement of the thoracic legs but minimal movement of the second pair of antenna. Indeed, as the second pair of antenna are mainly for swimming, their movement results in a distortion of the flow around the animal.

Setae and setule diameter of the four pairs of thoracic legs and the second pair of antenna was measured using SEM. The measurements were made at the middle point of each fibre. The intersetular distance was measured for each appendage as the centre to centre distance of two adjacent setules. Only the intersetae distance of the third and fourth pair of thoracic legs was measured. SEM also permitted observations of the surface texture to inform on the wettability of the appendages. Data for appendage and droplet velocities were obtained by analysing the high-speed videos in ImageJ. All four pairs of thoracic legs were tracked manually for several full cycles of filtering.

To validate that oil droplets were being ingested, a feeding experiment similar to the one on calanoid copepods in Letendre et al. (2020) was done. For each treatment, 20–30 D. magna individuals were introduced into a crude oil-in-water emulsion. The concentrations of the emulsions were 10, 50 and 300 μl l⁻¹. Prior to this, the individuals were starved overnight so they had an empty gut for better observation of ingested droplets. Animals were left in the emulsion for 48 h and were observed immediately afterward. As crude oil auto-fluoresces, observations of the antennae, gut and thoracic legs were made under a fluorescence microscope. To obtain information on the lipophobicity and surface texture of the filtering appendages, the contact angles of crude oil droplets captured by live specimens were measured with ImageJ. Only the contact angles of droplets that were captured by the antennae or filtering appendages and not agglomerated were considered.

To determine the droplet size distribution in the flume, a few drops of the crude oil-in-water emulsion were photographed under a fluorescence microscope using a TRITC filter. The oil droplet diameters in the emulsion were measured using the analyse particle tool of ImageJ. A Shapiro–Wilk test was done to verify normality at a significance of P≤0.05 using the open source software R 4.0.5.

Measurements of appendage morphology of B. glandula, B. crenatus and D. magna were done using SEM. Key morphology measurements of the barnacles are given in Table 1 and examples of barnacle morphology are given in Fig. 1. For B. glandula, the diameter of the rami and setae was, respectively, 91.4±5.2 μm and 5.5±0.6 μm and setae were evenly spaced at an average of 14.1±1.2 μm. The mean gap-to-diameter ratio of the setae was 2.6±0.3. The average distance between the middle point of each rami was 476 μm. The setae of this species are serrulate; the setules are sharp and needle-like (Chan et al., 2008). The insertion site of the setules alternates from side to side. The setules are almost parallel to the setae, meaning that they do not extend outward.

For B. crenatus, the diameter of the rami and setae was 51.8±1.4 μm and 4.6±0.5 μm, respectively. The setae spacing for this species was 10.9±1.4 μm and the rami spacing was 282 μm. The gap-to-diameter ratio of the filtering fibres was 2.4±0.2. As the flow velocity measured in our experiments varied roughly from 1.40 cm s⁻¹ to 24 cm s⁻¹, a wide range of Reynolds numbers and boundary layer thicknesses were witnessed. The setule morphology of B. crenatus is similar to that of B. glandula. The setae are also serrulate, and the setules remain close to the setae.

The Reynolds number, thickness of boundary layers and different capture intensities for both species of barnacles are compiled in Table 2. For B. glandula, the Reynolds number experienced at the scale of the rami ranged from 1.24 to 20.78. Using Eqn 2, the boundary layer thickness was estimated to be 82 μm at lower Reynolds numbers and 20.1 μm at higher Reynolds numbers. Around the setae, the Reynolds number ranged from 0.07 to 1.25. The boundary layer thickness around the setae was estimated to range from 20.1 μm to 4.9 μm. Considering that the spacing of the setae for this species was measured at 14.1±1.2 μm, the boundary layer was 1.3 times larger than the spacing at lower Reynolds numbers. Thus, boundary layers of adjacent setae overlap and appendage leakiness is very low, or null. At the higher Reynolds numbers observed, the boundary layer thickness to setae spacing ratio was estimated to be 0.3, meaning that boundary layers do not overlap, allowing a portion of the fluid to pass through the fibres at free-stream velocity.

The Reynolds number around the rami of the smaller B. crenatus was 0.70 and 11.78 at the lowest and highest velocities. At those speeds, the thickness of the boundary layer surrounding the rami changed from 61.8 μm to 15.1 μm. Balanus crenatus setae Reynolds number varied from 0.06 to 1.05 and the boundary layer thickness varied from 18.4 μm to 4.5 μm. Thus, at low Reynolds numbers, the thickness of the boundary layer was 1.7 times greater than the distance between two adjacent fibres. The leakiness of an appendage under this regime is then negligible. At the higher end of our measured Reynolds numbers, this ratio was 0.4, which would permit some fluid to pass in between the fibres. However, this amount would be less than that for B. glandula, as the boundary layers of two adjacent fibres would account for 80% of the area between them.

⁠, St and G, which are the dimensionless numbers for direct interception, inertial interaction and gravitational deposition, were measured for both species at all five tested velocities. As all three equations require the diameter of the droplet, the average diameter of the droplets found in the emulsion was calculated. To ensure that the droplet sizes followed a normal distribution, kurtosis and skewdness tests were done. The respective tests established a value of 1.699 and 0.919, both being in the acceptable range for a normal distribution. A Shapiro–Wilk test was also done (P=0.19), and showed that we cannot reject the null hypothesis of normality. The average droplet diameter, 2.4±1.3 μm, is relatively close to the median, i.e. 2.3 μm. Thus, we felt that the use of the average droplet diameter would be appropriate and relevant for the calculation of various capture intensities.

Values of for B. glandula and B. crenatus were respectively 0.443 and 0.529 (Table 2). At lower velocities, values of St and G for B. glandula were 1.35×10⁻⁴ and 3.56×10⁻⁵. At the highest measured velocities, the intensity of inertial interaction and gravitational deposition were 2.25×10⁻³ and 2.13×10⁻⁶. On B. crenatus, capture intensity at lower free-stream velocities was St=1.61×10⁻⁴ and G=3.56×10⁻⁴. At our highest measured velocities, capture intensity was St=2.69×10⁻³ and G=2.13×10⁻⁶. As the setae diameter used was measured at the middle of the setae, these intensities are relevant for capture around the middle of the fibre.

At low velocities, i.e. lower range of Reynolds number, barnacle cirri behaved as paddles and captured crude oil droplets in their thick overlapping boundary layers. Fig. 2 depicts Balanus crenatus actively feeding in an oil-in-water emulsion inside a flume at 1.4 cm s⁻¹ (see Movie 1 for an example of active feeding at that velocity). At low velocities, the barnacles would actively feed by repeatedly extending the cirri into the water column and then retracting them into the mantle cavity. This allowed the animal to trap parcels of water in the area created by the curved rami and then transport them near to the mouth. The cycle began with the opening of the operculum and the extension of the cirri into the water column (Fig. 2A). Then, it would spread its cirri, allowing water to rush into the space created by this movement (Fig. 2B). The curving of the rami thus creates a sheltered space which we refer to as the ‘cage’. Once the cage was filled, the animal would begin to retract the cirri into the mantle cavity, which would reduce the distance between individual rami (Fig. 2C). Then, it fully retracted into the mantle cavity, with the oil droplets that were trapped in the appendage's boundary layer inside its calcareous shell (Fig. 2D).

At 1.4 cm s⁻¹, the Reynolds number around the rami of B. crenatus was 0.70 (Table 2). For this particular experiment, the boundary layer around a setule was 18.42 μm. As the setule spacing of B. crenatus was 10.9±1.4 μm (Table 1), the boundary layers overlap and little to no fluid may pass through the setules. Considering the serrulate tip of the setules, it is unlikely that true sieving happens even at high flow for this particular level of ramification (Fig. 1A,C). With such a thick boundary layer, particles will not contact the rami and will be entrapped in its boundary layer.

There was a range of intermediate velocities where some droplets were captured by both mechanisms, i.e. the leaky-sieve transition zone (Koehl, 2001). Fig. 3 shows Balanus crenatus passively feeding in the flume's oil-in-water emulsion at 10 cm s⁻¹. In this particular system, the Reynolds number of the setae and the rami were respectively 10⁻¹ and 10¹ in order of magnitude. Considering the gap-to-diameter ratio of this filter-feeding species (Table 1), these Reynolds numbers represent the transition zone, where a change in spacing or behaviour can greatly influence the leakiness of an appendage (Koehl, 1993). This is in fact what we observed in Fig. 3. The circled droplet approached the appendage close to the rami's insertion and slowed (Fig. 3A), but did not pass between the fibres. Instead, it moved across all rami from left to right (Fig. 3B,C), around the animal, and re-entered the fluid stream (Fig. 3D). This is an example of an appendage behaving as a paddle, where little to no fluid passes between fibres. In contrast, the droplet identified by the white square approached the appendage with the same original velocity, but met the rami at a much higher point on the appendage. Near the tip, the gap-to-diameter ratio was higher than at the insertion point. This caused a local increase in the appendage's leakiness, and allowed the oil droplet to pass between the rami (Fig. 3C). If the droplet had been big enough, it could have been captured through sieving. In accordance with Koehl (1993), these flow regimes are where a change in this spacing causes the most increase in appendage leakiness. Droplets that are captured by a single fibre are likely to be captured via direct interception as it is the mechanism with the highest index (Table 2).

At higher velocities, fluid passed between the cirri and oil droplets and was captured mainly by direct interception (see Movie 2 for an example of a barnacle passively feeding). In true sieving, particles that are larger than the fibre spacing will be captured (Rubenstein and Koehl, 1977). However, as fluid passes much closer to the fibres, droplets smaller than the fibre spacing can contact the fibres and be captured via direct interception. Fig. 4 displays such a capture by B. glandula. Indeed, the circled droplet approached the rami at a 10 cm s⁻¹ free-stream velocity (Fig. 4A,B), and adhered to the rami. Fig. 4D shows that the droplet was captured by the rami and not by the setae. At this velocity, the values for direct interception, inertial interaction and gravitational deposition were respectively =0.443, St=9.42×10⁻⁴ and G=5.09×10⁻⁶ (Table 2), making direct interception the most likely mechanism. Once a droplet has been captured, the organism can decide to retract its cirri into its shell and scrape off collected particles using its mouthparts, e.g. maxillae and maxillipeds.

However, the setae of B. glandula do not all have the same length and width. Indeed, the sixth pair of setae is significantly shorter and narrower than the first pair, the first pair being the one inserted at the end of the segment closest to the tip of the appendage (Vo et al., 2018). This can have a major impact in the capturing potential of a setae. For example, the length of the sixth pair of setae was measured at 62±12 μm in Vo et al. (2018). Considering that the rami's boundary layer was 82.0 μm at our lowest measured velocity (Table 2), the tip of the setae is still well within the boundary layer. In these conditions, this setae serves little purpose as it is encapsulated in the boundary layer of the bigger fibre.

For D. magna, the diameter of the setae on the second antenna pair and that of the setule was 11.5±1.0 μm and 2.2±0.3 μm, respectively (Fig. 5B). The distance between setules was on average 7.5±0.6 μm (Table 1). The setule diameter of the first pair of thoracic legs was 1.3±0.3 μm and they were evenly spaced by 0.7±0.2 μm. The setules of this appendage were rigid and tooth-like, with little space between individual setules. Two different setae were observed on the second pair of thoracic legs (Fig. 5C,D). Consistent with the observations of Watts and Petri (1981), the second pair bear a setae with peg-like setules, giving it the appearance of a comb. The diameter of this setae was 7.8±0.5 μm. The setules of this setae were 1.2±0.1 μm in width and the centre-to-centre distance was 3.0±0.8 μm. These rigid setules were wide at their insertion but decreased in width, ending in a sharp tip. The second type of setae found on the second pair of thoracic legs bears setules that are more feather-like. The setae width was 9.8±0.3 μm and the setule width was 0.6±0.1 μm. The intersetular distance was 3.9±0.4 μm. The third and fourth thoracic legs have an extensive network of setae ramified with perpendicularly positioned setules (Fig. 5F). The spacing of each setae was regular and consequently this was the only setae spacing that could be measured, i.e. 5.4±0.9 μm. Opposing setules of adjacent setae touched near the tips, creating a regular grid of fibres. The diameter of these setae was 2.5±0.3 μm. The setules of these two pairs of legs were 0.20±0.02 μm in diameter and were 0.29±0.05 μm apart.

The order of magnitude of the second antennae Reynolds number was 10⁻¹ for the setae and 10⁻² for the setule. As it was not possible to measure the diameter of the first thoracic leg setae, its Reynolds number and its boundary layer thickness were not calculated. For the first four pairs of thoracic legs, the Reynolds number was 10⁻² for the setae and 10⁻³ for the setule. The second antennae had the highest velocity at approximately 4.24 cm s⁻¹. Table 3 summarises calculations for the boundary layer thickness and capture intensity for the different appendages.

Daphnia magna captured crude oil droplets by a metachronal paddle motion of the third and fourth thoracic legs by entrapment in the appendage boundary layers (see Movie 3 for an example of this metachronal motion). If left undisturbed, D. magna would filter feed with a constant beat of the appendages (Fig. 6). A full cycle for the thoracic appendages is roughly half a second. The four pairs of thoracic legs moved in a synchronous fashion creating a metachronal wave that started with the fourth pair of legs in a sequence similar to the Antarctic krill's pleopods (Murphy et al., 2013). Fig. 6A shows all four thoracic legs at the start of the cycle. The fourth thoracic legs initiate the cycle and begin to move posteriorly (Fig. 6B). With a 0.05–0.08 s lag, the next pair of thoracic legs would initiate its movement along the anterior to posterior axis (Fig. 6C–E). When the appendages finished their downward movement, they would move toward the centre of the animal where the food groove is located. However, the first pair of thoracic legs would move more latero-ventrally than the other appendages. Also, in agreement with Gerritsen et al. (1988), we observed that the first pair of thoracic legs did not always follow the metachronal wave. Indeed, the first pair can move independently to clean other appendages. The velocities of each appendage are compiled in Table 3.

Given its size and morphology, D. magna feeds at Reynolds numbers well below 1, where viscosity rules over inertia (Table 3). This means that a particle close to the animal will move or stop almost immediately in concert with the appendages. In the absence of external movement, we found that the particles would gradually approach the food groove with each metachronal wave. The velocity of an oil droplet approaching the food groove was 0.19 cm s⁻¹, until it arrived in the area above the food groove, where it accelerated rapidly to 1–1.67 cm s⁻¹, consistent with the findings of Gerritsen et al. (1988).

At these velocities and scale of the thoracic legs, the boundary layer of the setules was 20 times thicker than the intersetular spacing, and the fluid had difficulty passing through the appendage during the beating motion. Instead, water flowed with the appendage and was pushed toward the food groove, along with oil droplets. This finding is in agreement with several other studies on Daphnia sp., where sieving is said to be improbable and/or not the main filtering mechanism (Ganf and Shiel, 1985; Gerritsen et al., 1988; Porter et al., 1983). We found that in most cases, crude oil droplets were transported to the mouth of D. magna without touching an appendage.

Daphnids use their second pair of antenna to swim in the water column. Even though the Reynolds number of the antennae is one order of magnitude higher than that of the other appendages (Table 3), viscosity still dominates over inertial forces and the boundary layers are thick. Our results show that the boundary layer around a setae almost matches the intersetular distance, meaning that the antennae likely function as a paddle. This is good for propulsion but means that droplet capture by single fibres is unlikely. Indeed, using the antennae beating velocity (Table 3) and our average droplet diameter revealed a stopping distance of the order of 1×10⁻³ μm. In other words, the droplet loses all momentum almost instantly after entering the setae's boundary layer. In some cases, we found that droplets aggregated with organic debris, increasing the size of the particle and allowing it to move through the boundary layer and contact the fibre (Fig. 7C).This finding suggests that antennae of daphnids may be a site for droplet capture and oil fouling via flocculation. If droplets were captured by a single fibre, then direct interception is the likely mechanism (Table 3). However, for droplets or particles larger than 100 μm in diameter, inertial interaction starts to become another possible capture mechanism. We provide no further data on flocculation here.

Following the 48 h feeding period in the crude oil-in-water emulsion, individuals were photographed under a fluorescence microscope to observe autofluorescent oil droplets in the gut (Fig. 7A,B). Animals were starved prior to the feeding trials so that we could be sure that illuminated particles in Fig. 7B were captured crude oil droplets. Every individual observed from all three crude oil concentrations had oil droplets in their gut. Fig. 7C,D displays oil droplets that were captured by setules of the second pair of antenna. Furthermore, these droplets aggregate, which is a phenomenon of oil-in-water emulsions (Mehrabian et al., 2018). Fig. 7E,F shows oil droplets that were captured by the setae and setules of the third or fourth pair of thoracic legs. In this animal feeding trial, a single droplet was larger than the setal gap and was captured via sieving (Fig. 7F).

On wettability, we found that the filtering appendages of the three species studied exhibited lipophobic characteristics. Contact angles of captured crude oil droplets by live individuals were higher than 90 deg, replicating detachment conditions observed in Letendre et al. (2020). Observations of captured droplets revealed that the second antennae and filtering appendage setae of D. magna have a very low wettability for crude oil used. Indeed, the contact angle of all captured droplets was well above 90 deg and displayed a clam shape when captured (Fig. 7C–F) (Mehrabian et al., 2018). This clam configuration implies that the area of the droplet in contact with the fibre was minimal and oil did not fully coat the setae. Instead, the droplet rested on top of the fibre without surrounding it. Wettability is based on the shape, surface chemistry and texture of the fibre. Our SEM observations show that the appendages, setae and setules of D. magna and both species of barnacles had smooth surfaces (Figs 1 and 5). Moreover, all filtering appendages of D. magna, B. crenatus and B. glandula were lipophobic; the oil droplets touching the appendages in the flume had a spherical shape. The two barnacle taxa had similar appendage morphology, fibre arrangement and smooth filtering surfaces.

Naturally occurring and crude oils are omnipresent in the diet of aquatic filter feeders (Conover, 1971; Kattner et al., 2007; Nepstad et al., 2015). Here, we used experiments to understand how and under what conditions oil droplets are captured, and the variables that determine the capture mechanics. Our results indicate that oil droplets will be captured at both high and low Reynolds numbers. At low Reynolds numbers, the boundary layers of setae overlap and little to no fluid will pass between. Oil droplets were captured by the boundary layer and did not contact the setae. At high Reynolds numbers, direct interception is the predominant capture mechanism. Between these two extremes, there was a transition zone at which barnacles displayed paddle and sieve characteristics, where droplets were captured in the setae boundary layers and by direct interception, simultaneously.

When actively feeding, barnacles make full use of the thick boundary layer around their rami. Although fluid will pass through the appendage when it is fully extended, bringing the rami closer and reducing the gap:diameter ratio will decrease the leakiness of an appendage, depending on its Reynolds number. Koehl (2001) established that for Re=0.5, the maximum decrease in leakiness happens when the gap:diameter ratio goes below 5, which is the ratio of B. crenatus when it fully extends. Indeed, the animal needs only to reduce its rami spacing by half for the rami's boundary layer to overlap and shift toward a paddle behaviour. This exact process is shown in Fig. 2. Thus, capture by a single fibre is unlikely at low Reynolds numbers for its small filter morphology.

In all barnacle experiments, direct interception was the mechanism with the highest index. Indeed, inertial interaction and gravitational deposition are several orders of magnitude lower (Table 1). There are a number of possible reasons for such a gap in intensity, the main one being the small size of the oil droplets used in the experiments. As larger particles have higher inertia, they would deviate from their flow stream easier than small droplets. For example, using a theoretical droplet diameter of 100 μm, which is well within their feeding range (Nishizaki and Carrington, 2014), the intensity for direct interception, inertial interaction and gravitational deposition at our intermediate velocities is, respectively, 18.15, 1621.75 and 8.77. In this case, as it has the highest calculated index, inertial interaction is the most likely capture mechanism, and gravitational deposition the least. Increasing the particle size will then increase the indexes of direct interception, inertial interaction and gravitational deposition, but will have a higher impact on inertial interaction (Mehrabian et al., 2018). Also, the indexes St and G incorporate the density difference between the particle and water. In this sense, lighter oils are more likely to be captured by such mechanisms (LaBarbera, 1984). The capture intensity when increasing the flow velocity will have no impact on direct interception, but will increase the index for inertial interaction and decrease it for gravitational deposition. Considering this, a flow velocity edging toward zero would make gravitational deposition the main capture mechanism. However, when there is no flow, barnacles will either not feed or feed actively, essentially creating their own flow and capturing particles with other mechanisms. Gravitational deposition also highly depends on the orientation of the collecting fibres. As it requires particles to sink along the vertical axis, an appendage parallel to that plane, e.g. barnacle legs, is not optimal for such capture. Animals such as zoanthids and ophiuroids are better adapted for deposition feeding (Rubenstein and Koehl, 1977). In sum, direct interception is the main capture mechanism when the boundary layer is thin enough to allow fluid close to the rami. Inertial interaction would be a potential mechanism when studying big droplets and high flow. Gravitational deposition is not a probable mechanism for barnacles under any condition.

Barnacles are a good example of an organism that will alter its movement and setae spacing with changes in the flow environment. This adaptation permits them to live in low flow bays, rocky tide pools, wave-swept shores, and boat hulls. In these cases, the barnacles operate at a scale at which a small change in morphology can greatly affect the appendage's behaviour. Thus, the appendage can shift between the paddle and sieve feeding behaviour. This change in behaviour can in turn alter the main capturing mechanism by a setae (Koehl, 1993, 2001).

The main oil droplet capture mechanism for D. magna is entrapment in the overlapping boundary layers of the third and fourth pair of thoracic legs. Our results agree with those of Watts and Petri (1981) that the feeding current is created by the beating of the same legs. These capture observations, made with a high-speed camera, were supported by visualizing and measuring ingested crude oil droplets in the gut using fluorescence microscopy. After calculation of appendages velocity and measurement of setae and setules via SEM, we determined that sieving is not the main capture mechanism for this organism. However, our calculations of the boundary layers around fibres of all three species studied here are approximations. Indeed, these data were obtained assuming that the flow around the fibre is steady and does not vary in time. This is often not the case as the appendages often begin their filtering motion from a resting position, i.e. no moving velocity, thus creating an acceleration which influences the thickness of the boundary layers. Also, the filtering surfaces were assumed to be smooth to facilitate the calculations and their interpretation. Even though the filtering surfaces observed in this study are relatively smooth (Figs 1 and 5), other species could have rougher setae. These changes in surface texture could alter the flow profiles around the fibres and their boundary layers.

There is a certain range of particle size and flow velocity for which wettability plays a role in particle capture, e.g. up to 4 cm s⁻¹Conova (1999). Our flow velocities of the third and fourth appendages of D. magna, i.e. 1–1.67 cm s⁻¹, are within that range. Conova’s (1999) results also show that particles of 0.50 to 10 μm in diameter are less likely to be captured when they have high wettability. As this range of particle size is observed in droplets captured by D. magna, wettability might play a role in capture efficiency for this organism. Even though our results show that the surface of D. magna is lipophobic, its exoskeleton is also hydrophobic (Gerritsen et al., 1988). Considering that both the appendage and droplet surfaces are hydrophobic, the capture efficiency of oil droplets by single fibre, when possible, might be enhanced. Indeed, when both the collector and the particle have low wettability, capture efficiency is increased (Conova, 1999). This is because water is easily displaced between two hydrophobic surfaces. Therefore, for small droplets, the low surface wettability of the studied species may facilitate the capture of oil.

The low wettability and smooth texture of crustacean filter feeding appendages increase oil droplet capture and permit the manipulation and transfer of droplets between appendages. The filtering appendages of the two barnacles and D. magna were highly lipophobic and smooth in texture. The oil droplets adhered to the appendages with a high contact angle and minimal contact area. Several other fresh and saltwater filter feeding crustacean taxa also possess these qualities, highlighting a general phenomenon in nature. These taxa include calanoid copepods (Romano et al., 1999), shrimps (Felgenhauer and Abele, 1983), Triops (Møller et al., 2003) and rotifers (Silva-Briano et al., 2015). As droplet capture is greater when the appendage and the droplet have low wettability, the widespread lipophobicity and smoothness of appendages may be adaptations to feed on lipid droplets (Gerritsen and Porter, 1982). Decaying organisms will release lipid droplets that are rich in nutrients. An appendage with low wettability thus increases the probability of droplet capture, creating a feeding opportunity for these filter feeders. Also, oil fouling increases the energy needed for appendage movement by augmenting drag, and it clogs filtering surfaces. A captured droplet with a high contact angle requires less energy to allow detachment, lowering the risk of fouling (Becker et al., 2000).

This study is the first to characterize the capture of oil droplets by individual barnacles and a zooplankton. It is an experimental, lab-based study, where oil droplet size was less than 10 μm in diameter. We chose this size range because small droplets are close to neutrally buoyant and thus are more prone to remain in the water column. Small droplets are also appropriate to study because pelagic copepods will lower the size distribution of crude oil droplets via manipulation by the appendages and defecation (Uttieri et al., 2019), allowing these droplet sizes to persist in the environment. Nevertheless, work is needed to characterize the capture of large droplets. Larger droplets emerge from decaying organic materials and emulsified oil droplets from a tanker or oil rig spill range from 0.5 μm to several millimetres in diameter (Jordan and Payne, 1980). Even less is known about how aggregations of animals effect oil droplet capture. Pullen and LaBarbera (1991) showed that hill-shaped barnacle colonies will capture more particles than flat ones. This would indicate that at a certain flow, certain aggregations have more success at capturing oil than others.

In contrast, the harmful effects of oil, dispersed oil and its water-soluble fraction on zooplankton are well known (Almeda et al., 2013; 2014; Lee, 2013; Seuront, 2010). Here, we begin to understand the variables that govern the capture and ingestion of an oil droplet, and therefore how oil enters marine and aquatic food webs. These variables include appendage morphology, wettability and flow velocity. Future studies need to quantify droplet capture in a more realistic and complex mesocosm study, because population and community factors can alter capture (Almeda et al., 2013; Uttieri et al., 2019). Future efforts should also include particle image velocimetry (PIV) or other flow visualization tools to better understand the flows around these complex filtering structures. Analogous experiments with oil and surfactants are also needed to inform the debate about their efficacy.

The authors would like to thank the reviewers for their helpful remarks.