The fluid dynamics of barnacle feeding

Suspension feeding is a widespread and highly variable strategy in the marine environment, and suspension feeders can be found in almost all animal classes in the ocean (Riisgård and Larsen, 2010). Suspension feeding invertebrates display a diverse range of feeding mechanisms, relying on flagella, cilia, setae or tentacles to capture particles from the water (Riisgård and Larsen, 2010). Here, we explored the fluid dynamics of prey capture in suspension feeding, sessile barnacles.

To capture prey, barnacles rely on a cirral net, or fan, that consists of 12 specialized thoracic appendages (cirri), each carrying rows of setae along each side (Southward, 1955, 1987; Trager et al., 1990; Riisgård and Larsen, 2010) (Fig. 1). The cirral fan captures food particles as it sweeps through the water. During the power stroke, the cirral fan moves forward and creates a powerful flow of water past the barnacle (feeding current). This propelled flow field carries food particles into the capture zone, defined here as the region swept by the cirral basket. Previous visualizations of feeding currents generated by balanoid barnacles have suggested that a vortex is formed above the cirral fan at the end of the recovery stroke, and that this vortex transports food particles into the capture zone, where they may be captured during the subsequent power stroke (Trager et al., 1990).

Copepods and their nauplii form an important part of the diet of barnacles (Anderson and Buckle, 1983; Glasstetter et al., 1989; Hunt and Alexander, 1991). However, copepods and nauplii are sensitive to fluid disturbances and can perform powerful escape jumps in response to them (Fields and Yen, 1997; Kiørboe et al., 1999; Burdick et al., 2007; Kiørboe et al., 2010). This active avoidance strategy enables copepods to avoid capture in some situations. Trager et al. (1994) have shown that the capture efficiency of the barnacle Nobia grandis capturing Artemia salina, which does not display active avoidance, is more than twice that for copepods with active avoidance responses. Although Trager et al. (1994) found that many copepods entrained in the feeding current of the barnacles manage to escape, others have demonstrated that some copepods end up in the guts of the barnacles (Hunt and Alexander, 1991; Jianping et al., 1996).

Other small predators of copepods have evolved behavioral strategies to minimize the risk of being detected by their copepod prey. For example, larval fish that visually have identified a copepod prey at distance approach the prey very slowly to minimize the fluid disturbance (Kiørboe and Munk, 1986; Viitasalo et al., 1998). When at close distance, the larval fish rapidly strikes the prey while opening the mouth to suck in the prey before it can react (Holzman and Wainwright, 2009). Ambush-feeding copepods and arrow worms wait motionless for the (copepod) prey to come close before striking (Kiørboe et al., 2009). It is unclear how barnacles create a flow that is strong enough to allow a sufficiently large volume swept clear for prey without warning (all) the prey.

Here, we characterized the feeding flow of a barnacle using particle image velocimetry (PIV). We show that the beating of the cirral fan creates a feeding current that draws water into the capture zone both from behind and – counterintuitively – from the sides, but less so from the top. We found that the flow entering from the sides has low deformation rates and demonstrate that captured copepods are carried in this flow, whereas copepods that evade the feeding current mainly follow different paths. Finally, we used the Landau–Squire solution of flow due to a point force to rationalize the observed far-field feeding flow.

Balanus crenatus Bruguière 1789 were collected near Bergen, Norway, in the fall of 2019 (Fig. 1). The barnacles were kept in 70 liter plastic tubs in a recirculating system at 12°C and a salinity of 32 ppt and fed newly hatched Artemia salina twice a week. Barnacles were selected by measuring the cirri during feeding, and only individuals with cirri lengths of 8–10 mm were used in the experiments. Individual barnacles were isolated and fixed temporarily to PVC blocks using Tesa^® TACK adhesive putty. During filming, the barnacles were oriented such that the beat direction of the cirral fan was parallel to the aquarium side walls. Filming was performed at 12°C. Two barnacle individuals were used for the filming and PIV analysis presented below, and several individuals were used to film the trajectories of escaping and captured copepods. All individuals had orifice area ≅30 mm², basal length 20 mm, cirral fan height ≅10 mm, and cirral fan width between 8 and 10 mm.

Two individual barnacles were filmed in a 20×20×20 cm³ aquarium using a high-speed camera (Phantom V210; Vision Research, Wayne, NJ, USA) at 100 frames s⁻¹ and a maximum resolution of 1280×800 pixels on two separate occasions. The barnacles were placed with the base of the cirral fan 35 mm above the center of the aquarium bottom. A Cartesian coordinate system was defined with the origin of x and y at the base of the cirral fan and the x-axis parallel to the bottom and the lateral sides of the aquarium, positive in the direction of motion during the power stroke (Fig. 2). The origin of the z-axis was at the bottom of the aquarium. The aquarium was placed on a translating table that could be moved horizontally in the x- and y-direction.

For PIV measurements, the water was seeded with 10 μm hollow glass spheres (Potter industries) and a laser light sheet was shone perpendicular to the optical axis of the camera to intersect the barnacle. The laser used was a class 3B 500 mW laser (LaserKomponenten GmbH) with a wavelength of 645–660 nm and a laser sheet thickness of 2 mm. To resolve the flow structure near the barnacle, images were collected at a resolution of 1024×768 pixels at 200 frames s⁻¹ from two orientations facing the x–­z and y–z planes, respectively, yielding a spatial resolution of 0.6 mm between neighboring velocity vectors. In addition, we collected velocity measurements at multiple two-dimensional (2D) transects with a resolution of 1.18 mm between neighboring velocity vectors of the flow with the laser light sheet either in the x–­z or y–z planes, covering together a three-dimensional (3D) box around the barnacle. Each measurement consisted of capturing 35.7 s of video (∼40 beat cycles), followed by translating the aquarium 2 mm in either the x- or y-direction. We did 20 y–z transects separated by 2 mm in the x-direction, and 11 x–­z transects separated by 2 mm in the y-direction. We assumed that the flow is bilaterally symmetric with respect to the y=0 plane and, hence, mirrored the data from one side of the barnacle to construct the other side.

The PIV analysis was performed using the MatPIV1.16 package in MATLAB. We applied an interrogation area of 32×32 pixels and an overlap of 16 pixels, following a multi-pass cross-correlation using interrogation areas of 64×64, 64×64, 32×32 and 32×32 pixels. We analyzed five consecutive beat cycles extracted from each video. The signal-to-noise filter function in MatPIV that uses the cross-correlation results to evaluate the quality of each of the obtained velocity vectors was applied such that if the signal-to-noise ratio was below 1.3, the vector was replaced with the local mean. A local filter with a threshold of 1.9 standard deviations as well as a global filter with a threshold of 4.9 standard deviations were applied, and extraneous vectors removed by these filters were replaced by interpolation. The temporal mean percentage of removed and interpolated vectors was 11% in the x–z plane and 15% in the y–z plane for the 3D volumetric analysis, and only 4.3% in the x–z plane and 2.3% in the y–z plane for the close-up analysis. Most of the removed and interpolated vectors were within the cirral fan area, and in front of the barnacle shell as these parts were not masked in our analysis. The amount of water between the camera and the laser light sheet varies as the aquarium is translated horizontally during the experiment. To compensate for this, calibration images were recorded at each extreme of the domain, and calibration factors were computed for all transects by interpolation. The PIV analysis yielded velocity vector fields with 79×49 vectors for each image pair, resulting in a spatial resolution of 1.18 mm between neighboring vectors for the 3D volumetric analysis and 63×47 vectors with a spacing of 0.6 mm between neighboring vectors for the close-up images.

Because the duration of the beat cycles varied slightly (mean=1.04±0.08 s), we normalized the timing and length of each cycle and computed a representative time-dependent flow field based on five consecutive beat cycles, each divided into 60 time steps. This procedure was repeated for all transects to produce a 2D time-dependent representation of the flow field cycle. The 2D x–z and y–z transects were then combined into a 3D data structure cube for each time step. Because the resolution of the 2D flow fields (1.18 mm between vectors) was different from the distance between transects (2 mm), we used spatial interpolation to achieve a resolution of 2 mm between vectors in all directions. This 3D structure was used to calculate the force generated by the barnacle to drive the flow as described below. The obtained force was then used as an input to the Landau–Squire model presented below. The results from the 3D reconstruction were not sufficiently accurate to calculate the velocity derivatives necessary to determine the 3D maximum deformation rate, and therefore we used the detailed 2D flow fields to estimate the maximum deformation rate in the two orthogonal directions.

Copepods respond to fluid disturbances by escape reactions when the maximum deformation rate exceeds a threshold value of ∼0.5–10 s⁻¹ (Kiørboe et al., 1999). We define the maximum deformation rate, Δ, as the largest of the absolute values of the eigenvalues of the rate-of-strain tensor (Kiørboe and Visser, 1999). The corresponding eigenvector is in the principal direction in which a fluid element is either stretched or squashed the most. From the 2D flow fields, we estimated the maximum deformation rate for each transect. The smoothing and time-averaging leads to underestimation of the absolute magnitudes of the deformation rates. Also, the maximum deformation rate computed from a 2D slice of the flow field underestimates the actual 3D value. However, because we computed maximum deformation rates based on perpendicular transects showing the same spatial patterns, we feel confident that we have a fair representation of the spatial patterns.

Copepods of the species Temora longicormis and Acartia tonsa were filmed in separate experiments using a stereo camera setup. Three different recording sessions based on three similar sized individuals were recorded. Two synchronized cameras (DMK 33UP1300) fitted with 16 mm 1/2.5 inch lenses viewed the barnacle from perpendicular directions and covered a volume of 10×10×10 cm³ around the barnacle. The barnacle was placed in a 25×25×35 cm³ aquarium filled with seawater. Images were recorded using IC Capture (Imaging Source, version 2.5.1525.3931) image acquisition software at 100 frames s⁻¹ and a resolution of 1280×1024 pixels. 3D calibration and tracking of copepods were performed using the DLTdv8 digitizing tool for MATLAB (Hedrick, 2008). We recorded the tracks of copepods that were entrained in the barnacle feeding current, both captured copepods (n=36) and the tracks and escape positions of evading copepods (n=225). We analyzed all copepod captures and escapes from videos of two barnacle individuals that were filmed under identical conditions but on two separate occasions. Escape events are powerful jumps clearly different from routine swimming.

The PIV analysis revealed a feeding current consisting of two inflow regions at either side of the barnacle, an inflow region posterior to the cirral fan, and a narrow, high velocity outflow jet oriented downstream and slightly upwards (Figs 3 and 4A,B). With an order of magnitude of the beat frequency around f=1.0 Hz, width and the length of the cirral fan around a=b=10 mm, and the kinematic viscosity of seawater ν=1×10^–6 m² s⁻¹, we calculate a Reynolds number on the order of Re=abf/v≈100. We found that although the flow varies within the beat cycle (Fig. S1, Movie 1), particularly near the barnacle, its overall spatial structure is similar to the time-averaged flow, and we therefore used the time-averaged velocity field to compute the conservation of both mass and momentum. The time-averaged mass conservation (Eqn 1) applied on the control volume involved the flow rate through the back wall ⁠, the flow rates through the side walls ⁠, and ⁠, and the flow rate that exits through the front wall (Fig. 3). The flow rates through the bottom and ceiling of the control volume were small.

The results show that 44% of the water volume enter from behind (with an average velocity of 0.36 mm s⁻¹) and 56% (23%+33%) through the side walls (0.26 mm s⁻¹). The difference between the sum of the incoming flow rates (1814 mm³ s⁻¹) and the exit flow rate (1685 mm³ s⁻¹) is 7%, providing an error estimate for the PIV-based integral analysis. As the PIV measurements were collected sequentially, one cross-section at a time, variations in the barnacle behavior that took place during the measurement day have generated some deviations in the mass balance. The results were obtained first from the x–z cross-sections, and then from the y–z cross-sections, later in the day. The variations were apparent when we compared the measured outflow at the bottom (334 and ∼0 mm³ s⁻¹ at z=30 mm) and the inflow across the control volume ceiling (319 and 87 mm³ s⁻¹ at z=84 mm). These values were eventually omitted because their net contribution to the mass balance was negligible.

The results of the momentum integral balance (Eqn 2) are shown in Table 1. A summation of the momentum fluxes, pressure forces and shear forces results in an estimate of the force applied by the barnacle, ⁠. This value was used to estimate the coefficient c of the Landau–Squire jet solution as shown in the next section. Table 1 shows that the momentum flow rate that exits the control volume in the form of a high velocity narrow jet dominates the momentum contributions to the momentum balance equation.

The time-averaged maximum deformation rate shows regions of high values flanking the outflow jet, downstream from the capture zone (Fig. 4C). The time-averaged deformation rates in the feeding current coming in from the sides were low (mainly below 0.5 s⁻¹), but higher in the flow coming from behind the barnacle (exceeding 1 s⁻¹). This is evident both from the time-averaged flow (Fig. 4) and the time-varying flow (Fig. S2, Movies 2 and 3). Note that the deformation rates are temporarily much higher in the latter, with values up to 10 s⁻¹ in the flow arriving from the back, and up to 4 s⁻¹ in the flow arriving from the sides. Overall, the flow suggests a feeding current coming in from the sides with a maximum deformation rate signal too weak to be discovered by entrained zooplankton prey for some or most of the time. The time-resolved deformation fields indicate that the instantaneous maximum deformation rate is low from the sides during the recovery stroke (Fig. S2a,b), and highest immediately after the end of the power stroke while the cirri are inside the shell (Fig. S2d). Prey arriving from behind the barnacle may experience low maximum deformation rates, but often meet the cirral fan during the recovery stroke while it is unfolding. In these situations, the potential prey encounters the filter from the wrong side and will often escape on contact.

The point force flow depends strongly on the integration constant, c, and hence the magnitude of the force (Eqn 10) (Fig. 5). The low Reynolds number Stokes flow with c≫1 (Fig. 5A) has a fore–aft symmetry with flow arriving mainly from upstream of the force location and leaving downstream. With decreasing value of c corresponding to increasing Reynolds number, the flow becomes asymmetric in the fore–aft direction with an increasing fraction of the flow coming from the sides and less from behind (Fig. 5B–D). The force magnitude estimated above leads to the estimate c=0.0072 (Eqn 10 with ρ=1.0×10³ kg m⁻³ and ν=1×10^–6m² s⁻¹), with Fig. 5D thus best matching our study barnacle.

Of the 261 randomly tracked T. longicornis copepods, 36 were captured while the rest managed to escape (Figs 6 and 7). Most (30 out of 36) of the captured copepods arrived from the sides of the barnacle, while escape responses were recorded equally from both sides as well as behind and in front of the barnacle (Table 2, Figs 6 and 7). Captures of A. tonsa were too few to allow a meaningful mapping of the capture positions.

We have shown that the barnacle takes advantage of its counterintuitive fore–aft asymmetric architecture of the feeding flow to capture evasive prey in a way quite different from the ‘strategy’ of other small predators of copepods. Most captured copepods are brought into the capture zone with the flow arriving form the sides of the barnacle, whereas most copepods arriving from behind manage to escape (Table 2, Fig. 7). There are two potential explanations to this pattern: (i) prey arriving from the back must pass the beating cirral fan and are thus ‘warned’ by its activity, whereas prey are transported unimpeded to the capture zone when arriving from the sides; and (ii) the fluid rate of deformation is relatively low in the lateral flows, and higher in the flow from the back. We initially used copepodites of two different species, T. longicornis and Acartia tonsa, but none of the A. tonsa were captured. This difference in capture efficiency reflects the different responses to fluid disturbances between the two species: the threshold maximum deformation rate for escape in A. tonsa is approximately 0.5 s⁻¹, whereas in T. longicornis it is more than an order of magnitude higher (Kiørboe et al., 1999). These two extreme response thresholds cover the range recorded among a variety of zooplankton, including copepods, rotifers and ciliates (Kiørboe and Visser, 1999; Jakobsen, 2001). Although the first of the above mechanisms may be most important for T. longicornis, the spatial distribution of fluid deformation may additionally be important for more sensitive species. Differences in the sensitivity of potential prey may lead to selective feeding of barnacles, where the selection of prey is due to the sensitivity and evasive capabilities of the prey and not the preferences of barnacles. Some zooplankton, including Daphnia and Artemia, appear to have no escape responses to fluid deformation signals, and such species may serve as an easy prey for barnacles. However, in the ocean, such prey organisms are not as common. Our results focus on the flow into the capture zone and trajectories of prey from far upstream. The final interception by the cirri of individual particles may involve more complex flow, including a vortex which has been suggested to play a role in the capture of particles by barnacles (Trager et al., 1990).

The volumetric and momentum flow rate analysis showed that the feeding flow originates from the sides and behind the barnacle, and that the processed water left the control volume in a narrow jet in front of the barnacle (Fig. 3B, Table 1), with a maximum potential clearance rate between 1685 and 1814 mm³ s⁻¹. The actual clearance rate, however, will depend on the efficiency of the filter itself, and will therefore be a fraction of the maximum potential clearance rate. The unique feature of the feeding flow depends strongly on the force that the sweeping cirral fan creates, estimated here to be ⁠. From the rough, independent estimate of the force in Eqn 6 with the parameter values a=b=10 mm, f=1.0 Hz and ρ=1.0×10³ kg m⁻³, we found ⁠, largely consistent with the estimate from the flow field.

The force estimates are consistent with the formation of fore–aft asymmetry in the feeding current and the transport of potential prey through lateral feeding flows according to the Landau–Squire jet model, as can be seen in Fig. 5D. The rotationally symmetric and self-similar model disregards the effect of the bottom boundary, and it does not describe the details of the near-field flow around the beating cirral fan. However, the model captures essential qualitative features of the observed feeding current, i.e. the large volume of water that arrives at the capture zone from the sides of the barnacle and the flow leaving in the concentrated downstream jet (Fig. 4A,B). The point force model demonstrates that the large feeding current contributions coming in from the sides are not a consequence of some particular beat pattern or cirral fan deformation, and that such feeding flows can be expected to be found broadly for suspension feeders that actively generate feeding currents at intermediate Reynolds numbers.

Balanoid barnacles have two different feeding modes. In high ambient flow, the barnacle may orient the cirral fan into the current and thus passively strain water for prey, whereas in low flow conditions the barnacle may switch to the active feeding mode with rhythmic sweeping of the cirral fan (Trager et al., 1990; Pullen and Labarbera, 1991). We examined the active feeding mode of barnacles in quiescent water. However, barnacles are often exposed to external flow, which will change the feeding current and may affect their ability to capture evasive prey. High ambient flow may increase the transport of food particles in the capture zone and will likely change the overall pattern of flow around the barnacle, resulting in different abilities to capture evasive prey. Further studies into barnacle feeding under variable ambient flow conditions are needed to shed more light on this aspect of barnacle feeding.

The Reynolds number of the flow, generated by the beating cirral fan, is proportional to its linear dimension and the speed with which it is swept through the water. Because the beat frequency is almost independent of size (own observation), it implies that the Reynolds number scales proportionally to the linear dimension squared, and hence that small individuals operate at much lower Reynolds numbers. Thus, the flow generated by a newly settled individual will tend towards a Stokeslet flow with fore–aft symmetry and no ‘quiet’ and uninterrupted flow from the sides (Fig. 5A). Such feeding flows may lead to ‘hydrodynamic starvation’ of newly settled barnacles if they depend on evasive plankton prey. This would predict a diet shift during development of settled barnacles, from passive phytoplankton-type prey in newly settled specimens to inclusion of evasive zooplankton in larger individuals, but to our knowledge such a shift has not been examined, nor has the feeding flow of newly settled barnacles been described.

We thank Christoph Noever for his help in the collection of the barnacles used in this study. We also thank the reviewers for their careful consideration of our manuscript and the comments and suggestions for improvements they provided. This research was conducted at the Centre for Ocean life, National Institute of Aquatic Resources, Technical University of Denmark.

This article has an associated ECR Spotlight interview with Kristian Maar.