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1California State University, Fullerton, 800 North State College Boulevard, Fullerton,CA 92867, USA. 2Oregon State University, 3029 Cordley Hall, Corvallis, OR 97330, USA.*Corresponding author. Email: empaig-tran@fullerton.edu (E.W.M.P.-T.); james.strother@oregonstate.edu (J.A.S.)

Divi et al., Sci. Adv. 2018;4 : eaat9533 26 September 2018

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Manta rays feed using ricochet separation, a novelnonclogging filtration mechanismRaj V. Divi1, James A. Strother2*, E. W. Misty Paig-Tran1*

Solid-liquid filtration is a ubiquitous process found in industrial and biological systems. Although implementa-tions vary widely, almost all filtration systems are based on a small set of fundamental separation mechanisms,including sieve, cross-flow, hydrosol, and cyclonic separation. Anatomical studies showed that manta rays havea highly specialized filter-feeding apparatus that does not resemble previously described filtration systems. Weexamined the fluid flow around the manta filter-feeding apparatus using a combination of physical modelingand computational fluid dynamics. Our results indicate that manta rays use a unique solid-fluid separationmechanism in which direct interception of particles with wing-like structures causes particles to “ricochet” awayfrom the filter pores. This filtration mechanism separates particles smaller than the pore size, allows high flowrates, and resists clogging.

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INTRODUCTIONSeveral fundamental mechanisms for solid-fluid separation havebeen described in the biological and engineering literature, includingsieve (1, 2), cross-flow (3–6), hydrosol (7), and cyclonic separation(8). Sieve filtration passes a mixture of particles and fluid through astructure with regularly sized pores, causing the particles to be re-tained while the fluid is drained. Although effective, sieve filters musthave pore sizes smaller than the particle size, and they inevitably clogin use (2, 8, 9). Cross-flow filtration is similar to sieving, except thatthe incoming flow runs parallel rather than perpendicular to the fil-ter. This configuration shears captured particles off the filter’s sur-face, which reduces but does not eliminate clogging (5, 6). Unlikesieve and cross-flow filters, hydrosol and cyclonic filtration do notrequire regularly sized pores. Hydrosol filtration captures particlesusing “sticky” structures within the filters, which allow these filtersto capture particles smaller than their pore size, although they alsoinvariably become clogged (10, 11). Cyclonic filtration uses a high-speed, rotating flow that flings dense solid particles to the peripherywhile allowing fluid to pass through the center (8, 12, 13). This sep-aration mechanism requires the solid particles to be denser than thefluid but is resistant to clogging (12) and has been widely used withinthe bagless vacuum industry (12, 13).

A large diversity of aquatic animals feed by filtering plankton andother food particles out of the water. It had long been thought thatmany teleost fish species capture prey by sieving, passing plankton-laden water through elongate gill rakers that protrude from the gillarches into the pharynx. However, gut content analysis in several tel-eost fish species demonstrates that fishes routinely capture planktonsmaller than the openings between the gill rakers, indicating that thisprocess is more complex than simple sieving (14, 15). Several recentstudies have examined flow in the buccal cavity and suggest thatcross-flow filtration plays an important role in filter-feeding in tele-ost fishes (5, 15) and that separated vortices may generate additionalclearing action that further reduces clogging (16, 17). In addition,manyanimals are known to feed using hydrosol-based mechanisms, includ-ing bryozoans, crinoids, and sponges (10). It would be surprising for

large fishes to rely on hydrosol filtration, as this would require largevolumes of mucus and produce filter clogging. To our knowledge,cyclonic filtration has not been demonstrated in any organism.

Manta rays are large elasmobranchs that feed by swimming withopen mouths, capturing small zooplankton (51 to 100 mm), micro-crustaceans (101 to 500 mm), and mesoplankton (>500 mm) whileexpelling seawater through the gill slits (11, 18). The filtering appa-ratus in these animals is a highly modified gill raker, comprisinglong, parallel arrays of leaf-like filter lobes (11, 18–20). Water movesunidirectionally through the buccal cavity, over the filters, and isexpelled out the filter pores to the parabranchial chamber. The ori-entation of the filter lobes within the cavity suggests that water im-pinges on the filters in both forward (wing-like posterior filters)and reversed (spoiler-like anterior filters) directions (Fig. 1). De-spite an understanding of the anatomy, the separation mechanismused by this filtering apparatus is not clear. In contrast to what wouldbe expected for sieve, cross-flow, hydrosol, and cyclonic separationmechanisms, these animals capture nearly neutrally buoyant parti-cles smaller than the pore size using nonsticky filter elements with-out clogging (20).

RESULTS AND DISCUSSIONTo examine how these animals capture plankton, we examined flowover a physical model of the filtering apparatus. A three-dimensional(3D) printed model of an array of filter lobes was manufacturedusing morphological parameters measured in Manta birostris (Fig. 1,A and B). We positioned this model in an open-ended flow tank thatwas adjusted to mimic the flow conditions in the buccal cavity ofM. birostris (fig. S1A). Since experimental measurements of the flowvelocities in the buccal cavity are not available, the freestream and trans-verse flow velocities were estimated using swimming speeds, the conti-nuity equation, and anatomical data (see Materials and Methods).Neutrally buoyant particles larger than the pore size would be expectedto be filtered with 100% efficiency. To test the performance limits of thefilter, we examined neutrally buoyant particles (hydrated Artemia sp.cysts; average diameter, 275 mm) that were smaller than the pore size(>99%of the cysts smaller than pore size of 340 mm; fig. S1B) andwouldpass through the model if it were functioning as a sieve filter. Filteredand unfiltered water was collected and used to calculate filtration effi-ciency. We found that a large fraction of these particles were also

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excluded by the filter (wing, 19 ± 5% efficiency; spoiler, 62 ± 5% ef-ficiency; mean ± SEM), and visual inspection revealed no clogging.

These results suggest that the manta filtering apparatus can sepa-rate small particles from the fluid, but what is the mechanism behindthis effect? To address this question, we placed a 3D-printed physicalmodel of a filter lobe array into a recirculating flow tank, againmatch-ing the freestream and transverse flow velocities to estimates for thebuccal cavity. Flow around the filter was visualized by injecting dyeupstream and imaging the dye pathlines around the filter (Fig. 1, CandD). This approach allowedus to identify the flow structures aroundthe filter lobes, even in cases where small spaces, reflection, and oc-clusion would complicate quantitative analysis (for example, particleimage velocimetry). We found that the flow over the filter lobes ismarkedly different than expected for a typical sieve filter. In the wingorientation, flow separation occurred behind the leading edge of eachfilter lobe, resulting in a large, captive vortex within each pore. Filtersin the spoiler orientation displayed similar flow patterns, although thedirection of the freestream flow was reversed.

To better understand how solid particles interacted with the filter-ing apparatus, we next introduced neutrally buoyant particles (hydratedArtemia sp. cysts) into the upstream flow and recorded the trajectoryof these particles as they passed over the filter (Fig. 1, E and F). For thewing orientation, we observed that particles often directly impacted theleading edge and were then re-entrained within the freestream flow.Similarly, we observed increases in the vertical velocity at positionscorresponding to the leading edge of the filter lobes. In the spoiler ori-entation, particles passing over the filter appeared to glide over thetrailing edge of each filter lobe before being re-entrainedwithin the flow,and therewere similar increases in the vertical velocity at correspondinglocations.

What physical forces cause the particles to be repelled away fromthe filter while allowing fluid to pass through? To address this ques-tion, we constructed a computational fluid dynamics (CFD) modelof the flow over an array of filter lobes (Fig. 2A). As with the physicalmodels, the model geometry was based on morphological measure-

Divi et al., Sci. Adv. 2018;4 : eaat9533 26 September 2018

ments in M. birostris, and the freestream and transverse flow veloc-ities mimicked those in the buccal cavity. To visualize the flowfields, we calculated the fluid streamlines that pass through a porenear the center of the array. For the wing orientation, these stream-lines indicate thatwater glides above the lobe array, forms a thin bound-ary layer on the upstream surface of the lobe, is swept around acaptive vortex within the pore, and is then washed into the filtrateflow. The streamlines for the spoiler orientation are surprisingly sim-ilar, except that the streamlines exhibit more pronounced curvature asthey pass around the captive vortex. These flow fields closely mirrorthe results from our dye visualization experiments. In addition, thecomputed hydrodynamic resistance was very low for both the wingand spoiler orientations (wing, 1161 Pa s m−1; spoiler, 1673 Pa s m−1),consistentwith previous experimentalmeasurements (11). Since the en-ergetic cost of filtration is proportional to the hydrodynamic resistancefor a fixed flow rate, these lowhydrodynamic resistance valuesmayhavean important role in limiting energetic expenditure and achievingenergy balance in this group of animals.

To understand how these flow patterns produce solid-fluid sep-aration, we next constructed a computational model to simulate themotion of particles carried by the flow (Fig. 2B). Spherical particleswere introduced into the flow upstream of the filter array, with initialpositions distributed across the fluid streamlines that passed througha filter pore near the center of the array. Since the solid particles werereleased along fluid streamlines, deviation of a solid particle from thecorresponding streamline indicates solid-fluid separation and solidparticles that do not pass through the pore represent filtration events.

For the wing orientation, simulated solid particles initially followfluid streamlines and glide over the top of the filter array. However, asthe fluid approaches a filter element, streamlines pass very near to theleading edge of the filter lobe before being diverted into the filter pore.Since they have finite size, solid particles cannot follow this path andencounter the leading edge of the filter lobe by direct interception. In-stead of sticking as in classic hydrosol filtration, contact forces causethe particles to “ricochet” away from the filter pore and back into the

Fig. 1. The manta ray filtering apparatus effectively separates plankton from seawater. (A) Manta ray during feeding behavior (photo credit: S. Kajiura, FloridaAtlantic University). (B) Gill raker (left) and tracing of filter lobes (right) (20) [photo credit: E.W.M.P.-T., California State University Fullerton (CSUF)]. (C and D) Fluidpathlines visualized using dye injection for filter lobes in wing (C) and spoiler (D) orientations. (E and F) Trajectories of solid particles (hydrated Artemia sp. cysts)passing over filter apparatus and vertical velocity of particles (median ± SEM, n = 12) for wing (E) and spoiler (F) orientations.

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faster-moving freestream flow. This process repeats at the next filterlobe and causes the particles to be repeatedly excluded from the fil-trate. These conclusions and the simulated particle trajectories arein agreement with the results of our physical modeling experiments(Fig. 1, E and F, versus Fig. 2B). Contact forces also appear to play akey role in solid-fluid separation for filters in the spoiler orientation. Inthis case, we found that simulated solid particles initially followedstreamlines as they passed over the filter array. However, the fluidstreamlines then passed very close to the trailing edge of the precedinglobe. As for the wing orientation filters, solid particles with finite sizecannot follow these streamlines and contact forces cause the particlesto ricochet back into the faster freestream flow. This process hasparallels to direct interception hydrosol filtration in which a particlefollowing a streamline collides with a sticky surface and is captured(1). However, here, the particle recoils elastically from the surfaceand moves into streamlines that pass over the filter pore, resultingin concentration of particles in the water above the filter.

We next calculated the filtration efficiency for particleswith a rangeof sizes and densities. We found that filtration efficiency increasedmarkedly when the particle size exceeded ~200 mm, which is notablysmaller than the filter pore size of 340 mm (fig. S2B). In contrast,changes in particle density had relatively little effect on filtration effi-ciency, within a biologically realistic range of densities. This size selec-tivity agrees with our physical modeling and with estimates from wildmanta rays as well (11, 18). Insensitivity of the filtration process to par-ticle density is consistent with the ricochet solid-fluid separationmechanism, which results from contact forces that are not directlyaffected by the specific density of the solid particle. It is possible thatthe complex shapes and escape responses of zooplankton would alsoaffect capture dynamics (21, 22). Although these effects are difficult to

Divi et al., Sci. Adv. 2018;4 : eaat9533 26 September 2018

quantitatively model with the data available, the shear stress at the fil-ter lobes might be expected to elicit escapes responses away from thefilter, which could also enhance the observed filtration effects.

Since the freestream flow velocity appeared to have a major role inestablishing the flow fields that drive the solid particles to contact thefilter lobes (fig. S3, A and D), we next asked how the freestream flowvelocity affects filtration efficiency. The CFD model was solved for arange of freestream velocities (0.05 to 0.7 m/s), while the pressureacross the filter was held constant, and the filtration efficiency wascalculated for 300-mm neutrally buoyant particles (fig. S3, E and F).We found that filtration efficiency increased sharply when freestreamvelocity exceeded 0.300 m/s, which is about half of the estimated ve-locity. This dependence on the freestream flow velocity is consistentwith the proposed mechanism and also suggests that the mechanismoperates effectively over a large range of freestream flow velocities.

In classic direct interception filtration, capture efficiency increaseswith Reynolds number (Re) as a result of streamline compression(23, 24). To determine whether there is a corresponding effect inmo-bulid filters, the CFD model was solved for a range of Re values, andthe filtration efficiency was calculated for neutrally buoyant particles(fig. S3, G and H). To preserve similitude, Re was varied by changingfluid viscosity while holding freestream and transverse velocitiesconstant. For both spoiler and wing configurations, the predicted fil-tration efficiency was zero for low Re, increased with Re, and reached100% for Re greater than ~900. This threshold is just below the valueestimated for freely swimming M. birostris (Re = 1075), which maysuggest that Re is maintained at a value large enough to produce fil-tration but small enough to limit turbulence. These results also indicatethat smaller particles cannot be captured by simply scaling down thefilter morphology while holding fluid properties and flow velocities

Fig. 2. Computational modeling indicates that solid particles ricochet off manta ray filter lobes. (A) Flow field around the M. birostris filtering apparatus in wing(top) and spoiler (bottom) configuration, predicted using CFD model (streamlines in white; background indicates the velocity magnitude). (B) Calculated trajectories offluid (blue) and solid particles (center of mass, red; diameter, 350 mm; neutrally buoyant) as they pass over the filtering apparatus. The outline of a representative particle(dark red) shows the size of the particles relative to the filtering apparatus. Although they start from the same position, fluid passes through the filter pore, while solidparticles are excluded. (C) Predicted filtration efficiency of the apparatus as a function of solid particle diameter and density (in kg/m3), with the pore size indicated.Sizes of plankton indicated on the background. Small zooplankton (51 to 100 mm; dark gray), microcrustaceans (101 to 500 mm; medium gray), and large zooplankton(>501 mm; light gray).

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constant, since this is equivalent to decreasing Re and results in adecrease in filtration efficiency. However, smaller particles wouldbe expected to be filtered if the morphology was scaled down whilefluid velocities were increased to hold Re constant.

We also examined how qualitative changes in the filter morphologymight affect filtration. Micro–computed tomography (mCT) was usedto reconstruct the 3Dmorphology of the filtering apparatus ofMobulatarapacana, which have a similar filtering apparatus to M. birostrisexcept with pore sizes approximately four times larger (Fig. 3A andfig. S4). As above, a computational model was used to predict the flowfield and plankton trajectories around the filtering apparatus using free-stream and transverse velocities estimated forM. tarapacana. Althoughthe pore was 1100 mm wide, filtration efficiency rapidly increased forparticles larger than ~250 mm. Similar toM. birostris, simulated plank-ton particles were excluded by the filter following contact with thetips of the filter lobes. These results indicate that M. tarapacana andM. birostris feed using a similar solid-fluid separationmechanism andthat thismechanism can effectively filter particles that aremuch smallerthan the pore size (Fig. 3B). Compared toM. birostris, the filtering ap-paratus ofM. tarapacanawas predicted to operatewith approximatelysix times smaller transverse velocity (~10mm/s versus ~57mm/s) andrequire approximately seven times smaller pressure head (wing, 11 Paversus 56 Pa; spoiler, 11 Pa versus 100 Pa) but filter plankton particles ofsimilar size (Fig. 3C). These differences may reflect specialization of thefiltering apparatus for different foraging strategies. SinceM. tarapacanais predicted to have a lower flow rate and pressure head, it would beexpected to have reduced plankton consumption but would also beexpected to have decreased drag and energetic expenditure. A detailedcomparison would require more information on feeding behaviors andthe plankton size distribution where the fishes are actively feeding butwould be a very interesting area for future studies.

Our results suggest that the manta ray filtering apparatus operatesthrough a unique solid-fluid separation mechanism, which we havetermed ricochet separation. This solid-fluid separation mechanism

Divi et al., Sci. Adv. 2018;4 : eaat9533 26 September 2018

may have interesting industrial applications, since it operates at highflow rates, effectively filters neutrally buoyant particles, and resistsclogging. Captured particles are concentrated above the filter ratherthan forming a cake over the filter, which may obviate the need forsecondary cleaning mechanisms that are often costly and time con-suming (8, 25). In addition to the engineering applications, mobulidrays are increasingly being targeted by illegal commercial and artisanalfisheries (26–28), and an improved understanding of the physiology offilter feedingmay be useful for predicting the habitat usage of mobulidrays and implementing appropriate protective measures.

MATERIALS AND METHODSSpecimen collection and examinationThe morphology of theM. birostris filtering apparatus was measuredfrom two specimens (one provided by the Smithsonian Museum ofNatural History and one donated by R. Rubin and maintained byA. Summers). Calipers were used to measure the dimensions of thefilter lobes (fig. S2B). Themorphology ofM. tarapacanawasmeasuredby performing a mCT scan of a specimen provided by the Scripps In-stitution of Oceanography. M. tarapacana rakers were scanned usinghigh-resolution mCT imaging (Bruker SkyScan 1272) scanned at 60 kV,with a resolution of 38.9 mm at the University of Washington FridayHarbor Laboratories. mCT scans were then reconstructed from 8-bittagged image file format stacks as 3D images using Amira software(version 6.4). The mCTmodel was then used tomeasure the dimensionsof the filter lobes (fig. S4).

Construction of physical modelsMobulid filters are composed of repeating filter lobes connected by acentral cartilaginous raphe [see Paig-Tran et al. (18) for full description].Computer models of the filtering apparatus of M. birostris were con-structed from themeasuredmorphology (Autodesk software 123DDe-sign), and then, physical models were 3D printed. For the filtration

Fig. 3. Morphology of filtering apparatus determines filtration properties. (A) M. tarapacana filter (top) and a mCT reconstruction of a single row of filter lobes(bottom) (photo credit: E.W.M.P.-T., CSUF). (B) Calculated trajectories of fluid (blue) and solid particles (center of mass, red; diameter, 350 mm; neutrally buoyant) as theypass over the filtering apparatus. The outline of a representative particle (dark red) shows the size of the particles relative to the filtering apparatus. (C) Predictedfiltration efficiency of the apparatus as a function of solid particle diameter and density (in kg/m3), with the pore size indicated. Sizes of plankton indicated onbackground. Small zooplankton (51 to 100 mm; dark gray), microcrustaceans (101 to 500 mm; medium gray), and large zooplankton (>501 mm; light gray).

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efficiency experiments, multiple rows of filter lobes were positionedtogether so that they could be inserted into the bottom surface of theflow tank (fig. S1A). Models were printed at 1× scale [32-mm layerthickness, 10 filter rows in lateral direction, and 13 filter lobes instreamwise direction; ProJet 3510SD (3D Systems)]. For the dye visu-alization experiments,models consisted of a single row of filter lobes at4× scale [100-mm layer thickness, one filter row in lateral direction,and 13 filter lobes in streamwise direction; ProJet 460 (3D Systems)].For particle tracking experiments, models were also a single row offilter lobes but were printed at 1× scale [50-mm layer thickness, onefilter row in the lateral direction, and 13 filter lobes in streamwisedirection; Form 2 printer (Formlabs)].

Filtration efficiencyThe filtration efficiency was determined by placing 1× scale physicalmodels into a customized flume, introducing particles upstream of thefilter and measuring the particle concentration in the filtrate and un-filtered water (fig. S1A). The working section of the flume was cylin-drical (diameter, 48 mm), and the physical model was the bottom halfof the working section. The freestream flow velocity was adjusted sothat the Reynolds number in the flume was similar to the flow in thebuccal cavity of a freely swimming animal

Re ¼ rUDh

ð1Þ

where Re is the Reynolds number, r is the fluid density, U is the free-stream fluid velocity, D is the distance between the lobes, and h is thefluid dynamic viscosity. The Reynolds number was estimated as Re =1075, taking the freestream velocitywithin the buccal cavity for a freelyswimming animal as 550mm/s (80% of swimming speed of 680mm/s)(18). The flow rate through the filter was controlled using a valvedownstream of the filter array and was adjusted so that the ratioof freestream to transverse velocity matched estimates for a freelyswimming animal. This ratio was approximated from the continuityequation

ufut

¼ Ax

Amð2Þ

where uf is the freestream velocity, ut is the transverse velocity, andAx/Am is the ratio of the filter cross-sectional area to the mouth area.The ratio Ax/Am was estimated as 10:1 from available photographs offeeding animals and preserved gill arches (Fig. 1, A and B). HydratedArtemia sp. cysts were used as particles (size distribution in fig. S1B;density, 1.02 to 1.08 g/ml) and were introduced into the flow via aVenturi injector. This method of injection ensured that particles wereuniformly distributed throughout the upstream flow and were un-damaged. Water exited the experimental system by passing eitherthrough the filter array or through the unfiltered outlet. In eithercase, the flow was passed through a fine mesh filter (100 mm) to col-lect the particles and then into a reservoir to record the total water vol-ume. The particle concentration was calculated as the mass of theparticles divided by the water volume. The filtration efficiency wasthen calculated as

E ¼ 1� sfsu

ð3Þ

Divi et al., Sci. Adv. 2018;4 : eaat9533 26 September 2018

where E is the filtration efficiency, sf is the particle concentration inthe filtrate, and su is the particle concentration in the unfiltered water.Trials lasted for 2min each (n= 3). The size distribution of the injectedparticles was measured by imaging the hydrated Artemia sp. cysts(ZEISS Stemi 508, Carl Zeiss Microscopy) and then analyzing theimages using a custom-written MATLAB script (n = 4321 particles).

Dye injection flow visualizationPhysical models at 4× scale were suspended in the center of the work-ing section of a recirculating flume (Research Water Tunnel Model1520, Rolling Hills Research Corporation). Blue dye (ESCO Foods,Deep Blue Shade) was released upstream of the filter models andimaged passing over the model [resolution, 4000 × 3000 pixels;60 frames per second (fps); Panasonic Lumix DMC-FZ300]. Thefreestream flow velocity was adjusted so that the Reynolds numberin the flume (Re = 745) approximately matched the filtration efficiencyexperiments. The physical model was angled relative to the freestream(~20° angle of attack) until the ratio of freestream to transverse veloc-ity also matched the filtration efficiency experiments (10:1). This ratiowas measured by recording the angle at which the dye stream ap-proached the filter array [q = arctan(ut/uf) = 6°].

Particle trajectory analysisPhysical models at 1× scale were suspended in a flume, similar to dyeinjection experiments. Particles (hydrated Artemia sp. cysts) were re-leased upstream and imaged passing over the filter (resolution, 1280 ×1024 pixels; 240 fps; Edgertronic camera, Sanstreak Corp). To accu-rately follow these small particles, it was necessary to decrease theflow velocity (180 mm/s), so the Reynolds number was decreasedto Re = 309. Dye injection experiments were used to confirm thatthe flow patterns around the filter were qualitatively similar to thatat higher flowvelocities. In addition, CFD simulationswere performedmirroring this freestream velocity (180mm/s) and freestream to trans-verse velocity ratio (wing, 8.5:1 at 12 Pa; spoiler, 8.3:1 at 18 Pa), andpredicted particle trajectories and filtration efficiencies were similar tothose at higher freestream velocities (for 300-mm neutrally buoyantparticles: wing, 17%; spoiler, 54%). The trajectories of particles thatinteractedwith the physicalmodel were recorded using ImageJ software.The trajectories were shifted to a common origin using the first filterlobe that the particle interacted with as a reference point. Verticalvelocity as a function of position was then calculated by fitting thepositional data to a smoothing spline and taking the derivative (MATLAB,MathWorks Inc).

CFD modelingThe CFD model was constructed to mimic the geometry and flowconditions of the filtering apparatus of M. birostris (fig. S2A). Thismodel was designed to reproduce the flow fields around individualfilter lobes while avoiding the need to reproduce the complex geom-etry of the entire buccal cavity. Since individual filter lobes are nearlyprismatic in shape, the model was constructed as a 2D cross sectionthrough the filter. Flow enters from the left side of the geometrythrough an inlet with a prescribed uniform velocity boundary condi-tion (570 mm/s, Re = 990 similar to physical model) and then passesover a solid structure containing a filter lobe array (no-slip boundarycondition on all surfaces). A negative uniform pressure boundary con-dition is prescribed on the outlet behind the filter lobe array, whichdraws a fraction of the freestream flow through the filter pores. Themagnitude of the negative pressure was varied until the ratio of the

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freestream velocity to transverse velocity was approximately 10:1(wing, 12:1 at 56 Pa; spoiler, 9.3:1 at 100 Pa) similar to that estimatedfor M. birostris and that used for the physical modeling experiments.The remaining freestream flow exits the system through an outlet sur-face above the filter lobe array, with a prescribed zero-pressure bound-ary condition. Themodeled filter array consisted of 15 filter lobes, andto avoid edge effects, all analyses were performed on the fifth filter lobein the array.

This model was solved using a commercial CFD software suite(Adina 9.3.1). The geometry was meshed with three-node triangularelements, and mesh size functions were used to refine the mesh inregions with steep velocity gradients (fig. S2C). Mesh independencewas verified by decreasing themesh size and confirming that neither theflow patterns around the filter nor the flow rate through the filter wasaltered. The Reynolds number for this system is intermediate, so theflow was modeled using the unsteady, incompressible Navier-Stokesequations rather than Reynolds-averaged Navier Stokes equations ora subgrid-scale turbulence model. The governing equations were thensolved using a finite elementmethod (flow condition–based interpolationelements, second-order accurate time integration, 100-ms simulation,and 1-ms time steps). Although the model was solved using unsteadyequations, it converged to a steady-state solution, and that steady-statesolution was used for all subsequent analyses. For analyses in whichthe Re was varied, the viscosity was altered, while the geometry, free-stream velocity, and transverse velocity were held constant. Since thetransverse velocity is not directly controlledby any applied boundary con-dition, it was held constant by iteratively adjusting the downstream pres-sure using the secant method (fig. S3, G and H).

Simulations for M. tarapacana were performed similarly (fig. S4).In this species, the mouth area during feeding appears to be smallerthan the cross-sectional area of the buccal cavity, and continuity re-quires a corresponding decrease in the flow velocity. To capture thiseffect, the freestream flow velocity was approximated as 0.3 m/s (Re =1115) or 45% of the estimated swimming speed of 0.680m/s (18). Thetransverse velocity was estimated as 10 mm/s from the continuityequation (Eq. 1), with Am = 0.0057 m2, uf = 0.612 m/s (90% of theswimming speed of 680 mm/s), and Ax = 0.334 m2 (18). Using theseestimates, the magnitude of the negative pressure was varied until theratio of the freestream velocity to transverse velocitywas approximate-ly 30:1 (wing, 36:1 at 11 Pa; spoiler, 29:1 at 11Pa).

Solid particle trajectory simulationsThemovement of solid particles through the flow field was simulatedusing equations of motion that included pressure gradient, addedmass, drag, Saffman lift, and contact forces

∑F ¼ msdvdt

¼ Fp þ Fa þ Fd þ FSa þ Fc ð4Þ

wherems is the mass of the particle, andv is the particle velocity. Thepressure gradient and added mass are

Fp ¼ mfDuDt

ð5Þ

Fa ¼ � 12mf

dvdt

� DuDt

� �ð6Þ

Divi et al., Sci. Adv. 2018;4 : eaat9533 26 September 2018

where mf is the mass of fluid displaced by the particle, and u is thefluid velocity (29, 30). The drag was taken as

Fd ¼ 12CdrfApjurjur ð7Þ

Cd ¼ 24Re

1þ Re2=3

6

� �ð8Þ

whereur is the relative fluid velocity ður ¼ u� vÞ, rf is the fluid den-sity, Ap is the projected area of the particle, Re is the Reynolds num-ber ðRe ¼ 2arf jurj=hÞ, a is the particle radius, and h is the dynamicviscosity of the fluid (31). The shear-induced Saffman lift force wascalculated using the following approximation

FSa ¼ CLSa ur � w ð9Þ

CLSa ¼ 6:46 a2gffiffiffiffiffiffiffiffirf hjwj

rð10Þ

g ¼1� 0:3314 a1=2� �

exp �Re10

� �þ 0:3314 a

1=2Re < 40

0:0524ða ReÞ1=2

else

8><>: ð11Þ

a ¼ ajwjjurj ð12Þ

where w is the vorticity (32, 33). The contact force was calculatedusing a damped linear model that excludes tensile forces

Fc ¼ ks d � kd v⋅nð Þn d > 0 and ks d � kd v⋅n > 00 else

�ð13Þ

kd ¼ 2Dffiffiffiffiffiffiffiffiffiffiksmp

qð14Þ

where ks is the spring constant, kd is the damping constant, n is thenormal vector for the surface, d is the intersection distance betweenthe particle and the surface, and D is the damping ratio (34). A sen-sitivity analysis suggested that ks and D had little effect within a widerange of values, so ks was set to a large value to mimic infinitely stiffsolids, and D was set to 0.9. The Basset history term and Faxén’s cor-rection for velocity curvature were both neglected.

The equations of motion were solved using a custom-writtenprogram, which was implemented in C for efficiency. This programsolved the ordinary differential equation describing the particle tra-jectory using an explicit Runge-Kutta-Fehlberg method (0.025-mstime steps; GNU Scientific Library version 1.15). The fluid flow ateach particle position was calculated by linear interpolation of theCFD solution using the same triangular mesh and evaluating the ve-locity and velocity gradient (libMesh 1.2.1).

Similar to our CFD analysis, to avoid edge effects, our simulationsof particle trajectories were focused on a single filter pore (fifth lobe inarray). We first calculated the flow streamlines that passed through

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SC I ENCE ADVANCES | R E S EARCH ART I C L E

this filter pore by uniformly seeding the downstream edge of the filterpore with “virtual” fluid particles and then tracing the trajectories ofthese fluid particles backward in time to their upstream origin(solving dr/dt = −u). Solid particles (n = 30 for each condition) werethen introduced into the flow uniformly distributed across this rangeof upstream positions and with an initial velocity equal to the fluidvelocity, and the motion of the particles over the filter array was sim-ulated using Eq. 4. Since solid particles were introduced into the flowalong streamlines that are known to pass through the pore, deviationbetween the solid and fluid trajectory represents solid-fluid separa-tion and failure of the solid particle to pass through the filter porerepresents a filtration event. Conservatively, we considered particlesto be filtered only if they also passed over the filter pore immediatelydownstream of the selected pore. The filtration efficiency was thencalculated as the percentage of the solid particles that were filtered.

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SUPPLEMENTARY MATERIALSSupplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/9/eaat9533/DC1Supplementary Materials and MethodsFig. S1. Details of experiments used to measure particle filtration.Fig. S2. Geometry of the M. birostris filtering apparatus.Fig. S3. Computational modeling predicts particle filtration.Fig. S4. Geometry of the M. tarapacana filtering apparatus.

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Acknowledgments: We thank A. Daveler for assistance building our physical models andS. Karl for guidance with imaging. We also thank A. Summers, M. Kolmann, K. Ford,K. Evans-Jackson, and the Karel F. Liem Imaging Center at the University of Washington FridayHarbor Laboratories for assistance with mCT scanning and allowing us access to your flume;H. J. Walker, Smithsonian, and R. Rubin for providing our specimens; J. Javier for assistance withthe models and the CSUF 3D printing facility for printing our models; and S. Walker, E. Read,and A. Loh at CSUF. Funding: This study was supported by the CSUF Jr./Sr 2017–2018 IntramuralAward, the Stephen and Ruth Wainwright Fellowship, and the Sigma Xi Grant-in-Aid ofResearch Award. Author contributions: R.V.D.: conceptualization, methodology, and formalanalysis. J.A.S.: conceptualization, methodology, funding acquisition, formal analysis,visualization, and writing. E.W.M.P.-T.: conceptualization, methodology, funding acquisition,formal analysis, visualization, and writing. Competing interests: E.W.M.P.-T. is an inventor ona provisional patent related to this work filed by the University of Washington (provisionalpatent 2014, case 15-079-US, filed on 2016). The authors declare that they have no othercompeting interests. Data and materials availability: The code used for computationalmodeling is available from J.A.S. All data needed to evaluate the conclusions in the paper arepresent in the paper and/or the Supplementary Materials. Additional data related to thispaper may be requested from the authors.

Submitted 21 April 2018Accepted 15 August 2018Published 26 September 201810.1126/sciadv.aat9533

Citation: R. V. Divi, J. A. Strother, E. W. M. Paig-Tran, Manta rays feed using ricochet separation,a novel nonclogging filtration mechanism. Sci. Adv. 4, eaat9533 (2018).

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Manta rays feed using ricochet separation, a novel nonclogging filtration mechanismRaj V. Divi, James A. Strother and E. W. Misty Paig-Tran

DOI: 10.1126/sciadv.aat9533 (9), eaat9533.4Sci Adv 

ARTICLE TOOLS http://advances.sciencemag.org/content/4/9/eaat9533

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