Fig 1.
External and schematic (dorsal cutaway) views showing position of paired racks of 300 serial baleen plates between tongue and lips.
In dorsal cutaway view with oral roof removed (bottom of figure), blue arrows indicate direction of water flow though and around baleen filtering apparatus in life as well as in experimental flow tank trials and computational modeling calculations (hypothetical but predicted from data of current study and previously published experiments [23, 25]). Water can flow anteroposteriorly (AP) within mouth along the tongue (APT channel) or the lip (APL channel). Dashed red box indicates location of shortened mini-rack used in “free flow” conditions (without tongue and lips); dotted green box shows more complex “bounded” conditions including tongue and lips. Filtered water exits the mouth via paired posterior openings (PO). Oropharyngeal opening which leads to esophagus lies near oral floor caudal to the tongue root.
Fig 2.
Schematic diagram comparing arrangement of cross flow filtration (CFF) apparatus in general (A, top) vs. CFF in balaenid whale mouth (B, bottom).
Flow speeds and directions are represented by arrows, with the longest and shortest corresponding to the fastest and slowest speeds respectively. Dashed lines represent mesh screens used for industrial CFF (in A) or an array of ~300 fringed keratinous baleen plates suspended from the palate of balaenids (B). With the latter, anterioposterior flows on the lingual and labial sides of the baleen rack are shown as APT and APL respectively; lateral flows through baleen are shown as IB (intra-baleen). In both cases, and despite the drop of pressure longitudinally, the flows above the filter lose speed via mass loss through the lateral flows, per conservation of the mass rate (Fig 3); in contrast, longitudinal (AP) flows below the filter gain speed following its merging with IB flows. The double arrow on the right in (B) symbolizes the possibility of an open esophageal opening for engulfment of the filtered slurry.
Fig 3.
Schematic diagram of weakening axial flows (APT flows in balaenids) via mass loss via IB flows through a cross filter.
The principle of mass flow rate conservation dictates that the exiting axial flow (Uout) becomes weaker after sequentially losing mass to filter surface outlets (of cross-section area AIBi). In other words, and with the speeds through the outlets denoted as UIBi, the principle dermands that the inlet and outlet flow speeds be related as follows in the case of a schematic four-plate baleen system: ρUoutAin = ρUinAin - ρAIB UIB1 - ρAIB UIB2 - ρAIB UIB3 - ρAIB UIB4) = ρUinAin - ρAIB 4‹UIB›. Symbols ρ and ‹UIB› correspond to the flow’s mass density and to the IB canal flow speed averaged over all four outlets, respectively.
Fig 4.
Schematic diagram showing arrangement of baleen sections into mini-racks of six plates for flow tank testing, in dorsal (top left and center) and lateral (bottom left) views.
Endoscopic video sequences were shot and sensors (pressure transducers and impeller flow meters) were placed at various horizontal and vertical positions (A-J) to record flow data in multiple directions. Water flow is shown via blue arrows: in dorsal views (top left and center), from top to bottom of figure; in lateral (= medial) view (bottom left), from left to right. In dorsal views relative to whale’s oral cavity as well as flume (top left and center), sensors were placed in the same vertical position (water depth) but at varying positions anteroposteriorly, adjacent to different ‘plates’ (top left), or mediolaterally, between the same plates (top center). Lateral view also refers to whale’s oral cavity as well as flume. Clouds indicate primary disposition of flowing particles added to the flume for the experimental protocol; these accumulated mostly at the posterior and ventral regions of a mini-rack. Baleen fringes have been removed from diagrams for clarity; fringes are always located on plate’s leading edge, with position indicated by red circles. Leading/trailing edges refer to baleen location/position within whale’s oral cavity as well as within flume. Photo at top right indicates top of sectioned baleen, showing hydrofoil shape with medial lingual (leading) edge to left and lateral labial (trailing) edge to right. Photo at bottom right (same orientation as close-up photo) shows mini-rack experimental setup. Scale bars (red) = 5 cm.
Fig 5.
Schematic diagram indicating continuous unidirectional water flow (arrows) through idealized balaenid mouth (dorsal view), as in flow tank testing.
Water enters the mouth anteriorly through an opening between paired baleen racks, flows over the tongue, and exits laterally posterior to the lip. Inside the mouth, water can flow transversely through intra-baleen (IB) channels between plates, representing IB flow (horizontal arrows) in either through-put or cross-flow filtration (TPF & CFF), or tangentially along the inside (lingual) edge of the baleen rack, representing cross-flow filtration (CFF, vertical arrows). Anteroposterior (AP) flow can be on baleen’s medial side by the tongue (APT) or lateral side by the lip (APL). Part A (left) shows initial “bounded” setup with simulated tongue and lip; later trials (B) had free boundaries. IB channels are always of the same width (1 cm).
Fig 6.
Horizontal (anteroposterior, AP, top of figure) and vertical (dorsoventral, DV, bottom) flow data through baleen sections, with sensors at three positions.
For AP flow (top), many more particles were captured posteriorly rather than at the anterior of the baleen ‘rack’; flow pressure was highest at the center of the rack and lowest posteriorly; perpendicular intrabaleen (IB) flow velocity was greatest at the rear of the rack and least at its center. For DV flow (bottom), more particles were captured at the bottom of the rack than its top, with pressure declining and transverse (mediolateral) IB flow increasing from dorsal to ventral. Pressure and flow data (mean±SD) from trials with test tank flow of 94 cm s-1; particle capture data (mean±SD) combined from all illuminated (non PIV) trials at all flow velocities.
Fig 7.
Flow velocities at three positions within baleen rack (shown in Fig 3) showing that velocity of water flowing anteroposteriorly through simulated mouth is not matched by equal perpendicular intra-baleen flow (= mediolaterally between baleen plates of the mini-rack).
This plot combines data from 32 trials, including 18 (56% of all trials) bounded by simulated tongue lips and 14 (44%) in free-flow conditions. At all linear flow speeds, perpendicular IB flow (mean±SD shown) is greatest at the rack’s posterior and least in its center. With buoyant particles in water (simulating copepod prey), transverse flows (dotted lines) decreased slightly at all locations. In free flow conditions (with no simulated tongue or lips), IB flow further decreased.
Fig 8.
Fate of particles (mean±SD) moving along and through mini-racks in horizontal (anteroposterior, top of figure) and vertical (dorsoventral, bottom) directions.
Data are from trials with flow velocity 80 cm s-1. Particles either moved without contacting the baleen plates/fringes, bounced or slid off baleen before proceeding posteriorly or ventrally, or were captured and came to rest, remaining immobile in contact with baleen for at least five consecutive video frames. Particles were much more likely to rest in posterior and ventral regions of the baleen racks, suggesting tangential cross-flow filtration (CFF) rather than through-put filtration (TPF) in both AP and DV directions.