Theoretical analysis of the hydrodynamic filtering system in the balaenid whales suspension feeding

Abstract

Balaenid whales are giant filter feeders that feed on the dense aggregations of prey. Through their unique oral filters, they can effectively filter water out and leave prey in their mouths. In this study, a theoretical model is established to analyze the hydrodynamic filtering system in the balaenid whales suspension feeding. First, the appropriate velocity profiles in the anteroposterior and mediolateral directions are adopted to approximate the flow field in the anteroposterior channel along the tongue (APT channel). Then, a four-stage Runge–Kutta method is used to calculate the particle trajectories and predict the corresponding filter cake profile by solving the particle motion equations. Finally, the effects of three crucial parameters, i.e. the APT channel width D T , the fringe layer permeability K, and the food particle diameter d p, are discussed. The results show that the particle trajectories consist of a series of backward-outward arcs and the food particles tend to accumulate in the posterior region of the oral cavity. The growing parabolic filter cake profiles are formed except for the case of extremely low permeability. A small D T and large K make the tendency of particle posterior aggregation obviously. So squeezing the tongue and having larger fringe layer permeability are both conducive to the swallowing process. But the change in d p has less influence on this tendency. The proposed theoretical analysis method is a fast and low-cost calculation method. The study on the balaenid whales’ filter feeding biomechanics and hydrodynamics is helpful to guide the design of the high-efficiency bionic filters.

Baleen–Plastic Interactions Reveal High Risk to All Filter-Feeding Whales from Clogging, Ingestion, and Entanglement

“…Using particle counts, one starts by considering the total number (N tot ) of particles soon to arrive at the location of a baleen plate (Figure 1), a number also equal to the sum of the number of particles passing through baleen while following the crossflow between plates [67,81] (N through ), those bypassing the plate altogether (N bypass ), and the plastic entangling with fringes ("capture"; N entangle ). This sum can be further expressed in terms of the capture rate measurement described above (NCR), yielding N entangle /N bypass = NCR, and through fringebaleen crossflow [82], estimated via the ratio N through /N total = ϕ(ρ particles /ρ water )C CFF . Here, parameters ϕ, ρ particles , ρ water , C CFF correspond to fringe-plate section porosity [83], mass density of the plastic particulates, mass density of seawater, and water flow fraction passing through the baleen filter [81,82], respectively.…”

“…This sum can be further expressed in terms of the capture rate measurement described above (NCR), yielding N entangle /N bypass = NCR, and through fringebaleen crossflow [82], estimated via the ratio N through /N total = ϕ(ρ particles /ρ water )C CFF . Here, parameters ϕ, ρ particles , ρ water , C CFF correspond to fringe-plate section porosity [83], mass density of the plastic particulates, mass density of seawater, and water flow fraction passing through the baleen filter [81,82], respectively. Inserting this into the particle count expressed as a fraction of the total (N total ) yields the following equation, after solving for the bypass ratio, N bypass /N total :…”

“…An attempt was made to determine whether baleen taken from different regions of a complete baleen rack varied in its ability to capture plastic, given that baleen tissue may differ slightly between regions, particularly in terms of the length, diameter, and density of fringe "hairs" [67,82,83]. For three of the four whale species tested (fin, humpback, and right), mini-racks were compared using baleen from nine distinct spatial locations within the mouth (Figure 8): dorsal anterior (DA), mid-anterior (MA), ventral anterior (VA), dorsal central (DC), mid-central (MC), ventral central (VC), dorsal posterior (DP), mid-posterior (MP), and ventral posterior (VP).…”

“…Estimating such mass can be done via Equation (1), after inferring the value of N total and fringe porosity at each baleen plate (Figure 8), a step that was not possible with the circulating flow setup used here. Estimating filter bypass fraction (N bypass /N total ) at each plate can be achieved after considering likely values for porosity (ϕ~10-20%) [83], crossflow mass fraction (C CFF ~0.3-0.5 without fringes [81] and <0.1 with fringes [82]), and the plasticto-water mass ratio (ρ particles /ρ water ; kg/m 3 of plastic in the sample over kg/m 3 of sample's water.) Plastics encountered at densities of 10 or fewer particles per cubic meter [86] per Equation (1) would yield N bypass /N total ~(1 + NCR) −1 ~0.74-0.86 at each station per Figure 4.…”

Dynamic filtration in baleen whales: recent discoveries and emerging trends

“…Fortunately, the past two decades have witnessed an explosive rise in the application of new techniques and technologies, many long used in other fields of science, ushering in a new era for our understanding of mysticete feeding, and particularly of baleen filtration, both in specific details and general outline. Examples of these new techniques and studies notably include but are not limited to hypothesis-based laboratory experiments (e.g., Lambertsen, 1983;Werth, 2013), tag data (Goldbogen et al, 2017a), photogrammetry (e.g., Lambertsen et al, 1989), aerial drones (Werth et al, 2019b), engineering methods (Lambertsen et al, 2005), computational fluid dynamics (Zhu et al, 2020a, Zhu et al, 2020b, morphometrics (Werth et al, 2018a), histology (e.g., Werth et al, 2018b), mathematical modeling (Potvin et al, 2009;Potvin and Werth, 2017), and physical modeling (Werth, 2004).…”