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

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 widthD, the fringe layer permeabilityK, and the food particle diameterd_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 smallDand largeKmake 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 ind_phas 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.