Oral cavity flow distribution and pressure drop in balaenid whales feeding: a theoretical analysis

Balaenid whales, as continuous ram filter feeders, can efficiently separate prey from water by baleen. The feeding process of balaenid whales is extremely complex, in which the flow distribution and pressure drop in the oral cavity play a significant role. In this paper, a theoretical model coupled with oral cavity velocity and pressure in balaenid whales is established based on mass conservation, momentum conservation and pressure drop equations, considering both the inertial and the friction terms. A discrete method with section-by-section calculation is adopted to solve the theoretical model. The effects of four crucial parameters, i.e. the ratio of filtration area to inlet area (S), the Reynolds number of entrance (Re _in ), the ratio of thickness to permeability of the porous media formed by the fringe layer (ϕ) and the width ratio of the anteroposterior canal within the mouth along the tongue (APT channel) to that along the lip (APL channel) (H) are discussed. The results show that, for a given case, the flow distribution and the pressure drop both show increasing trends with the flow direction. For different cases, when S is small, Re _in is small and ϕ is large, a good flow pattern emerges with a smoother flow speed near the oropharynx, better drainage, better shunting and filtration, and higher energy efficiency. However, for smaller values of H, some energy efficiency is sacrificed to achieve additional average transverse flow in order to produce better shunting and filtration. The research in this paper provides a reference for the design of high-efficiency bionic filters.