Universal leaky channel inspired by mobula filters

The filtering apparatus of mobula rays resembles cross-flow filters but demonstrates unconventional anticlogging performance. The permeability and selectivity of cross-flow filters are rationally designed in industry, yet the rationales behind mobula filters largely remain elusive. To bridge both types of filtration, we analyze the permeability-selectivity trade-off in a universal leaky channel inspired by mobula filters, which contains a main channel and two parallel arrays of side pores for leakage. Through experiments, theory, and simulations, we investigate water flow at the pore scale, unveiling a phase diagram that includes pore-flow, transition, and vortex regimes. Each flow regime features distinct scaling laws for water permeability and particle selectivity. We further establish a diagram characterizing the trade-off between permeability and selectivity for our universal leaky channel. We demonstrate that mobula filters reside in a parameter space specified by physical and biological constraints, achieving an elegant balance between permeability and selectivity for breathing and filter feeding.