Abstract
Mobula rays have evolved leaf-shaped filter structures to separate food particles from seawater, which function similarly to industrial cross-flow filters. Unlike cross-flow filtration, where permeability and selectivity are rationally designed following trade-off analyses, the driving forces underlying the evolution of mobula filter geometry have remained elusive. To bridge the principles of cross-flow and mobula filtration, we establish a universal framework for the permeability-selectivity trade-off in a leaky channel inspired by mobula filters, where permeability and selectivity are characterized by the pore-scale leaking rate and the cut-off particle size, respectively. Beyond the classic pore-flow regime in cross-flow filtration, we reveal transition and vortex regimes pertinent to mobula filtration. Combining theory, physical experiments, and simulations, we present distinct features of water permeability and particle selectivity across the three regimes. In particular, we identify an unreported 1/2-scaling law for the leaking rate in the vortex regime. We conclude by demonstrating that mobula filters strike an elegant balance between permeability and selectivity, which enables mobula rays to simultaneously satisfy biological requirements for breathing and filter feeding. By integrating cross-flow and mobula filtration into a universal framework, our findings provide fundamental insights into the physical constraints and evolutionary pressures associated with biological filtration geometries and lay the foundation for developing mobula-inspired filtration in industry.