Ram suspension-feeding fish, such as herring, use gill rakers to separate small food particles from large water volumes while swimming forward with an open mouth. The fish gill raker function was tested using 3D-printed conical models and computational fluid dynamics simulations over a range of slot aspect ratios. Our hypothesis predicting the exit of particles based on mass flow rates, dividing streamlines (i.e. stagnation streamlines) at the slots between gill rakers, and particle size was supported by the results of experiments with physical models in a recirculating flume. Particle movement in suspension-feeding fish gill raker models was consistent with the physical principles of lateral displacement arrays ('bump arrays') for microfluidic and mesofluidic separation of particles by size. Although the particles were smaller than the slots between the rakers, the particles skipped over the vortical region that was generated downstream from each raker. The particles 'bumped' on anterior raker surfaces during posterior transport. Experiments in a recirculating flume demonstrate that the shortest distance between the dividing streamline and the raker surface preceding the slot predicts the maximum radius of a particle that will exit the model by passing through the slot. This theoretical maximum radius is analogous to the critical separation radius identified with reference to the stagnation streamlines in microfluidic and mesofluidic devices that use deterministic lateral displacement and sieve-based lateral displacement. These conclusions provide new perspectives and metrics for analyzing cross-flow and cross-step filtration in fish with applications to filtration engineering.