The ability to efficiently consume many small prey items involves adaptations for aggregating food particles prior to swallowing. Many teleost fishes, including clupeiforms, have an epibranchial organ (EBO) in the posterior pharynx for concentrating food captured by the gill rakers. Morphologically diverse and widely distributed among teleosts, EBOs nevertheless share some anatomical features that may be essential for particle aggregation. We describe the anatomy in a functional context by modelling fluid flow and particle aggregation in the EBO of the gizzard shad, Dorosoma cepedianum. Results from morphological surveys and physical modelling suggest that proper aggregation and expulsion of food can be described by transitions between inertial and viscous flow. The EBO serves as a fluid ‘spreader’ that takes an inertial input and rapidly decreases velocity and size scale to increase the effects of viscosity. The viscous environment of the EBO, created in part by abundant mucus, allows large numbers of particles to aggregate into a bolus. Thick walls of circumferential and longitudinal skeletal muscle enable rapid compression of the EBO which increases fluid speed and pushes the bolus into the esophagus. We propose that the input particle flow is an inertially dominated regimen, while the internal EBO flow is viscously dominated. It is possible that the output flow during bolus ejection is also inertially dominated. This conceptual model offers a framework for understanding the breadth of EBO diversity in clupeiform fishes. The variety of EBO morphologies could be related to differences in prey size, prey mobility, frequency of bolus formation, or density of encountered prey items.