Functional geometry of ciliated tentacular arrays in active suspension feeders

Parallel tentacular structures with lateral cilia that produce suspension-feeding and respiratory flows occur repeatedly in many diverse taxonomic groups. We use a computational hydrodynamic model of flow through ciliated tentacles to simulate flow rates through ciliated tentacle arrays. We examine the functional relationship of one performance measure, flow rate per unit length of array, to geometrical variables, such as cilia length, cilia tip speed and the gap between adjacent tentacles, and to hydrodynamic operating conditions, such as adverse pressure drops across the array. We present a scaling and interpolation scheme to estimate flow rates for a wide range of geometries that span many taxa. Our estimates of flow rate can be coupled with the hydrodynamic characteristics of biological piping systems to understand design trade-offs between components of these systems. As a case study, we apply the model to the blue mussel Mytilus edulis by investigating the effect on performance of changes in the gap between neighboring tentacles. Our model suggests that the observed gaps between tentacles in M. edulis reflect flow-maximizing geometries. Even relatively weak adverse pressure drops have strong effects on flow-maximizing geometries and flow rates. One consequence is that an intermediate range of pressure drops may be unfavorable, suggesting that animals may specialize into high-pressure and low-pressure piping systems associated with differences in organism size and with their strategy for eliminating depleted water.