Leakiness and flow capture ratio of insect pectinate antennae

The assumption that insect pectinate antennae, which are multi-scale organs spanning over four orders of magnitude in size among their different elements, are efficient at capturing sexual pheromones is commonly made but rarely thoroughly tested. Leakiness, i.e. the proportion of air that flows within the antenna and not around it, is a key parameter which depends on both the macro- and the microstructure of the antenna as well as on the flow velocity. The effectiveness of a structure to capture flow and hence molecules is a trade-off between promoting large leakiness in order to have a large portion of the flow going through it and a large effective surface area to capture as much from the flow as possible, therefore leading to reduced leakiness. The aim of this work is to measure leakiness in 3D-printed structures representing the higher order structure of an antenna, i.e. the flagellum and the rami, with varying densities of rami and under different flow conditions. The male antennae of the moth Samia cynthia (Lepidoptera: Saturniidae) were used as templates. Particle image velocimetry in water and oil using 3D-printed scaled-up surrogates enabled us to measure leakiness over a wide range of equivalent air velocities, from 0.01 m s^-1 to 5 m s^-1, corresponding to those experienced by the moth. We observed the presence of a separated vortex ring behind our surrogate structures at some velocities. Variations in the densities of rami enabled us to explore the role of the effective surface area, which we assume to permit equivalent changes in the number of sensilla that host the chemical sensors. Leakiness increased with flow velocity in a sigmoidal fashion and decreased with rami density. The flow capture ratio, i.e. the leakiness multiplied by the effective surface area divided by the total surface area, embodies the above trade-off. For each velocity, a specific structure leads to a maximum flow capture ratio. There is thus not a single pectinate architecture which is optimal at all flow velocities. By contrast, the natural design seems to be robustly functioning for the velocity range likely to be encountered in nature.