Optimal kinematics of the bee tongue for viscous fluid transport

Honey bees can forage nectar from a large spectrum of nectariferous flowers using their rhythmically erectable tongue hairs in a viscous dipping fashion that involves a faster protraction stroke toward the nectar pool and a slower retraction stroke backward. Since honey bees are capable of using their hairy tongues to adapt to various feeding environments, the kinematic characteristics of the bee tongue, especially the retraction time, would likely represent evolutionary optimization. However, the phenomenon and mechanism remain elusive. In this combined experimental and theoretical study, we established a mathematical model to analyze the effects of tongue retraction time on the energy intake rate considering the unfolding dynamics of tongue hairs in the retraction phase. The theoretical optimal retraction time at which the energy intake rate reached the maximum was governed by the dimensions of tongue hairs, which matched well with the in vivo tests. This study may not only bridge the connection between the kinematics and geometry of the bee tongue but also shed light on a control strategy for micropumps equipped with dynamic surfaces.