Passive transport of a particle attached to a flexible filament in a simple shear flow: Spiders’ ballooning flight as an energy extracting system*

Some spiders disperse aerially using their fine silks as a sail. Some of these spiders can travel hundreds of miles and reach as high as 15,000 feet above sea level. The passive motion of a flexible filament whose one end is constrained by the weight of a particle is not well studied. Here we introduce a bead-spring model to investigate the passive behavior of this ballooning structure (spider body + silk) in a simple shear flow, which is a major part of the flow structure in the atmospheric boundary layer. Our experimental simulation shows that the terminal speed of this structure is reduced, as the shear rate of the fluid increases. Interestingly, in sufficient shear rates, this terminal speed becomes smaller than that of maximum drag-producing configuration of a filament in a non-moving viscous fluid. This means that the integrated anisotropic drag of a flexible filament, which is laid in different flow velocity fields, produces fluid-dynamic lift forces opposite to the gravity force, which results in an additional increase of the resistance coefficient; and this in turn reduces the terminal speed of the ballooning structure. With this energy extracting mechanism, spiders can stay longer time in the air for their long aerial dispersal.