The Importance of a Filament-like Structure in Aerial Dispersal and the Rarefaction Effect of Air Molecules on a Nanoscale Fiber: Detailed Physics in Spiders’ Ballooning

Abstract

Synopsis Many flying insects utilize a membranous structure for flight, which is known as a “wing.” However, some spiders use silk fibers for their aerial dispersal. It is well known that spiders can disperse over hundreds of kilometers and rise several kilometers above the ground in this way. However, little is known about the ballooning mechanisms of spiders, owing to the lack of quantitative data. Recently, Cho et al. discovered previously unknown information on the types and physical properties of spiders’ ballooning silks. According to the data, a crab spider weighing 20 mg spins 50–60 ballooning silks simultaneously, which are about 200 nm thick and 3.22 m long for their flight. Based on these physical dimensions of ballooning silks, the significance of these filament-like structures is explained by a theoretical analysis reviewing the fluid-dynamics of an anisotropic particle (like a filament or a high-slender body). (1) The filament-like structure is materially efficient geometry to produce (or harvest, in the case of passive flight) fluid-dynamic force in a low Reynolds number flow regime. (2) Multiple nanoscale fibers are the result of the physical characteristics of a thin fiber, the drag of which is proportional to its length but not to its diameter. Because of this nonlinear characteristic of a fiber, spinning multiple thin ballooning fibers is, for spiders, a better way to produce drag forces than spinning a single thick spider silk, because spiders can maximize their drag on the ballooning fibers using the same amount of silk dope. (3) The mean thickness of fibers, 200 nm, is constrained by the mechanical strength of the ballooning fibers and the rarefaction effect of air molecules on a nanoscale fiber, because the slip condition on a fiber could predominate if the thickness of the fiber becomes thinner than 100 nm.