Nature has converged upon a variety of similar mechanisms of passive dispersal in both air and water for organisms smaller than 1 mm using structures made up of thin threads. One of the best-studied examples is spider ballooning where small spiders float through the air using a strand of silk that acts as a dragline. In general, these passive mechanisms are used for Reynolds numbers less than 10 where viscous forces become significant. The Reynolds number (Re) is often used when discussing scaling effects in fluid dynamics. It is given by the equation Re=ρLU/μ, where ρ is the density of the fluid, L is a characteristic length, U is a characteristic velocity, and μ is the viscosity of the fluid. It is likely that nature uses passive mechanisms at these scales because active flight and reciprocal methods of thrust generation become drastically inefficient for Re < 10.
Humphrey (1987) was one of the first to model the drag forces acting on the spider during dispersal. By modeling the silk thread as a rigid rod and the spider body as a sphere, he showed that the drag forces acting on the organism can account for its small settling velocity. Reynolds et al. (2006) formulated another model of ballooning that allowed for a totally flexible dragline that did not resist bending at all. In this case, the dragline was modeled as N spheres connected by linear springs. This model could account for the large dispersal ranges achieved by some spiders.
Computations become more difficult for multiple threads that resist bending where electrostatic forces may be important. The goal of this project is to consider the fully-coupled fluid-structure interaction problem of flexible, charged draglines attached to negatively buoyant spiders. Specifically, we will use the immersed boundary method to resolve the flow around draglines in various flow conditions. We will use the results to determine how spiders can be passively transported for hundreds or even thousands of miles.
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