Boundary integral methods for Stokes-flow parachutes

Many types of animals use appendages bearing arrays of hair-like structures to move. The performance of these functions depends on how much of the uid encountered by the array of hairs ows through the gaps between the hairs rather than around the perimeter of the whole array. Depending on the Reynolds number of the hair-like microstructure, the macrostructure can interact with the uid as a paddle or a rake [1].

One incredible example of this is in Thysanoptera (Thrips): the wings of these mm-sized insects are not membranous like conventional wings, but are comb-like (see inset, redrawn from [2]). Incredibly, the lift generated by these comb-like wings is approximately the same as that which a conventional wing generates. However, since very little material is required for these wings, massive gains in lift to weight ratio are achieved. Thrips have evolved to take advantage of the clustering effect of slender bodies in close proximity in slow ow conditions. By modelling the wing as a finite row of slender bodies, it can be shown that the majority of the fluid goes around the wings rather than through them [2].

This project aims to understand the hydrodynamical interaction between members of an array of slender bodies in the limit of vanishing Reynolds number using boundary integral methods. The array can be large or small, and neighbouring bodies may be arranged in any orientation. Unlike the wing of Thrips, most parachuting fruit comprise slender filaments that are arranged radially [3]. We will use this model to reveal the effect of varying proximity to neighbouring filaments.

[1] Cheer, A., Koehl, M., 1987. Paddles and rakes: uid ow through bristled appendages of small organisms. Journal of Theoretical Biology 129 (1), 17-39.

[2] Barta, E.,Weihs, D., 2006. Creeping ow around a finite row of slender bodies in close proximity. Journal of Fluid Mechanics 551, 1-17.

[3] Greene, D., Johnson, E., 1990. The aerodynamics of plumed seeds. Functional Ecology, 117-125.

Further Information: 

Closing Date: 

Tuesday, December 31, 2019
Thysanoptera (Thrips) insects (redrawn from [2])
Thysanoptera (Thrips) insects (redrawn from [2])

Principal Supervisor: 

Assistant Supervisor: 

Eligibility: 

Minimum entry qualification - an Honours degree at 2:1 or above (or International equivalent) in a relevant science or engineering discipline, possibly supported by an MSc Degree. Further information on English language requirements for EU/Overseas applicants.

Funding: 

Strong candidates may be considered for full EPSRC funding - open to UK/EU candidates only. Further information and other funding options.