Taylor's swimming sheet: Analysis and improvement of the perturbation series
arXiv:1302.4029 · doi:10.1016/j.physd.2011.06.023
Abstract
In G.I. Taylor's historic paper on swimming microorganisms, a two dimensional sheet was proposed as a model for flagellated cells passing traveling waves as a means of locomotion. Using a perturbation series, Taylor computed swimming speeds up to fourth order in amplitude. Here we systematize that expansion so that it can be carried out formally to arbitrarily high order. The resultant series diverges for an order one value of the wave amplitude, but may be transformed into series with much improved convergence properties and which yield results comparing favorably to those obtained numerically via a boundary integral method for moderate and large values of the wave amplitudes.
References in corpus (3)
Cited by in corpus (5)
- The mechanism of propulsion of a model microswimmer in a viscoelastic fluid next to a solid boundary
- Towards an analytical description of active microswimmers in clean and in surfactant-covered drops
- Competing effects of inertia, sheet elasticity, and fluid viscoelasticity on the synchronization of two actuated sheets
- A Taylor swimming sheet under a finite Brinkman layer
- Swimming of microorganisms in quasi-2D membranes