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Seminar by Shimon Haber
Tuesday, August 7, 2012 - 11:00am
Location: EBU II 479
Low Reynolds Number Swimmer Utilizing Surface Traveling Waves: Analytical and Experimental Study
Shimon Haber, Faculty of Mechanical Engineering, Technion-Israel Institute of Technology
Abstract Micro-scale slender swimmers are frequently encountered in nature and are now used in micro-robotic applications. The swimming mechanism examined in this talk is based on small transverse axisymmetric travelling wave deformations of a cylindrical long shell. The thin-shelled device is assumed to be inextensible at the middle-surface and extensible at the surface wetted by the fluid. Assuming low Reynolds number hydrodynamics, an analytical solution is derived for waves of small amplitudes compared with the cylinder diameter. We show that swimming velocity increases with (the ratio of cylinder radius to wavelength) and that swimming velocity is linearly dependent on wave propagation velocity, increasing to leading order with the square of the ratio of wave amplitude to wavelength, b2, and decreasing with the wall thickness.
The present mechanism was also compared with Taylor’s well known solutions of waving planar and helical circular tails. We show that the present approach yields higher velocities as increases, while the opposite occurs to waving tails. Indeed, in the region where, the present approach yields velocities nearly as fast as Taylor’s helical waving tail, while consuming less power and with a design that is considerably more compact. In this regime the axisymmetric swimmer is twice as fast as Taylor’s planar-tail swimmer for an additional investment of only one-third of the power. Experiments were conducted using a macro-scale autonomous model immersed in highly viscous silicone fluid. We outline how the proposed mechanism was realized to propel an elongated yet finite swimmer. Measured data demonstrate the effects of wave velocity and wavelength on swimming speed, showing good agreement with analytical results.