Continuous breakdown of Purcell's scallop theorem with inertia

Details Continuous breakdown of Purcell's scallop theorem with inertia Continuous breakdown of Purcell's scallop theorem with inertia

2007-06-25

arxiv.org/abs/0706.3652v1

Phys. Fluids 19, 061703, 2007

Physics

Condensed Matter

Soft Condensed Matter

6 pages, 1 figure

Scientific paper

10.1063/1.2738609

Purcell's scallop theorem defines the type of motions of a solid body - reciprocal motions - which cannot propel the body in a viscous fluid with zero Reynolds number. For example, the flapping of a wing is reciprocal and, as was recently shown, can lead to directed motion only if its frequency Reynolds number, Re_f, is above a critical value of order one. Using elementary examples, we show the existence of oscillatory reciprocal motions which are effective for all arbitrarily small values of the frequency Reynolds number and induce net velocities scaling as (Re_f)^\alpha (alpha > 0). This demonstrates a continuous breakdown of the scallop theorem with inertia.

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