A note on the reciprocal theorem for the swimming of simple bodies

Abstract

The use of the reciprocal theorem has been shown to be a powerful tool to obtain the swimming velocity of bodies at low Reynolds number. The use of this method for lower-dimensional swimmers, such as cylinders and sheets, is more problematic because of the undefined or ill-posed resistance problems that arise in the rigid-body translation of these shapes. Here we show that this issue can be simply circumvented and give concise formulas obtained via the reciprocal theorem for the self-propelled motion of deforming two-dimensional bodies. We also discuss the connection between these formulae and Faxén's laws.

References in corpus (3)

• The hydrodynamics of swimming microorganisms
• Hydrodynamic phase-locking of swimming microorganisms
• Locomotion in complex fluids: Integral theorems

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• Higher-order force moments of active particles
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