Efficiency of cargo towing by a microswimmer

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Abstract
We study the properties of an arbitrary microswimmer towing a passive load through a viscous liquid. The simple close-form expression for the dragging efficiency of a microswimmer dragging a distant load is found, and the approximation for finite mutual proximity is derived. We show that, while the swimmer can be arbitrarily efficient, the dragging efficiency is always bounded from above. It is also demonstrated, that opposite to Purcell’s assumption [E. M. Purcell, Proc. Natl. Acad. Sci. U.S.A. 94, 11307 (1997)], the hydrodynamic coupling can “help” the propeller to tow the load. We support our conclusions by rigorous numerical calculations for the rotary swimmer, towing a spherical cargo positioned at a finite distance.
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