Minimum Dissipation Theorem for Microswimmers.

Babak Nasouri,Andrej Vilfan,Ramin Golestanian

doi:10.1103/physrevlett.126.034503

Abstract

We derive a theorem for the lower bound on the energy dissipation rate by a rigid surface-driven active microswimmer of arbitrary shape in a fluid at a low Reynolds number. We show that, for any swimmer, the minimum dissipation at a given velocity can be expressed in terms of the resistance tensors of two passive bodies of the same shape with a no-slip and perfect-slip boundary. To achieve the absolute minimum dissipation, the optimal swimmer needs a surface velocity profile that corresponds to the flow around the perfect-slip body, and a propulsive force density that corresponds to the no-slip body. Using this theorem, we propose an alternative definition of the energetic efficiency of microswimmers that, unlike the commonly used Lighthill efficiency, can never exceed unity. We validate the theory by calculating the efficiency limits of spheroidal swimmers.

Highlights

Microswimmers are natural or artificial self-propelled microscale objects moving through a fluid at low Reynolds numbers, such that viscous forces dominate over inertia [1]
We derive a theorem for the lower bound on the energy dissipation rate by a rigid surface-driven active microswimmer of arbitrary shape in a fluid at a low Reynolds number
To achieve the absolute minimum dissipation, the optimal swimmer needs a surface velocity profile that corresponds to the flow around the perfect-slip body, and a propulsive force density that corresponds to the no-slip body

Summary

Minimum Dissipation Theorem for Microswimmers

We derive a theorem for the lower bound on the energy dissipation rate by a rigid surface-driven active microswimmer of arbitrary shape in a fluid at a low Reynolds number. To achieve the absolute minimum dissipation, the optimal swimmer needs a surface velocity profile that corresponds to the flow around the perfect-slip body, and a propulsive force density that corresponds to the no-slip body Using this theorem, we propose an alternative definition of the energetic efficiency of microswimmers that, unlike the commonly used Lighthill efficiency, can never exceed unity. Microswimmers driven by an effective surface slip velocity have two contributions to the dissipation: external (in the outer problem), due to the shearing motion of the surrounding fluid, and internal (in the inner problem), due to losses in the propulsive layer The latter, which focuses on the dissipation in the propulsive layer [10], has been the focus of several studies on the grounds that this is often the dominant contribution, for example, in ciliated microorganisms [22,23]. In this Letter, we propose a theorem that sets a fundamental lower bound on the external dissipation PA

Published by the American Physical Society

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