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Presented By: Department of Mathematics

Applied Interdisciplinary Mathematics (AIM) Seminar

Energetic efficiency and optimal propulsion of microswimmers

Energetic efficiency of microswimmers has long been considered as a non-issue, but it is now known that some microorganisms can use more than half of their energy for swimming. The efficiency is commonly defined through Lighthill's criterion as the power that would be needed to drag the body through the fluid at a given speed, divided by the dissipated power when the swimmer moves actively. Typical ciliated protozoa achieve efficiencies of the order of 1%, which raises the question how close this is to the upper limit that is theoretically possible. By numerically searching for the optimal cilium, we showed that the achieved efficiency is still within a factor of 2 of what is possible. These specific solutions lead to the question of more general minimum dissipation theorems for arbitrary swimmers. For swimmers that propel themselves by inducing an effective slip velocity on their surface, the minimum dissipation can be derived from a superposition of two passive problems: a passive body with a no-slip boundary and another one with a perfect-slip boundary (e.g., an air bubble). We finally apply our theorem to near-spherical swimmers and derive an analytical criterion that predicts whether optimal swimmers are pushers, pullers or neutral. Speaker(s): Andrej Vilfan (Max Planck Institute)

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