Theoretical efficiency limits for microswimmer propulsion

As a microswimmer displaces the fluid it is moving through, it inevitably dissipates energy. The dissipation consists of two contributions. The external dissipation takes place in the viscous fluid surrounding the microswimmer. Internal dissipation takes place in the propulsive layer on the swimmer's surface and is often the dominant contribution. Here, we solve the combined minimum dissipation problem for different classes of swimmers including surface-driven viscous droplets, swimmers driven by tangential forces and swimmers driven by normal forces. We have previously shown that a lower bound on the external dissipation can be derived with the knowledge of drag coefficients of two bodies of the same shape, one with a no-slip and one with a perfect slip boundary condition [1]. We now generalize the approach to a number of models where the lower bound on the dissipation by the active swimmer can be expressed with two passive drag coefficients [2]. We thus provide an exact analytical solution to a class of problems that were previously only tractable by numerical optimization.

[1] B. Nasouri, A. Vilfan and R. Golestanian, Phys. Rev. Lett., 126, 034503 (2021).

[2] A. Daddi-Moussa-Ider, R. Golestanian, A. Vilfan, arXiv:2302.07711