Optimal slip velocities of micro-swimmers with arbitrary axisymmetric shapes

TL;DR

This paper develops a computational method to find optimal slip velocities on axisymmetric micro-swimmers, aiming to maximize efficiency by minimizing power loss, and identifies prolate spheroids as the most efficient shapes.

Contribution

It introduces a boundary integral method for solving a quadratic optimization problem to determine optimal slip velocities on arbitrary axisymmetric shapes.

Findings

Prolate spheroids are the most efficient shapes for given reduced volume.

A scalar metric can classify shapes as pusher, puller, or neutral swimmer based on optimal slip.

The method effectively computes optimal slip velocities for various shapes.

Abstract

This article presents a computational approach for determining the optimal slip velocities on any given shape of an axisymmetric micro-swimmer suspended in a viscous fluid. The objective is to minimize the power loss to maintain a target swimming speed, or equivalently to maximize the efficiency of the micro-swimmer. Owing to the linearity of the Stokes equations governing the fluid motion, we show that this PDE-constrained optimization problem reduces to a simpler quadratic optimization problem, whose solution is found using a high-order accurate boundary integral method. We consider various families of shapes parameterized by the reduced volume and compute their swimming efficiency. {Among those, prolate spheroids were found to be the most efficient micro-swimmer shapes for a given reduced volume. We propose a simple shape-based scalar metric that can determine whether the optimal slip on a given shape makes it a pusher, a puller, or a neutral swimmer.}