Squirmers with arbitrary shape and slip: modeling, simulation, and optimization

TL;DR

This paper develops a mathematical framework for modeling arbitrary-shaped microswimmers with slip boundary conditions, deriving their velocities, and optimizing slip profiles for efficient motion.

Contribution

It introduces a Helmholtz decomposition-based method for expressing slip velocities and analyzes shape-dependent swimming efficiencies and optimal slip profiles.

Findings

Trajectory of microswimmers is a circular helix for given slip profiles.

Analytical expressions for velocities are derived for prolate spheroids.

Optimal slip profiles depend on shape symmetry and motion direction.

Abstract

We consider arbitrary-shaped microswimmers of spherical topology and propose a framework for expressing their slip velocity in terms of tangential basis functions defined on the boundary of the swimmer using the Helmholtz decomposition. Given a time-independent slip velocity profile, we show that the trajectory followed by the microswimmer is a circular helix. We derive analytical expressions for the translational and rotational velocities of a prolate spheroid swimmer in terms of its Helmholtz decomposition modes and explore the effect of aspect ratio on these rigid body velocities. Then, for a given arbitrary swimmer shape of spherical topology, we investigate which slip profile minimizes the total power loss. A partial minimization is performed in which the direction of net motion of the swimmer is prescribed, followed by a global optimization procedure in which the best net motion direction is determined. The optimization results suggest that the competition between linear and rotational optimal motion is linked to symmetries in the shape of the microswimmer.