Shape optimization of slip-driven axisymmetric microswimmers

TL;DR

This paper introduces a computational framework for optimizing the shape and slip velocity of axisymmetric microswimmers in viscous fluids to maximize swimming efficiency, using shape sensitivity analysis and boundary integral methods.

Contribution

It develops a novel shape optimization approach combining shape sensitivity formulas with boundary integral solvers for microswimmers in Stokes flow.

Findings

Optimized shapes significantly improve swimming efficiency.

Validated shape derivatives match finite-difference calculations.

Demonstrated effectiveness of the computational framework through examples.

Abstract

In this work, we develop a computational framework that aims at simultaneously optimizing the shape and the slip velocity of an axisymmetric microswimmer suspended in a viscous fluid. We consider shapes of a given reduced volume that maximize the swimming efficiency, i.e., the (size-independent) ratio of the power loss arising from towing the rigid body of the same shape and size at the same translation velocity to the actual power loss incurred by swimming via the slip velocity. The optimal slip and efficiency (with shape fixed) are here given in terms of two Stokes flow solutions, and we then establish shape sensitivity formulas of adjoint-solution that provide objective function derivatives with respect to any set of shape parameters on the sole basis of the above two flow solutions. Our computational treatment relies on a fast and accurate boundary integral solver for solving all Stokes flow problems. We validate our analytic shape derivative formulas via comparisons against finite-difference gradient evaluations, and present several shape optimization examples.