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Shape Optimization of Magnetic Micro-Swimmers

Introduction

Microorganisms swimming at low-Reynolds number, where fluid inertia is negligible, must use time-irreversible motions of their control surfaces (e.g. their bodies or flagellum) in order to have a net translation after one stroke. This is achieved by sperm and small nematodes by propagating bending waves along the length of a flexible slender body, and bacteria that utilize rotating helices whose shape couples the rotation and translation. The flow fields generated by the motion of the control surfaces couple the motion of nearby bodies leading to swarms that induce vigorous fluid mixing, which can have a large effect on the distribution of chemicals and nutrients within the fluid.


Shape Optimization

We analyze an infinite-dimensional shape optimization problem related to magnetically driven micro-swimmers and develop a variational method and discretization for computing these shapes. This is joint work with Eric Keaveny and Michael Shelley. See our papers for more details:



Optimal Shapes

Here are some movies showing the shape evolution (from our optimization method) that eventually leads to optimal shapes. Each frame of the movie is an iteration of the optimization. (Make sure you have the Microsoft Windows Media Player Firefox plugin installed if you are a Windows and Firefox user.) Here, Uz is the swimming speed of the locomotor.

--- Without Cargo

--- With Cargo