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arXiv · 2207.06023

Shapes optimising grand resistance tensor entries for a rigid body in a Stokes flow

Clment Moreau·Kenta Ishimoto·Yannick Privat
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Abstract

We investigate the optimal shapes of the hydrodynamic resistance of a rigid body set in motion in a Stokes flow. In this low Reynolds number regime, the hydrodynamic drag properties of an object are encoded in a finite number of parameters contained in the grand resistance tensor. Considering these parameters as objective functions to be optimised, we use calculus of variations techniques to derive a general shape derivative formula, allowing to specify how to deform the body shape to improve the objective value of any given resistance tensor entry. We then describe a practical algorithm for numerically computing the optimized shapes and apply it to several examples. Numerical results reveal interesting new geometries when optimizing the extra-diagonal inputs to the strength tensor, including the emergence of a chiral helical shape when maximising the coupling between the hydrodynamic force and the rotational motion. With a good level of adaptability to different applications, this work paves the way for a new analysis of the morphological functionality of microorganisms and for future advances in the design of microswimmer devices.

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Clment Moreau, Kenta Ishimoto, Yannick Privat. 2022-07-13. Shapes optimising grand resistance tensor entries for a rigid body in a Stokes flow. https://arxiv.org/abs/2207.06023

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