Squirmers with arbitrary shape and slip: modeling, simulation, and optimization
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915932958359552 |
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| author | Das, Kausik Zhu, Hai Bonnet, Marc Veerapaneni, Shravan |
| author_facet | Das, Kausik Zhu, Hai Bonnet, Marc Veerapaneni, Shravan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_19336 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Squirmers with arbitrary shape and slip: modeling, simulation, and optimization Das, Kausik Zhu, Hai Bonnet, Marc Veerapaneni, Shravan Fluid Dynamics Soft Condensed Matter Optimization and Control 76D07 (Primary), 76Z10, 65K10 (Secondary) 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. |
| title | Squirmers with arbitrary shape and slip: modeling, simulation, and optimization |
| topic | Fluid Dynamics Soft Condensed Matter Optimization and Control 76D07 (Primary), 76Z10, 65K10 (Secondary) |
| url | https://arxiv.org/abs/2602.19336 |