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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.08774 |
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| _version_ | 1866912371847462912 |
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| author | Shum, Henry Palaniappan, Devenayagam Young, Yuan-Nan |
| author_facet | Shum, Henry Palaniappan, Devenayagam Young, Yuan-Nan |
| contents | The hydrodynamic interactions between a sedimenting microswimmer and a solid wall have ubiquitous biological and technological applications. A plethora of gravity-induced swimming dynamics near a planar no-slip wall provides a platform for designing artificial microswimmers that can generate directed propulsion through their translation-rotation coupling near a wall. In this work we provide exact solutions for a squirmer (a model swimmer of spherical shape with a prescribed slip velocity) facing either towards or away from a planar wall perpendicular to gravity. These exact solutions are used to validate a numerical code based on the boundary integral method with an adaptive mesh for distances from the wall down to 0.1% of the squirmer radius. This boundary integral code is then used to investigate the rich gravity-induced dynamics near a wall, mapping out the detailed bifurcation structures of the swimming dynamics in terms of orientation and distance to the wall. Simulation results show that a squirmer may transverse along the wall, move to a fixed point at a given height with a fixed orientation in a monotonic way or in an oscillatory fashion, or oscillate in a limit cycle in the presence of wall repulsion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08774 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hydrodynamic interactions between a sedimenting squirmer and a planar wall Shum, Henry Palaniappan, Devenayagam Young, Yuan-Nan Soft Condensed Matter Mathematical Physics Applied Physics Computational Physics Fluid Dynamics The hydrodynamic interactions between a sedimenting microswimmer and a solid wall have ubiquitous biological and technological applications. A plethora of gravity-induced swimming dynamics near a planar no-slip wall provides a platform for designing artificial microswimmers that can generate directed propulsion through their translation-rotation coupling near a wall. In this work we provide exact solutions for a squirmer (a model swimmer of spherical shape with a prescribed slip velocity) facing either towards or away from a planar wall perpendicular to gravity. These exact solutions are used to validate a numerical code based on the boundary integral method with an adaptive mesh for distances from the wall down to 0.1% of the squirmer radius. This boundary integral code is then used to investigate the rich gravity-induced dynamics near a wall, mapping out the detailed bifurcation structures of the swimming dynamics in terms of orientation and distance to the wall. Simulation results show that a squirmer may transverse along the wall, move to a fixed point at a given height with a fixed orientation in a monotonic way or in an oscillatory fashion, or oscillate in a limit cycle in the presence of wall repulsion. |
| title | Hydrodynamic interactions between a sedimenting squirmer and a planar wall |
| topic | Soft Condensed Matter Mathematical Physics Applied Physics Computational Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2410.08774 |