We investigate the motion of a thin rigid body in Stokes flow and the corresponding slender body approximation used to model sedimenting fibers. In particular, we derive a rigorous error bound comparing a regularized version of the rigid slender body approximation to the classical PDE for rigid motion in the case of a closed loop with constant radius. Our main tool is the slender body PDE framework established by Mori et al. (Commun Pure Appl Math, 2019. https://doi.org/10.1002/cpa.21872; Arch Ration Mech Anal 235(3):1905–1978, 2020), which we adapt to the rigid setting.
Bibliographical noteFunding Information:
This research was supported in part by NSF Grant DMS-1620316, DMS-1516978, and DMS-1907583, awarded to Y.M., and a Torske Klubben Fellowship, awarded to L.O. L.O. also thanks Dallas Albritton for helpful discussion.
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- Rigid motion
- Slender body theory
- Stokes flow
- Thin fiber