# An error bound for the slender body approximation of a thin, rigid fiber sedimenting in Stokes flow

## TL;DR

This paper derives a rigorous error bound for the slender body approximation of a thin, rigid fiber sedimenting in Stokes flow, providing theoretical validation for the model in specific geometric conditions.

## Contribution

The authors adapt the slender body PDE framework to the rigid setting and establish a new error bound comparing the approximation to the classical PDE for closed-loop fibers.

## Key findings

- Error bound for slender body approximation established
- Validation of the approximation for fibers with constant radius
- Framework adaptation to rigid body motion in Stokes flow

## Abstract

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 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 the authors and D. Spirn in [18,19], which we adapt to the rigid setting.