Steady free fall of one-dimensional bodies in a hyperviscous fluid at low Reynolds number

TL;DR

This paper investigates the steady free fall of one-dimensional bodies in a hyperviscous fluid at low Reynolds number, establishing conditions for purely translational motion using a generalized Reciprocal Theorem.

Contribution

It demonstrates the existence of steady solutions and provides geometric conditions for translational motion in hyperviscous fluids.

Findings

Existence of steady free fall solutions.

Conditions for purely translational motion.

Application of a generalized Reciprocal Theorem.

Abstract

The paper is devoted to the study of the motion of one-dimensional rigid bodies during a free fall in a quasi-Newtonian hyperviscous fluid at low Reynolds number. We show the existence of a steady solution and furnish sufficient conditions on the geometry of the body in order to get purely translational motions. Such conditions are based on a generalized version of the so-called Reciprocal Theorem for fluids.