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In this article, we investigate the inertial settling of an arbitrarilyoriented cylinder settling under gravity. We focus on two regimes: the veryshort-time and long-time dynamic. By using the generalized Kirchhoff equationsto describe the particle motion, we demonstrate that during the very shortdynamic regime, a cylinder starting from rest behaves with sedimentingvelocities and angular velocity proportional to $t$ and $t^3$, respectively. Wethen explore the long-time behaviour and evaluate the validity of thequasi-steady assumption under which the fluid unsteady term can be neglected.Using a dimensional analysis, we establish that the quasi-steady assumption isonly applicable to Reynolds numbers much smaller than one. However, bycomparing the results of quasi-steady models to recent experiments and directnumerical simulations, we demonstrate that this assumption is valid for abroader range of Reynolds numbers, particularly for long fibres. We alsoanalyze the effect of particle inertia. We show particle inertia plays nosignificant role in the magnitude of the sedimenting velocities and angularvelocity. However, for sufficiently large inertia we reveal that thequasi-steady model takes the form of a damped oscillator when the particleapproaches its equilibrium position, which is broadside on to its direction ofmotion. We discuss the relevance of this solution in light of direct numericalsimulations.

Inertial settling of an arbitrarily oriented cylinder in a quiescent flow : from short-time to quasi-steady motion