Shape, confinement and inertia effects on the dynamics of a driven spheroid in a viscous fluid

TL;DR

This study explores how shape, confinement, and inertia influence the motion of spheroids in viscous fluids, revealing complex behaviors and optimal shapes for microfluidic applications through simulations and theory.

Contribution

It provides a systematic analysis of spheroid dynamics in confined flows, highlighting the effects of aspect ratio, wall interactions, and inertia on particle motion.

Findings

Prolate and oblate spheroids have maximum translational velocity at specific aspect ratios.

Confinement shifts optimal aspect ratio toward oblate shapes due to wall friction.

Fluid inertia alters trajectories, creating new stable fixed points and spiral behaviors.

Abstract

The dynamics of anisotropic particles in viscous flows underpin a wide range of processes in soft matter, microfluidics, and targeted drug delivery. Here, we investigate the motion of externally driven prolate and oblate spheroids suspended in a Newtonian fluid and confined within a square microchannel. Using lattice Boltzmann simulations, complemented by far-field hydrodynamic theory based on superposition of wall interactions, we systematically quantify how particle aspect ratio, strength of confinement, and fluid inertia influence the dynamics of a spheroid. For unconfined spheroids, we show that the translational velocity is maximized not for a sphere but for a prolate (end-on) or oblate (broadside-on) spheroid of a specific aspect ratio. Under confinement, the optimal aspect ratio shifts toward oblate shapes due to the dominant contribution of wall-induced frictional resistance. Off-center positioning introduces strong translation-rotation coupling, giving rise to two families of oscillatory trajectories - glancing and reversing - whose existence and structure are captured as closed orbits in phase space. Weak fluid inertia breaks these closed loops: glancing trajectories spiral outward and merge with reversing trajectories, and new stable fixed points emerge. Together, these results reveal how modest deviations from sphericity or creeping-flow conditions profoundly alter the dynamics of driven particles in confined geometries. The predictions offer guidelines for optimizing particle shape in microfluidic transport and highlight the rich nonlinear behavior accessible in confined suspensions of nonspherical colloids.