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

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 maximised not for a sphere but for a prolate (end-on) or oblate (broadside-on) spheroid of specific aspect ratio. Under confinement, the optimal aspect ratio shifts toward oblate shapes due to the dominant contribution of wall-induced frictional resistance. Off-centre 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 the 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 optimising particle shape in microfluidic transport and highlight the rich nonlinear behaviour accessible in confined suspensions of nonspherical colloids.