Chaotic rotation of a spheroidal particle in simple shear flow

The angular motion of a neutrally buoyant prolate spheroidal particle in simple shear flow has previously been found to follow two-dimensional dynamics similar to a Duffing-van der Pol oscillator as a consequence of inertia of the surrounding fluid. This behavior was however only present if the aspect ratio is large enough. When decreasing the particle aspect ratio, the particle could be found to perform period-doubled or chaotic orbits as effects of particle inertia also influence the dynamics. In this work, it is demonstrated that the onset of complex dynamics is through a Shilnikov bifurcation as the log-rolling state (particle is rotating around its symmetry axis, which is parallel to the vorticity direction) is transformed from a regular saddle node into a saddle focus when particle inertia is increased. Furthermore, it is shown that the same also applies for the two dimensional Duffing-van der Pol oscillator when including inertial terms. These results open up the possibility of developing a reduced model to mimic the influence of both fluid and particle inertia on the angular dynamics of spheroidal particles in simple shear flow, which can be used in fluid simulations with Lagrangian particles.