Effect of fluid and particle inertia on the rotation of an oblate spheroidal particle suspended in linear shear flow.

This work describes the inertial effects on the rotational behavior of an oblate spheroidal particle confined between two parallel opposite moving walls, which generate a linear shear flow. Numerical results are obtained using the lattice Boltzmann method with an external boundary force. The rotation of the particle depends on the particle Reynolds number, Re(p)=Gd(2)ν(-1) (G is the shear rate, d is the particle diameter, ν is the kinematic viscosity), and the Stokes number, St=αRe(p) (α is the solid-to-fluid density ratio), which are dimensionless quantities connected to fluid and particle inertia, respectively. The results show that two inertial effects give rise to different stable rotational states. For a neutrally buoyant particle (St=Re(p)) at low Re(p), particle inertia was found to dominate, eventually leading to a rotation about the particle's symmetry axis. The symmetry axis is in this case parallel to the vorticity direction; a rotational state called log-rolling. At high Re(p), fluid inertia will dominate and the particle will remain in a steady state, where the particle symmetry axis is perpendicular to the vorticity direction and has a constant angle ϕ(c) to the flow direction. The sequence of transitions between these dynamical states were found to be dependent on density ratio α, particle aspect ratio r(p), and domain size. More specifically, the present study reveals that an inclined rolling state (particle rotates around its symmetry axis, which is not aligned in the vorticity direction) appears through a pitchfork bifurcation due to the influence of periodic boundary conditions when simulated in a small domain. Furthermore, it is also found that a tumbling motion, where the particle symmetry axis rotates in the flow-gradient plane, can be a stable motion for particles with high r(p) and low α.