  Motion of elongated particles in shear is studied. In applications where
particles are much heavier than the carrying fluid, e.g. aerosols, the
influence of particle inertia dominates the particle dynamics. Assuming that
the particle only experiences a local linear velocity profile, its rotational
and translational motion are independent. However, we show that quadratic terms
of the local velocity profile combined with particle inertia cause a lateral
drift of prolate spheroidal particles. We find that this drift is maximal when
particle inertial forces are of the same order of magnitude as viscous forces,
and that both extremely light and extremely heavy particles have negligible
drift. In the non-inertial case, the particle rotates according to the local
linear velocity profile, with each instantaneous orientation corresponding to a
velocity that gives zero force on the particle. This results in a translational
motion in the flow direction with periodic velocity fluctuations. With added
particle inertia, the particle is slow to react to the surrounding fluid motion
and the particle will switch between slower and faster rotation compared to the
zero-force solution. The final motion that gives zero integrated force over a
rotational period, is a motion with a lateral drift. We show that this drift is
purely an effect of the non-sphericity of the particle and its translational
inertia, while rotational inertia is negligible. Finally, although this
inertial drift will contribute to the lateral motion of heavy elongated
particles in channel flow, sedimentation due to gravity will dominate in any
practical application on earth.
