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

Parabolic velocity profile causes drift of inertial prolate spheroids -- but gravity is stronger