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We consider sedimentation of a rigid helical filament in a viscous fluidunder gravity. In the Stokes limit, the drag forces and torques on the filamentare approximated within the resistive-force theory. We develop an analyticapproximation to the exact equations of motion that works well in the limit ofa sufficiently large number of turns in the helix (larger than two, typically).For a wide range of initial conditions, our approximation predicts that thecentre of the helix itself follows a helical path with the symmetry axis of thetrajectory being parallel to the direction of gravity. The radius and the pitchof the trajectory scale as non-trivial powers of the number of turns in theoriginal helix. For the initial conditions corresponding to an almosthorizontal orientation of the helix, we predict trajectories that are eitherattracted towards the horizontal orientation, in which case the helix sedimentsin a straight line along the direction of gravity, or trajectories that form ahelical-like path with many temporal frequencies involved. Our results providenew insight into the sedimentation of chiral objects and might be used todevelop new techniques for their spatial separation.

Sedimentation of a rigid helix in viscous media