Chiral sedimentation of non-chiral particles at zero Reynolds number? Really? Yes!

Thursday 22nd January 14:00-15:00
Maths 311B

The sedimentation of rigid particles at low Reynolds number is a classical

problem in fluid mechanics, starting with the work of Stokes who

determined the settling speed of spherical particles whose

symmetry causes them to sediment purely vertically. More complex

particles (disks and rods, say) tend to drift sideways while sedimenting,

and propeller-like (chiral) particles also rotate in a direction that

is determined by their chirality.

The study to be presented here is motivated by the question of what

happens to the well-known behaviour of a sedimenting planar circular

disk when the fluid traction acting on the disk becomes sufficiently large

that it bends the disk into a U-shape.

We initially focus on rigid U-shaped disks and show that the equations

governing their motion can be reduced to two ODEs that describe

the disk's inclination against the direction of gravity. A phase-plane

analysis reveals the existence of two instabilities which generally cause the

disk to sediment along complex spiral trajectories while it alternates

between pitching- and rolling-dominated motions. The chirality of the

resulting trajectories is set by the initial conditions rather than

the (non-chiral) shape of the disk. For certain initial orientations,

the disk retains its inclination and sediments along a perfectly

helical path. Since this behaviour is fundamentally different from

that displayed by flat circular disks (which, as mentioned above,

sediment without any reorientation) we analyse how in the limit of

vanishing curvature the behaviour of a flat disk is recovered.

Finally, we assess the robustness of our results to perturbations in

the shape of the disk, and discuss the implications of our findings for the

sedimentation of dilute suspensions made of such particles.

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