Uniplanar Jeffery motion ↩

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created: 2022-04-19 18:14:13
modified: 2022-04-19 20:01:21

Jeffery (1922)¹ described the motion of an ellipsoidal particle in a viscous fluid where a shear flow is given with vanishing Reynolds number

so in a slow shear flow.

Now we look at a special case of this with the following assumptions:

The coordinates are fixed in space
The shear flow describes a linear velocity profile: where is the shear rate (or the velocity gradient)
The principal axis of the ellipsoid is kept parallel with throughout the motion (the axis which is perpendicular to the plane of the figure)

This is shown on the following figure:

In this case the particle is periodically rotating and its angle and angular velocity is given by (as a function of time):²

And

The angular velocity depends on the orientation!

From this, it's clear that the period of the rotation is:

Dependence on elongation

The rotation becomes less uniform as the investigated particle is more elongated. (in the animations, is the elongation, instead of )

When , the rotation is uniform with the period:

Jeffery, G.B., 1922. The motion of ellipsoidal particles immersed in a viscous fluid. Proceedings of the Royal Society of London. Series A, Containing papers of a mathematical and physical character, 102(715), pp.161-179.
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Ding, E.J. and Aidun, C.K., 2000. The dynamics and scaling law for particles suspended in shear flow with inertia. Journal of Fluid Mechanics, 423, pp.317-344.
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