The motion of ellipsoidal particles in a viscous fluid

In a recent paper* Dr. G. B. Jeffery has discussed the equations of motion of ellipsoidal particles immersed in a moving viscous fluid. He has solved the problem completely in The case of spheroidal particles immersed in a very viscous fluid which is moving parallel to a plane with a uniform shearing motion. his so1ution shows that the motion depends on the initial conditions of release of the Particle. The motion is periodic, and there appears to be no tendency for a particle to set itself so that its axis 1ies in any Particular direction. The Particle, in fact, takes up the rotation of the fluid, and its axis of symmetry describes a kind of elliptic cone round the direction of the vortex filaments, that is, round the direction which is perpendicular to the plane in which the motion of the fluid takes places. Though the ana1ysis, which neglects the inertia terms in the equations of motion, gives no indication of any tendency for the axis to set itself in any particular direction, Dr. Jeffery considers that ultimate1y the axis would probably adopt some special position, and he puts forward a " minimum energy ” hypothesis, which leads to the following definite, though unproved and unverified, results:— 1. A prolate spheroid, subject to the restriction imposed by this hypothesis, would set itself so that its long axis was Parallel to the vortex lines, and therefore perpendicular to the plane in which this undisturbed motion of the fluid takes places. It would then rotate with the fluid, which would move in steady motion relative to it.