Slow steady fall of rigid bodies in a second-order fluid (vol 90, pg 81, 2000)

We consider the steady, slow translational fall of a rigid body B in a seco nd-order fluid, under the action of the acceleration of gravity g. We find a general expression for the total force and torque acting on B. In particu lar, the force per unit area is always compressive, if the first normal str ess coefficient psi(1) is positive. We then specialize these formulas to th e case when B is a prolate spheroid of eccentricity e, and show that, when 0 < e < 1, there are only two orientations of fall allowed, namely, when th e major axis of B is either perpendicular or parallel to g. However, we sho w that if psi(1) > 0, only this latter orientation is stable to small disor ientations, in agreement with the recent experimental results of Joseph and coworkers. (C) 2000 Elsevier Science B.V. All rights reserved.