Slow steady fall of rigid bodies in a second-order fluid

We consider the steady, slow translational fall of a rigid body B in a seco nd-order fluid, under the action of the force of gravity g. We find a gener al expression for the total force and torque acting on B. In particular, th e force per unit area is always compressive, if the first normal stress coe fficient psi(1) is positive. We then specialize these formulas to the 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 the major axis of B is either perpendicular or parallel to g. However, we show that if psi(1) > 0, only this latter orientation is stable to small disorientati ons, in agreement with the recent experimental results of Joseph and cowork ers. (C) 2000 Elsevier Science B.V. All rights reserved.