Orientation of Symmetric Bodies Falling in a Second-Order Liquid at Nonzero Reynolds Number

We study the steady translational fall of a homogeneous body of revolution around an axis s, with foreand-aft symmetry, in a second-order liquid at nonzero Reynolds (i‚ ) and Weissenberg (G‚ ) numbers. We show that, at first order in these parameters, only two orientations are allowed, namely, those with s either parallel or perpendicular to the direction of the gravity /. In both cases the translational velocity is parallel to /. The stability of the orientations can be described in terms of a critical value o for the elasticity number o ) G‚ bi‚ , where o depends only on the geometric properties of the body, such as size or shape, and on the quantity w d L 1Db d, where d and 1 are the first and second normal stress coefficients. These results are then applied to the case when the body is a prolate spheroid. Our analysis shows, in particular, that there is no tilt-angle phenomenon at first order in i‚ and G‚ .