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

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Galdi, G. P., Pokorny, M., Vaidya, A., Joseph, D. D. &
Feng, J. J.

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*Mathematical Models and Methods in Applied Sciences*
Vol. **12**, No. 11, 1653-1690 (2002).

**Abstract - **We study the steady translation fall of
a homogeneous body of revolution around an axis a, with fore-and-aft symmetry,
in a second-order liquid at nonzero Reynolds (*Re*) and Weissenberg
(*We*) numbers. We show that, at first order in these parameters,
only two orientations are allows, namely, those with a either parallel
or perpendicular to the direction of the gravity g. In both cases, the
translational velocity is parallel to g The stability of the orientations
can be described in terms of a critical value *E**c*
for the elasticity number *E=We/Re*, where *E**c*
depends only on the geometric properties of the body, such as size and
shape, and on the quantity (*F*1+*F*2)/*F*1,
where *F*1 and *F*2
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 *Re* and *We*.