Orientation of Symmetric Bodies Falling in a Second-Order
Liquid at Nonzero Reynolds Number
Galdi, G. P., Pokorny, M., Vaidya, A., Joseph, D. D. &
Feng, J. J.
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 Ec
for the elasticity number E=We/Re, where Ec
depends only on the geometric properties of the body, such as size and
shape, and on the quantity (F1+F2)/F1,
where F1 and F2
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.