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W. G. Pritchard Lab Seminar: 2:00-3:00 PM, 112 Thomas Building
**Thursday May 27, 2004**
Orientation of rigid bodies freefalling
in Newtonian and non-Newtonian liquids
Ashwin Vaidya
Department of Mechanical Engineering
University of Pittsburgh
The problem of fluid-solid interaction is one with a broad variety of
applications in natural sciences and industry, and has given rise to
very interesting and complex mathematical questions. In this talk, we
focus on the steady orientation of a rigid body falling in Newtonian and
non-Newtonian liquids. It is well known that a long, rigid body such as
a cylinder or a prolate spheroid sedimenting in a Newtonian fluid will
orient itself with its major axis perpendicular to the direction of
gravity, in its steady state. However, in a viscoelastic fluid, these
eventually becomes parallel. Remarkably, in polymer solutions of certain
concentrations, the major axis is found to settle at an angle between
the horizontal and vertical. We formulate a mathematical theory that
attempts to explain these phenomena using different fluid models,
Newtonian and non-Newtonian, at low Reynolds and Weissenberg numbers.
The talk will highlight some mathematical results pertaining to the
formulation, well-posedness and steady state behavior of the problem. We
also present experimental results regarding the behavior of bodies of
different shapes sedimenting in different liquids. While our theoretical
predictions match perfectly with our experimental observations, we also
note several other interesting phenomena which still need theoretical
resolution.
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