%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%