Ashuwin Vaidya, Department of Mathematical Sciences, Carnegie Mellon University
"Mathematical Analysis of Orientation of Rigid Bodies in Newtonian and Viscoelastic Liquids"
In this talk, we focus on the steady orientation of rigid bodies 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 above mentioned problem.
TUESDAY, January 25, 2005