Ashwin Vaidya
Dept. of Mathematics, University of Pittsburgh.
| 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 'a' perpendicular to the direction of gravity g, in its steady state. However, in a viscoelastic fluid, 'a' eventually becomes parallel to g. Also, remarkably, in polymer solutions of certain concentrations, the axis 'a' is found to settle at an angle between the horizontal and vertical states, with respect to g. This last phenomenon is referred to as the 'tilt-angle' in the literature. In this talk, we will formulate a theory that attempts to explain these phenomena using different fluid models, Newtonian and non-Newtonian, such as Navier-Stokes, Power-Law and Second-order fluid equations, at low Reynolds and Weissenberg numbers. The talk will highlight some mathematical, computational and experimental results pertaining to the terminal motion of bodies of arbitrary shape in different liquids. |
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