Nonlinear Behavior of Thin Slender Free Surface Non-Newtonian Elliptical Rings

by Kuanchung J. Lin, Natl Chung-Hsing Univ, Taichung, Taiwan,

Abstract: This paper analyzes the nonlinear motion of a slender concentric thin elliptical ring of an incompressible, non-Newtonian fluid. This study includes the physical effects of surface tension, gravity, relaxation time, retardation time and viscosity. For non-Newtonian rings including the effects of surface tension, transverse and axial inertia, nonlinear oscillation of the elliptical ring can be found. The elliptical ring of proportional thickness (same ratio of principal thickness to principal radii) distorts to a circular ring and then continually distorts to another elliptical shape by exchanging major principal axes. However, the nonproportional thickness elliptical ring can only oscillate between elliptical shapes and can not distort to a circular ring. Excluding the transverse inertia effect, non-Newtonian proportional thickness elliptical rings distort to circular rings far down the flow. However, nonproportional elliptical rings can only distort to elliptical rings.

Subject Headings: Surface Tension (water properties) | Thickness | Fluid flow | Inertia | Oscillations | Free surfaces | Relaxation (mechanics)

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