The Weissenberg effect is a phenomenon in viscoelastic fluids where the fluid climbs up a rotating rod inserted into it. This is contrary to the behavior of Newtonian fluids, which are pushed outwards by centrifugal force, forming a vortex. The effect is caused by normal 强调 differences that develop in the fluid under shear.
The Weissenberg effect is a direct consequence of the elastic nature of certain 非牛顿 fluids. When a simple fluid like water is sheared between a rotating rod and a stationary container, the fluid elements are stretched in the direction of flow (the tangential direction). In a purely viscous Newtonian fluid, this results in shear stress but no stress perpendicular (normal) to the shear plane. However, in a viscoelastic fluid, such as a polymer solution, the long polymer chains resist this stretching, creating an elastic tension along the curved streamlines, much like stretched rubber bands.
This tension creates a “hoop stress” that acts inwards, towards the center of rotation. This inward-directed force generates a pressure gradient, pushing the fluid up the rotating rod, which is the path of least resistance. The magnitude of this effect is related to the first normal stress difference, [latex]N_1 = \tau_{\ heta\theta} – \tau_{rr}[/latex], a key parameter in rheology that quantifies the fluid’s elasticity. The Weissenberg effect is a powerful visual demonstration of fluid elasticity and is a fundamental concept in the study of polymer melts and solutions.
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