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Localized Jeffery-Hamel Flows of Viscoelastic Fluids

By Thomas Hagen and Jonathan D. Evans

Abstract

The planar, steady flow of an incompressible viscous liquid in a wedge with a line sink is given by a purely radial flow: the Jeffery-Hamel solution of the Navier-Stokes equations. H. Giesekus 1968, see [2] For viscoelastic wedge flows little is known. A notable exception is the exact, radial solution found by Hull for the creeping sink flow of an upper convected Maxwell (UCM) fluid in a 180 o wedge. Experimental work by Giesekus indicates that radial solutions are still important for viscoelastic liquids (Fig. a), but that viscoelasticity introduces strong nonlinear effects leading to flow recirculation and the occurrence of vortices (Fig. b), even for small Reynolds numbers. Problem: Can we characterize the flow behavior of basic viscoelastic fluids near the wedge apex? The Governing Equations: UCM-Fluid We consider the planar, steady, incompressible sink flow of a UCM fluid in a wedge. In dimensionless form, the governing equations are the momentum equation the incompressibility condition and the constitutive relation Here the rate-of-strain tensor is given b

Topics: Asymptotics Near The Wedge Apex
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.363.710
Provided by: CiteSeerX
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