Wall Boundary Layers for Maxwell Liquids |
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Authors: | Michael Renardy |
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Affiliation: | (1) Department of Mathematics?Virginia Tech?Blacksburg?VA 24061-0123, US |
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Abstract: | Flows of viscoelastic liquids at high Weissenberg number exhibit stress boundary layers near walls. These boundary layers
are caused by the memory of the fluid: while particles at the wall remain in their position, particles at some distance from
the wall move a long distance within one relaxation time if the Weissenberg number is high. Since the stresses depend on the
flow history, this causes a steep boundary layer to form. A rescaling of the variables exploiting the thinness of this boundary
layer can be used to derive a reduced set of boundary layer equations.
This paper addresses the question of existence of solutions for these boundary layer equations. Using an implicit function
argument, we prove the existence of a large class of solutions which arise from spatially periodic perturbations of uniform
shear flow. The solutions we find can be characterized by the shear rate outside the boundary layer, which can be prescribed
arbitrarily.
Accepted: September 27, 1999 |
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