Boundary layers for the upper convected Maxwell fluid

We discuss boundary layers arising in the high Weissenberg number limit of viscoelastic flows and the scalings that arise in analyzing them. Two quite distinct mechanisms for the formation of viscoelastic boundary layers exist: One mechanism is analogous to that of the Prandtl boundary layer and is linked to the enforcement of the no-slip boundary condition. The other mechanism has nothing to do with the no-slip condition, but is linked to long memory which manifests itself in different stresses near the wall versus some distance from the wall. In certain situations, these stress boundary layers may be embedded within Prandtl type boundary layers.

► We discuss boundary layers at high Weissenberg number for the upper convected Maxwell fluid.
► There are two quite distinct types of boundary layers: Prandtl boundary layers and stress boundary layers.
► The mechanisms and scalings for these boundary layers are presented in a systemtatic fashion.