Stress singularities and the formation of birefringent strands in stagnation flows of dilute polymer solutions

TL;DR

This paper investigates how stagnation points in dilute polymer solution flows lead to stress singularities and the formation of birefringent strands, revealing a general mechanism linked to flow geometry and stress behavior.

Contribution

It demonstrates the formation of birefringent strands due to stress singularities at stagnation points in simplified flow models, highlighting a universal mechanism.

Findings

Birefringent strands form downstream of stagnation points.

Stress singularities are linked to flow geometry and flow type.

The mechanism is applicable to various flow models like UCM and FENE-P.

Abstract

We consider stagnation point flow away from a wall for creeping flow of dilute polymer solutions. For a simplified flow geometry, we explicitly show that a narrow region of strong polymer extension (a birefringent strand) forms downstream of the stagnation point in the UCM model and extensions, like the FENE-P model. These strands are associated with the existence of an essential singularity in the stresses, which is induced by the fact that the stagnation point makes the convective term in the constitutive equation into a singular point. We argue that the mechanism is quite general, so that all flows that have a separatrix going away from the stagnation point exhibit some singular behaviour. These findings are the counterpart for wall stagnation points of the recently discovered singular behaviour in purely elongational flows: the underlying mechanism is the same while the different nature of the singular stress behaviour reflects the different form of the velocity expansion close to the stagnation point.