Materialization of the second asymptotic solution for UCM-like fluids

Determine whether the second solution of the core-region Riccati equation for the log-conformation orientation variable materializes for an Upper-Convected Maxwell-like fluid in other constitutive models or settings, including unsteady bifurcation problems.

Background

The core-region analysis reduces the equation for the orientation angle to a Riccati equation with two explicit solutions. The solution selected in the paper matches the slope inherited from the stick boundary layer and is the stable solution for the viscometric behavior considered.

The alternative solution is identified as unstable and does not match the viscometric behavior of the present steady Giesekus stick-slip configuration. Nevertheless, the authors note that it could become relevant for other constitutive models or settings, such as unsteady bifurcations, leaving its actual realization unresolved.