Predict maximal dead-zone size in WLM serpentine flow from elastic stresses

Establish whether considering elastic stresses generated by streamline curvature in the flow of semi-dilute wormlike micelle solutions through serpentine channels suffices to predict the maximal area of stagnant dead zones (A_DZ^max), and formulate a predictive relation for A_DZ^max based on this mechanism.

Background

The experiments reveal that, above a critical Weissenberg number, flow of a semi-dilute wormlike micelle solution in serpentine channels develops persistent, fluctuating stagnant regions (“dead zones”) that are spatially localized in channel bends. Their presence is linked to the fluid’s ability to support shear localization and the generation of elastic hoop stresses by curved streamlines.

Motivated by this behavior and analogous studies of viscoelastic eddies, the authors propose a geometric rationale based on minimizing local streamline curvature to reduce elastic stresses. They conjecture that such an elastic-stress-based consideration should predict the maximal dead-zone size. They present a simple geometric construction (a tangent-line bound) that agrees reasonably well with measurements as an upper bound, but a general, established predictive relation remains to be determined.