Determinants of the pore-specific critical Weissenberg number in ordered 3D sphere packings

Determine the factors that set the pore-specific critical Weissenberg number Wi_c,pore for the onset of elastic instability in flow of dilute partially hydrolyzed polyacrylamide (HPAM) solutions through microfabricated simple-cubic and body-centered cuboid sphere packings, explicitly identifying the geometric and flow features (such as stagnation point density, local curvature, and pore-scale topology) that control Wi_c,pore in each geometry.

Background

The study directly visualizes viscoelastic flow in microfabricated simple-cubic (SC) and body-centered cuboid (BC) arrays of spherical grains and quantifies the transition from steady to unsteady flow using pore-scale velocity fields. For each geometry, the authors define a pore-specific critical Weissenberg number Wi_c,pore marking the onset of unsteadiness.

They find a collapse in the transition behavior across pores and geometries when rescaled by Wi_c, but observe that the distribution of Wi_c,pore values differs between SC and BC packings, with the BC packing exhibiting overall lower thresholds. Despite these observations, the precise determinants of Wi_c,pore for each geometry remain unidentified, motivating a concrete open question about the origin of these thresholds.