Conjecture on onset differences: stagnation point density controls Wi_c in BC versus SC packings

Test the conjecture that the lower critical Weissenberg number for the onset of elastic instability observed in body-centered cuboid sphere packings, compared to simple-cubic sphere packings, primarily results from a higher net density of stagnation points arising from the combination of inter-grain contact stagnation points and polar upstream/downstream stagnation points.

Background

Using ordered packings, the authors show that inter-grain contacts generate stagnation points that dominate the onset of elastic instability. In BC packings, both contact-associated and polar stagnation points are present, whereas in SC packings polar stagnation points are screened and contact-associated points dominate.

The measured Wi_c is lower in BC than SC. To explain this difference, the authors explicitly propose a conjecture linking the onset to a higher net stagnation point density in BC, suggesting a specific geometric control mechanism that remains to be tested.