Foam flowing through a channel past an obstacle can exhibit two qualitatively different plastic flow behaviors. In ordered, monodisperse foam, bubbles slide along crystallographic planes in coordinated sheets — the rearrangements are directional and collective. In disordered, polydisperse foam, rearrangements are scattered and amorphous, with no preferred sliding direction (arXiv:2603.20736).
A critical polydispersity threshold demarcates the transition. Below the threshold, the foam's crystalline order imposes a discrete set of slip planes. Above it, the disorder eliminates preferred directions and the plastic flow becomes isotropic. The transition is sharp — not a gradual crossover but a bifurcation in the topology of the deformation field.
The obstacle also introduces a yield drag. Below a critical driving force, the foam stops flowing entirely — the obstacle pins the structure and no rearrangements occur. The critical force depends on packing fraction. At low packing, the foam flows freely. At high packing, the foam jams against the obstacle and requires a threshold force to resume. The yield point is a collective property — it emerges from the interaction between obstacle geometry, bubble deformability, and confinement pressure.
The structural insight: the same material system produces qualitatively different mechanical responses depending on a single parameter (polydispersity) that controls internal order. The obstacle doesn't change — the foam's relationship to the obstacle changes. Order creates anisotropy; disorder creates isotropy. And the yield threshold appears not because individual bubbles can't deform, but because the collective rearrangement pathway is geometrically blocked. The failure mode is topological, not energetic.