Establish the exact granular buoyancy law

Establish whether the buoyancy force on an intruder in a dense granular flow is exactly the classical Archimedes buoyancy force obtained by integrating the macroscopic granular stress tensor over the intruder surface.

Background

The paper compares several competing definitions of granular buoyancy, including pressure-based, slip-independent, Voronoi-volume, and contact-density formulations. The proposed force model adopts the classical Archimedes expression, while attributing additional pressure-gradient-dependent effects to the effective drag force.

The distinction between buoyancy and gradient-induced drag is difficult because both contributions can scale with pressure-related quantities. The paper therefore identifies the exact status of the classical Archimedes expression as unresolved.

References

Hence, the only plausible buoyancy force model currently is the classical Archimedes buoyancy force. Even though the current model can't prove that it should be exactly a classical Archimedes buoyancy force.

— A force model for dense granular flows and particle segregation  (2609.09398 - Lantman, 8 Sep 2026) in Section 5, “Buoyancy forces”