Measuring effective surface energy in non-equilibrium granular fluids using an innovative orbital tensiometer apparatus

Dense granular media lack a well-established analog of classical liquid tensiometry, although localized interfacial barriers can strongly influence segregation, buoyancy, and intruder stability. Using a calibrated dual-mode orbital calorimeter-rheometer, we show that a partially submerged intruder can serve as an in situ mechanical probe of the grain-mediated restoring response in an orbitally driven dense bed. In the rigid-body core-rotation regime at low peak acceleration, Γ=2.5, and low granular temperature, Tg≈10-7m2s-2, the intruder follows a stable circular orbit with negligible radial drift and intrinsic spin. This kinematic state indicates that the inward centripetal force required in the laboratory frame is balanced predominantly by a localized restoring interaction associated with the air-grain-intruder contact configuration. By combining the measured density-contrast centrifugal demand with the specific interfacial area of the ternary bead mixture and a geometry-calibrated effective radial transmission area, we obtain an effective granular interfacial-stress scale of γgm≈2.38×10-2Jm-2. The inferred value agrees within 1.2% with an independently obtained thermomechanical reference at the corresponding low granular temperature. The result provides a mechanical explanation for the granular Archimedean anomaly, in which the intruder remains stably surface supported while the displaced granular volume supplies less than half of its static weight under a conventional hydrostatic estimate. At the fluidization threshold, Γ=6.02, kinetic thermalization raises the granular temperature to Tg≈10-4m2s-2; the localized restoring configuration is then destabilized, and the intruder exhibits orientation instability, rapid inward migration, intrinsic rotation, and deep convective submersion. A 10 000-trial Monte Carlo analysis yields a coefficient of variation of ∼3.4% under realistic composition tolerances. These results establish a non-invasive, trajectory-based methodology for quantifying an effective localized granular interfacial-stress scale in actively driven dense particulate systems.