Ramon Planet, Iker Zamorano, Caleb Anderson
Granular matter refers to a physical system composed of discrete solid particles that interact with each other through physical forces, such as collisions and friction. The study of granular matter encompasses a wide range of systems, from everyday materials like sand and soil, to industrial products like powders and pills. Thermal effects in granular materials are negligible compared to gravitational and frictional effects, hence, granular packings would be expected to remain frozen in local states. Due to the complex interparticle interactions and the resulting collective behavior, granular matter behaves different from fluids, solids, or gases.
One example of this unusual mechanical behavior is the well-known “Janssen’s effect”. When filling a cylindrical column with grains, the weight measured at the bottom of the column does not scale linearly with added mass, but asymptotically saturates towards a constant value. The weight is partially supported by the lateral walls through frictional interactions with the grains. However, we recently observed that the weight measured at the bottom can become larger than the total added mass when the columns are sufficiently small compared to the diameter of the grains [1].
Figure 1: Experimental results for the dependence of the apparent mass, ma, on the added mass, m, for a cylinder with diameter D ≃ 172.00 mm ≃ 29σ, panel (a), and D ≃ 49.10 mm ≃ 8.2σ, panel (b), with σ the grain diameter. (c) Dependence of the ratio of the apparent to added mass, ma=m, on the filling height relative to the grain diameter, h=σ, for different D. Full lines are fit to the theoretical model. (d) Characteristic length scales corresponding to (ha) the height where the deviation from the hydrodynamic expectation starts, (h*) the height corresponding to the maximum in ma=m, and (hd) the height to the right of the maximum where ma/m = 1.
We also used grains with different geometries (spherical, oblate, and prolate particles), and find that all three geometries display the overshoot in weight. By varying the size of the cylindrical container, we observe a decaying in magnitude of the overshoot proportional to D-1 for the case of the spheres. However, non-spherical geometries show a faster decay of the overshoot peak with the size of the container column.
Figure 2: Experimental and numerical results for the dependence of the maximum of the reported anomaly on the cylinder diameter relative to the grain size. Blue dots correspond to experiments performed with oblate particles (lentils), red dots correspond to experiments performed with prolate particles (beans), and finally, the dashed line correspond to the results obtained with spherical particles.
We argue that packing effects are behind the quantitative differences between spherical to non-spherical grains. Ellipsoids pack in a more efficient way than spheres.
Finally, we can connect these results with recent experiments using fire ants as an active version of granular matter. Despite the inherent activity of the ants and their natural tendency to rearrange, the ants also develop force-chain structures that help support the weight of the column (see Fire Ants research section for more details).
[1] S. Mahajan, et al., Phys. Rev. Lett., 124, 128002 (2020).