Hysteresis and packing in gas-fluidized beds

The packing fraction and the pressure drop across gas-fluidized beds of granular media exhibit hysteresis as the gas-flow rate is cycled up and down across the fluidization transition. Presumably this is due to contact forces and transfer of stress to the surrounding walls, and hence should vary nontrivially with the aspect ratio of the sample. Here we present systematic measurements of the variation of hysteresis with particle size and aspect ratio of the sample. Remarkably, the hysteresis scales in a trivial way with these parameters, showing no evidence of long-range effects of the wall. Our measurements also show that the packing fraction becomes $0.590\pm 0.004,$ independent of particle size and container shape, when the fluidizing flow of gas flow is slowly removed.