Measurement of velocity and density profiles in discharging conical hoppers by NMR imaging

Nuclear magnetic resonance (NMR) imaging was used to measure velocity and density profiles in 3-D conical hoppers fed from an open vertical silo. Discharge of a 200 μm-diameter powder in both mass and plug flow was studied with hoppers of different half angles, of 10° and 80°, respectively. An analytical solution for compressible (variable density) mass flow in the 3-D axi-symmetric geometry was also developed following the procedure outlined in Tardos (1997) and Tardos and Mort (2005). The density variation and velocity profiles obtained experimentally were compared to predictions of this theory for dense, compressible granular flows. We found, from both theory and experiment, that the powder has to exhibit significant dilation (compressibility) as it is accelerated through the constriction in the hopper. The degree of compressibility was found, experimentally, to be lower than that predicted by the mass flow hopper theory. The powder unexpectedly exhibited a boundary layer with a fully-rough boundary condition in the mass flow hopper. In the funnel-flow hopper, the expected “dead zone” was found around the orifice and extended about one diameter length into the silo. The centerline velocity increased according to an exponential function.