(83c) Measurement of Solid Fraction and Its Fluctuations in Dense Granular Flows Using a Capacitance Probe

We measured the solid fraction (porosity) and its fluctuations in dense granular flows using a capacitance probe employed earlier by Louge at al (1996). The probe, originally developed to measure distance (Capacitec, Inc., Boston, Ma), is used here to measure the dielectric constant of the granular bed as it changes due to variations in solid fraction. Two geometries that of a Couette device, where granular material is sheared between two concentric cylinders and a flat-bottom bin-hopper device, were used. The annular Couette cell was modified to allow changes in solid fraction inside the bed by super-imposing a slow axial flow on the radial shearing.

As a result, a small decrease in solid fraction partially breaks the force chains between particles and provides enough space for random collision to occur inside the bed. This results in a significant decrease in shear stresses on the rotating cylinder and shifts the regime of flow from quasi-static to intermediate. We were able to find the actual change in solid fraction required for this change to happen. During batch Couette experiments, where there is no axial flow, the solid fraction is at its maximum while by continuous removal of small amounts of material, the solid fraction decreases and the shear stress becomes shear rate dependent. We found that fluctuations of solid fraction only occur with axial-flow while in a no-flow (static) experiment, there are no fluctuations. We also observed that increasing the axial flow rate does not significantly change the solid fraction. The capacitance probe was originally mounted flush to the outer stationary wall but more recent experiments were carried out by pushing the probe inside the shearing zone. As the probe moves from the stationary wall towards the rotating wall, the fluctuations of solid fractions increase. Inside the shearing zone, the solid fraction is also shear rate dependent.

In the flat-bottom hopper (funnel flow), the solid fraction is mostly constant when the material is stagnant (not moving), but as soon as the material starts to flow, the solid fraction decreases and remains approximately constant for all flow rates. It fluctuates around an average value but when the flow is stopped the solid fraction does not change and the fluctuations also stop. It appears that the material remains in its ?flowing? arrangement and when the flow is restarted, the solid fraction remains essentially unchanged and starts to fluctuate again. It seems that when the solid fraction on the wall reaches a certain value the material keeps its arrangement no matter if it is flowing or is static. This behavior is consistent with our previous stress measurements (Kheiripour Langroudi, et. al., 2008) that show that as soon as the material stops flowing (shearing) the stress ?freezes? at its existing value and only changes if the flow is restarted. This appears to also confirm that stresses measured in a static powder are random and depend on the previous history and stressing of the powder as particles are arranged in a certain geometrical matrix.

Reference

1.M. Louge, M. Tuccio, E. Lander, and P. Connors, Rev. Sci. Instrum. 67, 1869-1877

2.M. Kheiripour Langroudi, S. Turek, A. Ouazzi, and G. Tardos; Submitted to Powder Technology, 2009