Han,

such observations are not unusual when designing a critical outlet size for a more or less free-flowing product. What can be the reason? I would like to mention a few points:

- The shear tester: Since we can measure similar flow functions with different kinds of shear testers like the Jenike tester or the ring shear tester (assumed that they are operated and evaluated correctly - but if not, this usually would result in too low flow functions and, thus, too small calculated critical outlet dimensions), I would exclude that the over-design results from the shear tester.

- The theory: There is definitely some safety in the Jenike theory. The safety is not visible as a safety factor which we commonly use in other fields of engineering, e.g., the design of steel constructions, but it is included, e.g., in Jenike's assumptions.

- The particular design process: The critical outlet size is determined by the point of intersection of the flow frunction with the major stress in the arch. Especially for materials with lower strength (the better flowing materials), this point of intersection is relatively close to the origin of the fc-sigma1-diagram, i.e., the point of intersection is at small consolidation stresses. Often it is not possible to measure at so small consolidation stresses, but it has to be mentioned, that the ring shear tester allows to measure at much smaller stresses compared to the Jenike shear tester, especially the large ring shear tester RST-01.pc which is equipped with a counterweight system. In your case the point of intersection may be at a consolidation stress of little more than 200 Pa (if the bulk density is about 1000 kg/m3, if density is smaller, the stress is also smaller). So I assume that you had to extrapolate the flow function to the left in order to obtain a point of intersections with the major stress in the arch, determined by the ff-line. Since in reality flow functions are curved, especially close to the origin, a linear extrapolation of the flow function usually results in some additional safety against arching, and the the larger the distance of the point of intersection to the lowest measured point of the flow function, the larger the safety margin. Furthermore, in case of a large extrapolation small deviations of the measured points of the flow functions can results in much stronger deviations of the point of intersection.

Summary:

We all benefit from Jenike's theory since many decades. But although this theory has been a great step forward in silo design, it requires some experience and is to be used with care. I think that Jenike's theory has been made for cohesive materials, where the overdesign as described above is small. If the theory is applied on good-flowing materials which require outlet openings of only few centimeters, and no points of the flow function have been measured at corresponding small stresses, it usually leads to an overdesign, and often it is just not necessary to determine outlet dimensions in this range because alone due to flow rate requirements larger openings are needed.

I hope that this will help a bit. Please allow me to mention my recent book "Powders and Bulk Solids" (Springer, 2007) where the design procedures are described in detail, and where also some calculation examples are presented.

Best regards

Dietmar Schulze (www.dietmar-schulze.de) ■

Han,

yes, it can be difficult to measure at very low stresses. The reason is that at very low stresses the "stress and deformation history" the powder has experienced during filling the shear cell may play a role. We once did a research project where we measured flow properties of cohesive powders at very small consolidation stresses and came to the conclusion, that at consolidation stresses of few 100 Pa a special filling process is required (e.g., filling through a stiff sieve in order to avoid any consolidation during the filling process).

Therefore, tests at too small consolidation stresses of only some 100 Pa are less reproducible due to the influence of the deformation and stress history.

If you deal with a nearly free-flowing material, it probably consists of larger particles than a cohesive powder. So in your shear cell is a smaller number of particles which may be another reason for decreasing reproducibility at low stress (so it is strongly recommended to use a large shear cell). In addition, effects like the dilation at shear to failure may have a stronger impact on the measured shear stress at lower normal stresses than at higher normal stresses (something about this is written in my book, chapter 5).

From my experience, the shear velocity does not play a role in the range of some millimeters per minute.

Best regards

Dietmar ■