Bulk strength (unconfined yield strength) is one of the major principle stresses causing material in an unconfined state to fail in shear. In process equipment, it is the primary flow property governing the development of hang-ups. Bulk strength is used to compute critical arching and rathole dimensions for a given material in a hopper or bin.
Furthermore, all hang-ups in process equipment cause the formation of a free surface. By default, the stress acting normally on any free surface is zero. However, Figure 1 shows that stresses acting along the free surface may not always be zero. For instance, in a hang-up condition, the material on a free surface is supported by stresses acting along the free surface, and are therefore equal to the material’s unconfined yield strength.
Figure 1. Typical arch in process equipment.
Critical Conical Arching Dimension
The smallest span of a conical hopper that prevents arching of the bulk material is its critical conical arching dimension. In other words, it is a function of the material’s unconfined yield strength as well as its storage time in the vessel.
To prevent the occurrence of stable arch formation, the conical hopper is required to have an outlet at least this big. Meanwhile, plane flow hoppers can possess hopper widths about ó as wide and still prevent stable arch formation. Further, the critical arching dimension also functions as a small function of the bin size and, thus, is usually associated with a calculation basis which represents the approximate size of a given bin geometry
Critical Rathole Dimension
The size of the largest flow channel that will result in stable rathole formation in a funnel flow bin design is termed the critical rathole dimension. In a funnel flow bin, the active flow channels must be greater than this value in order to prevent stable rathole formation.
Interestingly, ratholes cannot form in mass flow hoppers. Thus, the critical rathole dimension acts as a function of the maximum stress level in the bin and, thus, depends on the maximum diameter of the bin.
On the surface, bulk density may seem like an intrinsically simple property to grasp. In reality, it is the weight of the particles divided by the combined volume of the particles as well as the interstitial voids that surround the particles.
Further, it is a function of the material’s stress level and strain history and is used to determine the limiting rates of particulate materials. In addition, it is also used to determine the ability of a given powder to store entrained air.
Strength is the key property considered by the process engineer in order to determine whether a bulk material will arch or form stable ratholes in process equipment. Given that the goal of powder processing is the maintenance of a reliable flow, the arching and rathole tendencies are considerable problems.
Moreover, strength is a far-reaching flow property controlling the behavior of the bulk material in many processes. Since excessive powder strength can induce difficulties in the bulk material’s ability to fluidize, it could result in channeling and poor process control.
Even worse, blending may be rendered impossible due to excessive strength. In addition, excessive strength can also cause powder material to agglomerate when agitated.
It can also cause material to arch over die cavities, which makes capsule filling and tablet production difficult even in the best of scenarios. Strength can also cause variations in weight in filling machines. Lastly, excessive strength is capable of causing stagnant zones from powder during operation.
Bulk strength can also be a good thing in certain cases. Given the right amount of yield strength, it could often prevent unwanted particle segregation in powders. Strength can also cause compacted material to stay together after compaction, a situation that makes tableting and ceramic part production possible.
Moreover, serendipitously, strength causes agglomeration in cohesive bulk material when it comes to roll press operations. This allows for easily handled materials to form and prevents a variety of the problems caused by bulk strength.
It is possible for bulk strength measurements to provide early warning signs pointing to potential process upsets caused by arching and ratholing. This makes it an ideal measurement for the quality control of powder processes.
Many of today’s methods used in the measurement of material strength necessitate the significant training of technicians in order to get reliable results. Moreover, many of the existing test methods require a significant quantity of bulk solid material. It is often difficult to get this quantity of material or the material may prove to be expensive.
The typical process of bulk solids strength test measurement requires several hours of testing and calculation in order to achieve reasonable results. However, the method proposed in this article is simple, and can measure the strength of a very small quantity of sample material in the matter of a few minutes.
SSSpinTester Measurement Methodology
The test technique involves placing a small quantity of material into an enclosed conical cavity; consolidating it using centrifugal force; and then removing the obstructions at the bottom of the conical cavity. Furthermore, centrifugal force is used to cause the material to fail, yield, or extrude from the cavity. Steps 1 to 4 summarize the steps required. The key parts of the test procedure are also highlighted below:
The first step involves inserting a guard under the smaller diameter opening of the conical orifice, while material gets placed carefully into the cell by passing or vibrating the powder through a coarse sieve in order to break agglomerates.
During filling, over-compaction pressures arise, which are reduced by the gentle filling process. This step is necessary for the measurement of strength at very low consolidation pressures. Furthermore, over-consolidation due to excessive handling is reduced.
Step 2 involves placing a guard at the top of the cell and then setting the cell in a rotary cavity, in such a way to induce the axis of the conical cavity so that it is 90 degrees from the rotation direction.
The third step necessitates the rotation of the cell and rotor to a prescribed speed, and then subsequently holding it at that prescribed speed for an allotted time. Such a move causes centrifugal forces to act on the bulk material in the conical cell and thus compact the material within the cell.
In addition to the position being relative to the axis of rotation, the rotor speed and the weight of the material are handy tools to compute the consolidation pressure.
Lastly, the final step involves halting the rotation and removing the guards. Presumably, the bulk material has strength and will arch over the conical cavity. Following this, the rotation speed is increased incrementally until the compacted material completely exits the conical cavity, owing to centrifugal force.
Three factors are used to compute the force needed to fail the compacted material in the conical arch. These are the weight of the material, the position relative to the axis of rotation, and the rotation speed at the point when the material leaves the cell. Finally, this data is then analyzed to compute the bulk unconfined yield strength.
Relation of Test Results to Process
To get it right the first time, the ability to relate measured material properties to actual production parameters is essential, especially from the standpoint of both development and manufacture, for example both product and process.
For instance, all drugs in the pharmaceutical industry must be ‘packaged’ somehow with excipients in order to be marketable. Further, material bulk properties must compulsorily be measured at some point in the development process to quantify drug formulations for use in tablet press and tablet fill.
If the bulk strength of the material is an unknown variable, decisions relating to packaging are based on the ‘guess and check’ method.
Real powder packaging systems tend to operate at 40 to 200 Pa pressure. Further, traditional instruments are able to measure bulk strength at pressures of 500 Pa or greater. In instances where pressures are measured at values of 500 Pa, 1,000 Pa or higher, it is necessary to conduct mathematical extrapolation to scale measured values to real systems. However, extrapolation results in poor deductions because strength behavior is non-linear.
The SSSpinTester accurately quantifies the bulk solids’ strength at consolidation pressures down to 30 Pa with reasonable repeatability. Given that the user will indicate the pressure at which the SSSpinTester will measure strength, it is no longer necessary to rely on inherently inaccurate extrapolation for answers.
Moreover, the SSSpinTester is equipped to directly measure bulk strength at consolidation pressures that are low enough to scale to real industrial processes.
Results of SSSpinTester Analysis
The unconfined yield strength and bulk density of a Cancer Drug API was measured using the SSSpinTester. Figures 2 and 3, and Table 1, depict the relevant results. As can be observed, this material is compressible, with densities ranging from between 351 kg/m3 and 499 kg/m3, depending on the consolidation pressure (shown in Figure 2).
Figure 2. Unconfined Yield Strength of a Cancer Drug API.
Figure 3. Density of a Cancer Drug API.
Table 1. Unconfined Yield Strength and Density as a Function of Stress
|Bulk Unconfined Yield Strength
The density leaving the bin will be around 378 kg/m3 in the case of typical feed bins. Moreover, the maximum density in a 1.2 meter diameter bin with a vertical section that is 2.4 meters tall would be about 544 kg/m3.
For a Cancer Drug API, both rathole and arching indices were computed. The results can be seen in Table 2. It is likely that arching will be somewhat of a problem with this material. Furthermore, the flow properties suggest that the critical conical arching after 0 hours of storage is 0.16 meters.
Table 2. Summary of Flow Properties of a Cancer Drug
|Flow Rate Indices
Indices Basis: Dbin= 1.20 m Dout: 0.15 m
|Bin Density Index
|Feed Density Index
|Flow Rate Index
Indices Basis: Dbin=1.20 m Dout= 0.15 m
|Storage Time in
|Arching Index AI
|Rathole Index RI
This information has been sourced, reviewed and adapted from materials provided by Particulate Systems.
For more information on this source, please visit Particulate Systems.