Comparing the Schulze Method and the Bulk Strength Measurement Technique

Typical fluids tend to behave differently from bulk solids. For instance, upon placing a fluid in a container with an opening, it often flows through that opening. The pertinent question here is: how quickly does it pass through that particular opening? In contrast, when a bulk solid gets placed into a container and allowed to flow, there is a possibility that it may or may not pass through the opening.

These behavioral differences between liquids and solids result from the unique differences between fluids and powders. Within the bulk, a powder has the capacity to maintain and resist different stresses in several directions. However, the same is not true for liquids.

Take the example of a simple fluid at rest using a container. At a given point, the pressure two meters below the top surface will be a unique value, no matter what the direction of the container wall is, or even whether the surface is an internal or an external surface. At this prescribed elevation, if the fluid comes into contact with the surface, the pressure’s magnitude will inevitably be a unique scalar value.

On the other hand, in the case of powders, the situation tends to be significantly more complex. Consider a powder made to come to rest in a container. Within the powder, at any given point, there are a variety of different stresses acting in mutually orthogonal directions.

Furthermore, it is entirely possible that close to the container outlet, the outlet direction’s stress level is zero, while the stress level that acts against the container wall close to the outlet is more significant.

What’s more, if the material has an unconfined yield strength, and the stress against the wall is lower than this yield stress, it follows that the powder strength can create a situation where flow is completely stopped from the outlet.

As a result, this forms a stable arch across the outlet. The definition of unconfined yield strength is the major principle stress that acts on a bulk material in an unconfined state, thus causing that material to initially fail or yield in shear.

Strength is the key property which determines whether a bulk material will arch or form stable ratholes in process equipment, in the process engineer’s world. Considering that the goal of powder processing is the maintenance of a reliable flow, considerable problems include arching and rathole tendencies.

Strength is a far-reaching flow property controlling the behavior of the bulk material when it comes to many processes. For instance, the bulk material may become difficult to fluidize due to excessive powder strength, ultimately resulting 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 in the best of scenarios. Strength can also cause variations in weight in filling machines. Lastly, excessive strength is capable of causing stagnant zones in powder during operation.

It is worth noting that bulk strength can 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 possible tableting and ceramic part production.

Moreover, 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 often caused by bulk strength.

Since a large number of powder flow behaviors depend on the material’s bulk unconfined yield strength, measuring this key property should occupy a prominent position of place when it comes to standard powder characterization tests undertaken for the pharmaceutical, chemical, ceramic, powdered metal, food, cosmetic, battery, and nutraceutical industries.

Measuring yield strength must be done almost as frequently as particle size in order to quantify potential flow problems in key process areas.

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. Thus, this begs the question: why are bulk strength measurements not used more frequently in the characterization of bulk powders?

It is partially because a majority of the current methods to measure this quantity require significant technician training in order to achieve reliable results. For instance, if it were just a question of filling a test cell and letting the machine do the rest, perhaps this method might be used more often.

Moreover, many of the existing test methods necessitate 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.

What’s more, if there was a testing method that required only as much material that is used in a typical laser diffraction particle size analysis, it could be possible to conduct more bulk unconfined strength measurements. Lastly, the answer to the above question relates to the time required to run typical bulk solid strength tests.

Usually, this measurement process means several hours of testing and calculation in order to achieve reasonable results. If the strength measurement could be accomplished within a few minutes, naturally this would lead to more measurements of bulk cohesive strength, with engineers being able to use this to correlate product characteristics with process behavior.

An important factor here is the ability to measure a flow property directly correlating to problems in the process. More often than not, engineers rely on secondary measurements in the correlation of material strength with process behavior. For instance, an easily measured property is particle size, and this is used by quite a few engineers to predict process behavior.

However, assuming  that a particular dust collection system receiving vessel gets constantly plugged with powder during operation, it is possible that the upstream process is creating a stream of consistently sized particles, with fluctuations in moisture content, static charge, particle hydrophobicity, particle roughness, or even particle shape being the true causes of these cohesive hang-ups.

Meanwhile, given the fact that changes in particle size can cause differences in bulk strength, there are a number of other reasons that could cause the bulk yield strength of a powder to change. It is true that there is some merit in analyzing and understanding the cause of cohesive strength, more often than not, the problem lies in wanting to simply identify the problem and change process variables in order to prevent the cohesive hang-up issue.

In such scenarios, it is much more prudent to directly measure the property causing the process problem (such as bulk unconfined yield strength) than to have to measure multiple properties (for example size, shape, moisture content, surface roughness, and surface energies), as well as to infer the effect of each on the primary property of interest (bulk strength).

Many times, engineers sincerely want to understand the relationship between particle scale properties and bulk unconfined yield strength. Therefore, an easy method to measure strength is needed, in order to avoid undertaking a rigorous study of the variables that cause bulk unconfined yield strength of fine powder.

Moreover, this method must be relatively fast, should not require much material, and should ideally cover the full range of stresses that the material may be subjected to.

This article proposes a new test methodology, which allows the user to easily measure the bulk strength of a small ~0.1 cc sample of material in the matter of a few minutes. Additionally, this test method will enable the user to measure cohesive strength values at a consolidation pressure which is two orders of magnitude smaller than what is currently possible using existing test equipment.

The advantage of this low pressure measurement capability is due to the fact that a number of hang-ups occur in the low stress regions near the outlet of small diameter hoppers or over the small die cavity during the filling of a compaction machine.

More often than not, weight variation in tablets occurs as a result of problems in the initial die or capsule filling process. Traditional strength measurement methods cannot measure the key cohesive flow properties at these low stress values, while extrapolation must be used to estimate bulk strength at low stress values found in real powder processing systems, therefore this new technique is preferred.

Further, this new method enables the direct measurement of unconfined yield strength at low stress levels, from as low as 10 Pa. As far as this article is concerned, it describes a new method for measuring the unconfined yield strength of bulk powders.

Moreover, a comparison between strength measurements obtained with this novel method to traditional measurements and direct shear testers (like the Schulze tester commonly used in industry) is undertaken.

Measurement Methodology

The test technique involves placing a small quantity of material into an enclosed conical cavity. This is then consolidated using centrifugal force; then obstructions at the bottom of the conical cavity are removed and centrifugal force is used to cause material to fail, yield, or extrude from the cavity. Steps 1 through to 4 summarizes this process, and  the key parts of the test procedure are highlighted below:

Step 1

The first step involves inserting a guard under the smaller diameter opening of the conical orifice. Material then 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 handling should be reduced, but this is not as critical when conducting measurements at large consolidation pressures.

Step 2

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 as to induce the axis of the conical cavity so that it is 90 degrees from the rotation direction.

Step 3

The third step necessitates the rotation of the cell and rotor to a prescribed speed, and then subsequently the user must hold 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 compacts the material within the cell. In addition to the position relative to the axis of rotation, the rotor speed and the weight of the material are handy tools to use when computing the consolidation pressure.

Step 4

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.

Test Time Requirements

About 0.1 cc of material is needed for the entire process, which can be completed in a matter of minutes. Testing begins by the user interface requiring a cell to be filled and a couple of guards to be removed at key points during the test. The entire test can be undertaken in a matter of about five minutes for each strength measurement of interest.

Given the concerns surrounding quality control, this is a very reasonable time expenditure to analyze the cohesive properties of powder created by the process. In the design or research mode, where a complete strength profile is needed as a function of compaction pressure, the procedure will require about 30 minutes and 0.6 cc of material to generate a six point strength profile and fully characterize the hang-up behavior of the bulk material.

Additionally, a formulation engineer attempting to design a free-flowing material by adding flowaids or glidents to the formulation can comprehensively examine the effect of five flow-aid concentrations at six compaction pressures in just two and a half hours.

Thus, such a methodology equips engineers to generate the data, determine the optimal flow-aid concentration, write the report, and send it to their boss, all in the matter of a few short hours. Using traditional methods, the same task would require much more time. At times, several days of testing and data extrapolation would be required to accomplish the same goal.

Comparison of Data

Between 1989 and 1992, the European solids flow community conducted a host of research involving the standardization of flow properties measurements1,3 with the help of a standardized material.

While it is still controversial to be able to create and maintain a standard test sample to be used for calibration of test equipment, this particular standard material, BCR limestone,  has been used to compare test equipment measuring bulk unconfined strength of powder materials.

Shear measurement data was collected using the work of two past researchers5,6. In addition to this, the bulk unconfined yield strength of a current sample of BCR limestone was independently measured using a Schulze direct shear tester2. Figure 1 depicts this data.

Comparison of BCR Limestone data generated from three different studies.

Figure 1. Comparison of BCR Limestone data generated from three different studies.

The data collected spans a fairly wide range of major principle stress values, ranging from 1,700 Pa to 36,000 Pa. Noteworthy is the fact that the available data is limited to stress values above 1,786 Pa. This is because the direct shear test technique cannot reliably generate strength data below this value when it comes to solid stress levels.

In some cases, certain researchers have been able to collect strength measurements for some materials at pressures as small as 1,000 Pa. Nevertheless, there is usually some amount of error in these measurements.

Moreover, the collection of this data shows that the strength as a function of major principle stress tends to level off as the stress level increases, as it is a nonlinear function. However, it could be argued, that for at least some stress ranges, the data generated from this direct shear test technique can be approximated by a linear curve.

This procedure also measured the bulk unconfined yield strength with the help of the new method described above, which is commercially available as the SSSpinTester. The bulk unconfined yield strength was measured at 26 distinct stress levels between 30 Pa and almost 30,000 Pa, which can be seen in Figure 2.

Comparison of BCR limestone data generated from three different studies and new test technique (SSSpinTester).

Figure 2. Comparison of BCR limestone data generated from three different studies and new test technique (SSSpinTester).

It is vital to note that the data from the SSSpinTester fits with the data generated using the direct shear method of all three researchers over the major principle stress levels for the entire data set. Thus, this data depicts a distinct nonlinear behavior, which acts as a function of consolidation pressure.

Further to this, consider the data in the lower pressure range of the curve seen in Figure 3. This figure plots strength values measured for major principle stress levels below 5,000 Pa, including data from other researchers as a comparison. It is clear to see in this figure, the strength points measured from the new test method (SSSpinTester) pass through the middle of the data points obtained by the other researchers.

Comparison of low stress level BCR limestone data generated from three different studies and new test technique (SSSpinTester).

Figure 3. Comparison of low stress level BCR limestone data generated from three different studies and new test technique (SSSpinTester).

What’s more, there are 10 additional strength measurements at consolidation stress values between 1,786 Pa and 30 Pa, which suggests that the new test method extends the test measurement range to almost twice the magnitude. Due to this, the characterization of the strength of bulk solids at consolidation pressures down to 30 Pa is now made possible with reasonable repeatability.

In addition, the bulk unconfined yield strength of Argo corn starch was also measured, using both the Schulze direct shear tester and the SSSpinTester (see Figure 4). Figure 4 also shows good correlation between the data.

Comparison of the unconfined yield strength of Argo cornstarch measured with the Schulze direct shear method and the new test technique (SSSpinTester).

Figure 4. Comparison of the unconfined yield strength of Argo cornstarch measured with the Schulze direct shear method and the new test technique (SSSpinTester).

For cornstarch, the strength values are lower than those for the limestone. Nevertheless, this material would still be considered to be of the cohesive variety. Data from both the Schulze and SSSpinTester point to the fact that the strength tends to level off considerably at higher consolidation stress levels.

Using the Schulze test, the lowest stress level that could be measured was about 1,500 Pa, while the SSSpinTester method was able to generate 11 points between 1,500 Pa and 30 Pa (as demonstrated in Figure 5).

Comparison of the lower stress level unconfined yield strength of Argo corn starch measured with the Schulze direct shear method and the new test technique (SSSpinTester).

Figure 5. Comparison of the lower stress level unconfined yield strength of Argo corn starch measured with the Schulze direct shear method and the new test technique (SSSpinTester).

From the perspective of an astute and skeptical solids flow practitioner, one cannot really validate the strength measurements using standard testers in the low stress regime. The implication is that one cannot actually identify whether this tester is actually measuring strength in an extremely low-pressure zone. The astute researcher would be correct because there is no way of validating the data using accepted direct shear measurement techniques.

However, to compute critical arching dimensions in conical hoppers and plane flow hoppers4, traditional strength measurements are routinely used. Currently, the theory used to predict these arches has been well-accepted all-round, since it has been vetted for nearly three decades.

The implication of this theory is that the arching diameter over a conical outlet is a function of the strength evaluated at a critical consolidation stress level (see Equations 1 through to 3).








σcrit = the major principle stress level at the arch
fccrit = the strength value at the arch.
Hθ = an arch geometry factor (2.2 for a typical cone).
ff = the flow factor relating the stress in the arch to the stress required to break the arch (typically 1.2).
γ = the bulk density of the powder.
g = the gravitational acceleration.

The corn starch was placed in various conical hoppers, each having different openings. It was discovered that it arched over an opening of about 8.8 cm. Then, the critical strength and major principle stress associated with this arching condition was computed, and subsequently plotted on the strength curve (shown in Figure 5 as a black dot).

Results showed an excellent agreement between the strength computed from the arching analysis and the strength measured directly with the SSSpinTester. Thus, while there isn’t yet a standard tester that can validate the strength data in the low pressure regime, the data obtained is consistent with arching observations in real systems.

To validate the SSSpinTester at low stress values, arching behavior can be used, thus indicating the distinct advantage of using this test technique to measure bulk unconfined yield strength of powders, especially when it pertains to low pressure regimes.

One of the typical use cases for these measurements is the prediction of arching of bulk materials in hoppers and bins. As per the above example, the use of data from traditional techniques (such as the Schulze test) requires extrapolation of strength data by at least one order of magnitude, which is a very risky extrapolation.

To extrapolate an order of magnitude is to ask a great deal from a set of experimental data, even if the data is consistent and excellent. However, using this new test methodology, the use of interpolation is possible to determine this value. All in all, it produces a much safer analysis.

Finally, the strength of FMC’s PH-102 MCC was measured, using both the Schulze tester and the new SSSpinTester methodology (described in Figure 6).

Comparison of the unconfined yield strength of FMC PH-102 MCC measured with the Schulze direct shear method and the new test technique (SSSpinTester).

Figure 6. Comparison of the unconfined yield strength of FMC PH-102 MCC measured with the Schulze direct shear method and the new test technique (SSSpinTester).

PH-102 MCC is a relatively free flowing material, but it is also elastic in nature, often proving to be difficult for researchers and formulators to acquire reliable data from direct shear measurements. PH-102 MCC also seems to predict values that are not consistent with observed arching behavior in process equipment.

For instance, placing FMC’s PH-102 MCC powder in a conical hopper, will produce an actual critical arching dimension of approximately 1.77 cm. However, it would not be unheard of when using traditional shear methods that tested PH-102 MCC powder will predict an arching dimension of between 10 cm to 15 cm.

Another researcher may test the same PH-102 MCC and obtain a negative arching value. Thus, the issue tends to be the accuracy of the direct shear methods in an attempt to measure the powder at very low strength levels.

It bears noting that the strength values from the Schulze measurement data appears to concave upward, and increases more than a typical linear curve at higher consolidation pressure. If the higher pressure data is included, and linear least squares curve fitting routines are used to regress the data, the resulting strength plot would likely predict a negative intercept on the strength axis.

Thus, a negative result for the arching dimension would be predicted. Conversely, if just the lower points are used to regress the PH-102 MCC data, then the strength plot may produce a significantly positive intercept of the strength axis, thereby predicting a large positive arching dimension. As seen from the above, there tends to be significant variability in the PH- 102 MCC strength data measured using the Schulze tester.

A potential cause for this variation in the use of the Schulze tester can be friction losses during shear. Measurement at very low strength values the friction losses in the Schulze lever arm system for the normal load, as well as the friction due to the vanes scraping on the cell’s side, thus causing significant changes in the yield locust during measurement.

For the purpose of this article, a detailed analysis of the friction conditions in the test cell are not explored, but only their effects relative to PH-102 MCC are quantified.

For instance, consider the load application level in the Schulze tester, which can cause a small (35 gm) change in the actual load applied to the material. This normal load may only vary by a measly 1%, but will naturally result in a change in the measured yield strength value of 15% to 20%. The addition of the other potential friction losses can cause a variation in strength values by up to 50% at 4,000 Pa.

Such losses are not proportional to the normal load. Moreover, if the Schulze tester was able to measure at lower stress values, the error in the strength would be still higher due to friction losses in the tester.

To conclude, measuring strength values less than 200 Pa using the Schulze tester is effectively impossible to accomplish with any degree of reasonable accuracy. Such a scenario explains some of the scatter observed in the PH-102 MCC measurements with the Schulze tester (the blue diamonds seen in Figure 6).

Strength values down to about 4,000 Pa in major principle stress were measured. What’s more, it would have been possible to obtain lower values, possibly around 2,000 Pa, using the Schulze tester if the data wasn’t scattered.

However, similar to other materials, the SSSpinTester method enabled the acquisition of 14 points between 4,000 Pa and 30 Pa (as shown in Figure 7). Also, under computation was the strength from the observed arching dimension of about 1.77 cm. Such a small arching dimension was created by a significantly small strength value of 28.6 Pa at a stress level of 34.3 Pa.

Comparison of the low stress unconfined yield strength of FMC PH-102 MCC measured with the Schulze direct shear method and the new test technique (SSSpinTester).

Figure 7. Comparison of the low stress unconfined yield strength of FMC PH-102 MCC measured with the Schulze direct shear method and the new test technique (SSSpinTester).

However, although this stress level is extremely low, the measured strength data values obtained from the SSSpinTester nevertheless resulted in interpolation and not extrapolation to reach these values. Thus, this new method makes it possible to measure the arching tendency directly of FMC’s PH-102 MCC powder with a decent level of accuracy. SSSpinTester’s strength data resulted in a computed arching dimension of 1.81 cm while the observed arching dimension was 1.77 cm.


Based on the use of centrifugal force to measure strength of bulk materials, this new test technique provides data that is comparable to the data obtained from traditional testers for achievable stress levels. However, this new method also facilitates measurement at major principle stress values that is two orders of magnitude less than those currently possible using traditional test techniques.

Consequently, this test method is able to provide accurate strength data for moderately free flowing materials and predict accurately the arching potential in process equipment even in small diameter hoppers. Moreover, it can also quantify strength values that are at par with those that might cause flow problems when filling capsules and tablet press dies.

To make any credible arching predictions or flow behavior predictions in capsule filling or tablet filling, other test techniques need significant extrapolation, of at least one order of magnitude. However, this new method doesn’t require any extrapolation. Physical observations causing flow problems in equipment are obtained by interpolating the SSSpinTester data.

Thus, for the first time ever, data measured by a strength measurement device abides by the conditions observed in real industrial systems. Such strength measurements are also made possible with just 0.1 cc of material, implying that a complete flow function characterization of the material can be done on 0.6 cc of material in approximately 30 minutes.

Naturally, it is expected that this new tester will significantly extend the accuracy of process prediction for cohesive materials.

However, everything stated here is just the tip of the iceberg. As observed, the small amount of material required for the test enables the correlation of strength measured from single samples collected from capsules to fill (weight variation) behavior.

Since it is possible to measure the strength of the material in a capsule directly, and compare this to the weight in that particular capsule, it allows researchers to develop strong correlations between weight fluctuations in packing systems and cohesive strength.

As a result, strength can now be measured on the same level as the smallest packages that industry now uses (such as pills). Simultaneously, the large pressure strength tests (above 2,000 Pa) correlate well with those obtained from traditional techniques.

This implies that the data obtained from this methodology can easily be used to design processes with extremely large bins and hoppers. At the same time, it can also be applicable in the design of very small feed systems that create individual pills or small packages.

In addition, this data may be applicable to regimes such as material flowing down a pile, where cohesion at very low stress values governs the segregation of material during process operation, because of the ability to measure strengths at low stress values.

As a result, this will create a new venue to explore the relationship between bulk flow properties and particle scale behaviors without the loss of billions in revenue and product due to segregation and quality issues.

Such a tester will prove to be invaluable to the formulator that must create a product with the right cohesion to prevent segregation while still maintaining enough free flowing ability to successfully fill the desired package size.

Lastly, the cohesion of fine powders prevents them from being easily fluidized. Nevertheless, the solids stress level in a fluidized condition is extremely low. Up until this point, it hasn’t been possible to measure the strength of powder at stress levels in fluid bed systems.

In other words, it has only been possible to infer cohesive properties through repose angle measurements of semi-fluidized materials or changes in torque measurements in fluid bed system with cohesive material. However, these properties have not been easy to obtain through direct measurement.

As seen, the SSSpinTester will provide a tool for those dealing with fluid beds to directly measure the parameter causing flow problems at the stress level expected in the beds. This invention can further lead to new models that describe the fluidization of cohesive materials, as well as give the ability to determine, in quality control mode, whether a catalyst has expended its useful life in a fluid bed device.

Since the SSSpinTester needs just five minutes for one strength measurement, not to mention minimal training to use, the tester lends itself perfectly to quality control measurements. A simple five minute measurement window will allow the monitoring of process changes in real time by quality control personnel, in order to ensure optimal control of many solid flow processes.

References and Further Reading

  1. Akers, R. J., The certification of a limestone for Jenike shear testing. Community Bureau of Reference, Brussels, Belgium, 1992.
  2. ASTM, Standard shear test method for bulk solids using the Schulze ring shear tester. Annual book of ASTM standards, 04.09 no D6773-02. ASTM, Philadelphia, USA, 2002.
  3. EFCE, Standard shear testing technique for particulate solids using the Jenike shear cell. Working Party on the Mechanics of Particulate Solids. The Institution of Chemical Engineers, Rugby, UK, 1989.
  4. Jenike, A. W. Storage and flow of solids: Bulletin 123. University of Utah, Salt Lake City, USA, 1964.
  5. Saraber, F., Enstad, G. G., Haaker, G., Investigations on the anisotropic yield behavior of a cohesive bulk solid. Powder Technology, 64(3), p. 183-190, 1991.
  6. Verwijs, Marinus Jacobus, Stick-slip in powder flow: a quest for coherence length, PhD Thesis, University of Florida, 2005.

This information has been sourced, reviewed and adapted from materials provided by Particulate Systems.

For more information on this source, please visit Particulate Systems.


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