Powder flowability - FFC, FF, ff, and WTF!

Scientists and engineers working in the pharmaceutical industry often investigate solid dosage formulations that contain new active pharmaceutical ingredients (API). Experimental designs are carefully planned so that the effects of input variables such as API content and the amounts of fillers, binders, disintegrants, glidants, and lubricants can be quantified during early stages of development. The inputs are thrown into JMP, which spits out a DOE (design of experiments) to follow. Once the outputs are entered, JMP will tell the investigator which of the inputs are significant.

Typical outputs include tablet properties such as weight, API content (or potency, which is the product of the two), uniformity, stability, and dissolution rate. Of course, it's challenging to produce tablets if the powder blend won't flow into the tablet press or the granulator upstream of the press, so we add one more column labeled flowability. Powder flow is very important, but what is the best way to define flowability?

Many laboratories are equipped with a shear cell tester, such as one made by Dietmar Schulze, Brookfield Engineering, E&G Associates, and Freeman Technology. I've used all of them. Some I like better than others, but I gave all of them 4 stars on Yelp. Lyn Bates also has a good one. If you want a Schulze tester and you live outside Europe, you'll need to contact Jenike & Johanson. Shear cell testers measure the cohesive strength, internal friction, compressibility, and wall friction of powders. It is best to measure these properties over a range of pressures. Then the test results can be used to predict if and how a formulation will flow in an existing hopper, or they can be used to design a new hopper that will handle a powder reliably.

Many investigators, however, attempt to define flowability by a single parameter or index. FFC, which is the ratio of the consolidation pressure (σ1), to the cohesive strength (fc) is frequently used. My recommendation: DON'T!

FFC again is the consolidation stress divided by the cohesive strength. The ratio is often erroneously called the flow function or the flow factor. This may be partly due to the way Andrew Jenike, who pioneered powder flow property testing and bin design, defined the ratio in his classic manuscript Bulletin 123. (Bulletin 123 is the Bible of hopper design. I have a copy that I keep on my desk. I genuflect whenever I open it. I also have a copy of Andrew Jenike's Bulletin 108, but when I tried to read it, I passed out. Unfortunately Berlitz does not have a mechanical engineering to chemical engineering dictionary. Bulletin 123 is the Readers' Digest version of Bulletin 108.) In Bulletin 123, Jenike presented a table of FF values that could be used as a general classification of flowability. <genuflect> Below is a copy of the table from my Bulletin 123: </genuflect>

In Bulletin 123, Jenike defined FF as the ratio of the major consolidation stress to the unconfined yield strength, i.e., the ratio of the consolidation pressure to the cohesive strength. Much later on in Bulletin 123, he also defined FF as the Flow Function, the relationship between the material’s strength (fc) and the major consolidation pressure σ1, not the ratio. FF can therefore be either the ratio of the major consolidation pressure to the cohesive strength or the Flow Function, which is the relationship between the major consolidation pressure and the cohesive strength. Jenike also defined the flow factor ff as the ratio of the major consolidation stress σ1 to the stresses on the abutments of an arch σ1bar of powder at the hopper outlet. The flow factor is used to calculate the size of a hopper outlet required to prevent bridging. 

Actually, Bulletin 123's stresses are expressed as forces divided by 13. The forces were those recorded by Jenike's shear cell tester, and 1/13 is the cross-sectional area in square feet of his 3 3/4-in. diameter cell. But I digress. I have a difficult time telling a story without first bringing up prenatal memories. In any event, FFC should never be called the Flow Function or the flow factor. FFC is equal to σ1/fc, the ratio of the major consolidation stress to the cohesive strength. It best to refer to FFC as the flowability coefficient, or the flow function coefficient if you want a word for each letter in FFC, or you can just call it FFC.  

A nice thing about modern shear cell testers is that they are computer controlled, and their software will calculate the consolidation pressure and cohesive strength as well as the effective angle of friction, the angle of wall friction and the compressibility for you, and you won't have to multiply your results by 13. The angle of wall friction is similar to a friction coefficient; actually, the tangent of the wall friction angle is the friction coefficient. The effective angle of friction has something to do with internal friction. Compressibility is the relationship bewteen bulk density and consolidation pressure.

Now suppose we want to compare the flowability of two formulations: Blend A and Blend B. We perform cohesive strength and wall friction tests on each material over a range of pressures. The internal friction and compressibility are conveniently measured during the cohesive strength tests. We use a wall coupon of the same material that was used to fabricate our existing hopper.

After one afternoon in the lab, we obtain the following shear cell test results:

Great! Now we need values for flowability that we can input into our statistics program. How 'bout FFC? It seems useful. FFC is the ratio of the consolidation pressure and the cohesive strength; cohesive strength is in the denominator, so a big FFC will mean that we have good flowability. We want big numbers, although we hope that we don't have any non-cohesive powders because then the denominator will equal zero, and we're not sure if JMP will like ∞ (infinity).

FFC is easy to calculate, so let's go ahead and do it. Here are the results:

It looks like the flowability of Blend A is superior to that of Blend B. Its range of FFC values is higher. According to Jenike's table, Blend A is "easy-flowing" while B is "cohesive". A is our choice. Let's go ahead and make several kilograms of Blend A, confident that it will reliably discharge from our feed hopper into our press or granulator. But WTF (why the face?), it bridges over the outlet! We keep poking at the obstruction to reinitiate flow only to generate a rathole! As Eminem might say... Snap back to reality. Oh, there goes gravity. But nothin' is flowin' by gravity alo'ne...

I tried to warn you that FFC will not necessarily tell you which of the formulations, A or B, is the optimum from a flowability perspective. We have plenty of test results. Let's use them in their entirety to determine what kind of hopper is needed to handle our blends. If we have an existing hopper, we had better make sure that its outlet is large enough to ensure that the stresses on the powder at the outlet are greater than the material's cohesive strength. Otherwise it will arch. And if we want to avoid ratholes, we'd better use a hopper with walls that are steep enough to allow mass flow so that powder will flow throughout the hopper. Knowing how to calculate outlet and hopper angle requirements entails some effort and training, so contact me if you need help. There are several documents that you can download form my website (www.mehos.net) that detail the analyses including my textbook on powder testing and bulk solids storage and handling.

So here are the results of the analysis:

The analysis is revealing! Blend A requires a larger outlet (120 mm vs. 23 mm for Blend B) and a much steeper hopper (13° from vertical vs. 36° for Blend B). No wonder Blend A would not flow out of our conical hopper. After all, it has a 1-in. diameter outlet and walls sloped 30° from vertical! It turns out that FFC was a misleading metric. Don't tell me you weren't warned.

Blend B is actually less cohesive at the low pressure condition of the outlet of a mass flow hopper, and its higher bulk density allows gravity to do its job more effectively. In addition, Blend B has lower wall friction and therefore hopper walls do not have to be that steep. Had we defined flowability by at least two terms, critical arching diameter and recommended mass flow hopper angle, we would have proceeded with Blend B.

Shear cell testers are a big investment. If you have one, you might as well get your money's worth. Powder flow is just too complicated to be described by a single index. Don't rely on FFC. Rather, use your shear cell tester to determine if your formulation will reliably discharge from an existing hopper or use its test results to design a new hopper that will reliably handle your powder blend.

The analysis is a bit tasking, but you can download the Excel workbook that I use to perform the calculations. FFS, stop using FFC!

Greg Mehos, Ph.E., P.E. ? 978-799-7311 ? [email protected]