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Curves Ahead: A Guide to Particle Size Distributions

March 9, 2016
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Interior view of a jet mill
Interior view of a jet mill
Wet mill
Wet mill
Air-swept roller mill
Air-swept roller mill
Ball mill
Ball mill
Jet Mill
Jet mill

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Materials are exposed to a wide set of processing and technology applications to control chaos, instill order, and ultimately create an engineered powder. One of powder’s more dominate physical attributes is Particle Size Distribution (PSD) characteristics. Particle size and shape play an important role in the performance of any powder. Assurance of a powder’s consistency, faithfulness of reproduction, and adherence to design are provided by any number of systems that produce the statistical distributions we know as curves.
    
This tutorial is not intended as a statistical discussion for a particle physicist. Instead, it acts as a high-level view of curves and some of the many size reduction technologies required to make powders. Analytical systems process powders, to generate data that in part represent powder as curves so that users have a consistent and reproducible basis for interpretation.
    
A PSD curve for a powder results from an input material, a processing technology and its application, and the resultant powder’s ability to meet the intent of a designer. Every powder’s mission should assist the user in achieving their meaningful business goals.

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An Elementary Understanding

An image of a PSD curve can appear intimidating, but there is actually nothing to fear. The data that makes up the report is nothing more than a mathematical model of the analytical systems interpretation of the powder that system has processed. A user should have the knowledge that the system doing the analysis is calibrated, maintained and suited for the powder type it is representing.
    
Systematic analysis of powder may occur at most any stage of processing but most likely upon process completion by judging the size, count, and volume of the particles in the sampled powder. The analyzer’s computer quickly assesses how many particles group into a number of size categories within the analysis. The more common example of this type of assessment is the bell shaped curve used in educational grading systems.
    
In Figure 1, a typical classroom grading system would consist of five possible grades: A, B, C, D, and F. Many classically trained teachers often design tests and courses so that the grade distribution creates a histogram where the majority of the classroom scores a C grade, a lesser number of students score B’s and D’s. And the fewest number of students score A’s and F’s. Thus students’ distribution make up these five grades. The histogram in Figure 1 appears balanced and the overlaying bell curve is symmetrical.
    
Figure 2 more closely represents the actual “reality” of the classroom. Seldom is a bell curve perfectly balanced at a mid-point. Teachers and professors attempt to balance the distribution by awarding additional points known as “curving”. This “grade curve” is used to adjust for some number of issues within the student population, an exam itself, the quality of the instruction, or efforts to relate student populations to an overall larger group.
    
It is not common for a powder PSD curve to be symmetrical distribution either. Technicians make adjustments and selections to PSD analyzers to account for the type of material, shape of the particle, and, like with educational grading, other variables.
    
Figure 1 and Figure 2 both have a mode or peak that indicates where “most” of the distribution is within a population or data set. Both have a median or a middle point, and a mean or an average calculation. These broad terms are important descriptors that allow an independent general inference to occur that facilitates a discussion among associates when using data to understand the PSD curve as a powder’s significant physical product profile.
    
PSD analyzers measure particles size in microns (millionth of a meter, micrometer, µm). Human hair thickness is about 100 microns in thickness. Different analyzers have a range of size from many thousands of microns down to the nanometer (billionth of a meter or nm) range. Having the appropriate PSD analyzer is critically important.
    
PSD evaluation is the first foremost task for curve generating analyzers. PSD describes the placement, location or arrangement of the particles within a powder. Describing a powder’s PSD using one particle size placement is limited in its ability to characterize the material. Using two particle size placements within the PSD is better but it is also limited in its ability to adequately facilitate overall “control” parameters of the material. Three particle size placements - near largest particle size or top size, the approximate middle particle size or mid-point size, and the near smallest particle size or bottom size - provide reasonable three-point control within a PSD curve.
    
The primary control point of a three point control is one of these three points.
•    Typically one of the mid-point, mean value or D50 (Distribution - 50% of the powder PSD is less than and greater than a specific micron size) are used.
•    The top size or D95, (distribution - 95% of the powder PSD is less than specific micron size while 5% is greater than that micron size) is used to specify how large the particles are in a powder.
•    Finally, the bottom size or D10 (distribution - 10% of the powder PSD is less than specific micron size while 90% is greater than that micron size)
•    The order of priority, the tolerance applied, and the specific Dv (value) is subject to the designer’s discretion.
•    More control or record points can be included as feasibly determined by the designer.
    A powder’s curve, as described above, will not convey many other physical and chemical attributes. A good understanding of the PSD is probably a leading factor in most powder applications.

Powder Fingerprints
PSD specification or analysis often indicates the processing technology category that aligns with the material. The shape of the curve the PSD can produce is like a processing technologies fingerprints. Figure 3 shows four PSD curves from left to right: wet milling, jet milling, air-swept roller milling, and ball milling curves are compared.
•    Wet milling produces an ultra-fine particle with a very narrow distribution
•    Jet milling produces a very-fine particle with a narrow distribution
•    Air-swept roller milling produces a fine particle with a controlled distribution
•    Ball milling produces a fine particle with a less-controlled distribution

Each of these technology categories have substantially different operating variables and applied technology principles. Experts in these fields are able to exploit the capabilities of each category to benefit the powder’s physical attributes. Each category works in tandem with the feed material attributes. The combination of the technology, the material, and the operating variables produce outputs that address specific needs across many different industries.

Right Tool for the Job
It is difficult to assess powder performance without understanding the purpose of the material. Most powders are “purpose-driven” materials. The powders ability to perform is dependent on several key performance attributes. These attributes are specific to the company’s intended use and are assessed and then re-assessed. When PSD is a key performance attribute, the correct optimum associated milling technology should be used.
    
While it is possible to use a straight screwdriver with a Phillips head screw, it is more efficient and safer to use a Phillips head screwdriver. Better yet, a cordless driver with a Phillips head bit is the right tool for the job, and so on. The same is true in the production of powders. In some industries, highly uniform and narrow PSD are critical, in other industries the same could be wholly damaging to product performance.
    
Many powders are converted and are a sub-set of a larger solid or liquid. The powders contribute to the physical, chemical, and performance attributes of a finished product. The powder’s influence on outcomes may or may not be visible to the users. Both competitive advantage and disadvantage are in the balance.

Economic “Curves”
The price of a powder is not the same as its cost. Price is typically understood as the amount of money per unit of measure. Dollars per pound or kilogram appear on an invoice or are internally calculated by a user. That cost is incorporated into the bill of materials that rolls-up as a product’s cost of goods on a profit and loss statement.
    
General Accepted Accounting Practices (GAAP) do not account for the benefit or liability of materials. In contrast, activity based costing and management will account for “cost-drivers” if the users choose to make it so. It may be considered instinctive that anyone observing a common material’s association with rejection rates or non-conformance would act swiftly to remedy that situation, but this is not always the case. Unfortunately, organizations can have different objectives for different business units and manufacturing materials may or may not have a strategic link to a material’s performance.
    
Powder PSD curves and the verified optimization of the correct production technologies and performance attributes are a vital imperative. For companies whose business involves powders, understanding curves as they relate to the individual mission of specific powder is essential to achieving meaningful business goals.
    

William K. Lavelle Jr. is VP for business development, Custom Processing Services. For more information, call 610-779-7001or visit www.customprocessingservices.com.

Get more information or register for the International Powder & Bulk Solids Conference & Exhibition, May 3-5, 2016
 

Custom Processing Services Inc.