As a young engineer, I suggested to a soon-to-be-retiring engineer that he should write a book which documented his experiences and preserved his understanding of engineering phenomena for future generations. He declined because he said, "It is too great a task! Where would I begin?"

Later in my career, I had the privilege of participating as co-author with James E. Funk, who was a Professor of Ceramic Engineering at Alfred University, in the Predictive Process Control textbook (Kluwer Academic Publishers, 1994).  The practical applications chapters in the latter half of this book document much of Jim’s knowledge, experiences, and understanding of ceramic processing. That book successfully preserved much of his understanding of ceramic processing so it is available to be shared with new generations of ceramic engineers.

The books in this ... for Ceramists series are my attempts to do the same in my own career. My reason for entering academia was to teach the fundamentals of ceramic engineering to new engineers, and these books represent the fulfillment and culmination of that purpose.

The books in this series are also designed to fill a void that I perceive to exist: fundamental, easy to understand, textbooks which cover many of the essential, foundation phenomena of ceramic engineering.

The specific purpose of this book is to introduce and discuss the major characterization techniques and instruments used in today’s ceramics and materials laboratories.

Many ceramic and materials engineers, technicians, and managers are responsible for selection of characterization techniques, purchase of instruments or analytical services, performance of routine analyses, interpretation of data, and application of test results to their processes. Many of these same technical people do not want, need, nor care to know the complete derivations and the full equations governing each available characterization technique. In fact, it is unnecessary for anyone to wade through differential equations, complex physics, quantum mechanics, chemistry, or geometric derivations, before they can decide whether or not they need to use a particular characterization technique, or before they can perform an analysis using an instrument.

Most technical people simply want to know which techniques are available, what each technique can do, and how each type of characterization procedure is useful. This book was written for these engineers, technicians, and managers.

In this book, discussions will cover the fundamental purposes of each technique, how each works, what each does, how results generated by each can be used, and how each characterization tool fits into the grand scheme of materials characterization.

Those of you who want (or need) to learn more details concerning a specific characterization technique are referred to the many available advanced textbooks and technical articles.

Generally, this book is organized as follows: the most commonly used ceramic processing characterization techniques are covered in greater detail toward the front of the book; and less commonly used techniques, most of which are used primarily for research, are covered in less detail toward the back of the book.

This book should be appropriate (1) as a handy reference for all ceramic and materials engineers, technicians, and managers, (2) as a textbook for characterization survey courses at the undergraduate level, and (3) when supplemented with personal research (that is, with detailed homework assignments) into technical articles and advanced textbooks covering each characterization technique, this book should be appropriate as the basis for graduate characterization courses.

Consistent with the other books in this series, I will do my best to give clear and useful descriptions and discussions of each of these characterization techniques.

Dennis R. Dinger
12 August 2004

Settling rates of particles during unhindered settling can be calculated for each particle size using Stoke’s Law:

Assumptions applied with sedimentation analysis include:

(1) all particles, regardless of shape, behave as if they are spheres; and

(2) all particles are separated by sufficient distance to allow each particle to settle independently (i.e., without hindrance of, or by, any other particles.)

An Example of a Sedimentation Analyzer

The main example of an automatic sedimentation analyzer that is used throughout the ceramics industries is the Micromeritics SediGraph (Micromeritics Instruments Corporation, Norcross, GA).  SediGraphs use X-ray absorption to measure the mass of particles in the analysis plane during the analysis process.  Measurements proceed from coarse to fine as particles settle. This method directly produces CPFT (Cumulative Percent Finer Than) data because at each instant during the analysis the instrument measures the mass of particles remaining after all coarser particles have settled past the plane of analysis in the sample cell. Since all particles finer than each measured size contribute to the X-ray absorption measurement, SediGraph output can accurately be plotted in CPFT form, and/or in histogram form (mass % in each size class). 

This may appear to be a statement of the obvious, but it should be noted that other PSD analysis methods, such as laser scattering techniques which measure particles residing in specific size classes, can only accurately produce histograms, not CPFT distributions.  To display a true CPFT distribution, one must know the total mass of particles finer than each specific size.  Sedimentation analyses measure the total masses of particles finer than each specific size.  Laser scattering techniques cannot detect particles finer than their lower size analysis limits -- which means they cannot present their data as true CPFT distributions.

Unlike laser scattering techniques which cannot see particles outside their detection limits, SediGraphs can and do measure the mass of particles that remains suspended at its lower detection limit. SediGraphs cannot analyze the distribution of particles in those size classes smaller than their lower analysis limit, but they do measure the total mass of particles in that size range. The reason for the lower size analysis limit in sedimentation analyses is not that the detectors cannot see particles (because they can!), but because colloidal particles no longer settle predictably, consistent with Stoke's law.  True CPFT distributions (that is, those accurately based on the total mass of particles finer than each size) can be and are produced by sedimentation analyses.

Sedimentation Considerations

Coarse Particles

Sedimentation analysis procedures are subject to several limitations. The desire to use sample suspensions with the lowest possible solids contents to produce unhindered settling is offset by the necessity to use sufficiently high solids contents to produce statistically significant results and to provide sufficient masses of particles for the instruments’ detectors to precisely measure the particles. At the trade-off point where solids contents are sufficient for detectors and settling is acceptably unhindered, large diameter particles can still affect (hinder) the settling of other particles.

Large particles settle fast enough to produce a wake which disturbs the settling of nearby particles. To predict this phenomenon, Reynolds numbers for particle settling must be calculated. The following equation shows the Reynolds number equation for settling particles:

Re = (DVr)/m                                              

where D   = particle diameter (equivalent spherical diameter),
          V   = velocity of a settling particle,
         D_L  = liquid medium density, and
          :   = liquid medium viscosity.

To produce unhindered settling conditions in an analysis, all particle Reynolds numbers must be less than ~0.3. Since the Reynolds number is a function of particle diameter, this effectively places an upper limit on particle sizes that can be included in samples being analyzed. This typically produces a practical upper particle size limit for sedimentation measurements of common ceramic powders in the 75-150:m range.

Fine Particles

Limitations exist at the fine size extreme, as well. Colloidal particles are so small that they are affected by Brownian motion and they don’t settle predictably. Colloids are defined as particles with sizes 1:m and smaller. Gravity causes all particles to settle, but Brownian motion causes particles to move randomly in all directions. For colloidal particles, Brownian motion has greater influence on particle motion than gravitational forces. The overall motion of colloidal particles is therefore unpredictable. This effectively limits the smallest sizes that should be measured using sedimentation techniques to about 1:m.

Combined Effects of Coarse and Fine Limitations

Because of these two limitations, sedimentation analyses of many ceramic powders are effectively limited to particles in the size range from ~1–150:m. This size range includes not only important sub-sieve sizes, but it includes most particle sizes found in traditional and modern ceramic systems. This size range overlaps the smallest traditional sieve sizes, so sedimentation analyses can be combined with sieve analyses to cover systems containing substantial amounts of coarse particles.

CPFT Outputs Are Valid

An important advantage of sedimentation analyses is that the total mass of colloidal particles below sedimentation instruments’ lower size detection limits can be measured, and therefore, is known.  Even at the lower size analysis limit of these instruments, the percentage of finer particles that remain unsettled is measured and known.

This is very useful information, especially when other techniques are not available to measure the size distribution of colloidal particles. Sedimentation techniques may not describe the size distribution of particles smaller than ~1:m, but the mass percentage of particles below 1:m will be measured, and true CPFT distributions can be displayed.

Single Densities

Another limitation on sedimentation analyses is that particles in any single sample must all have the same particle density. Sedimentation analyses cannot be performed on body samples containing powders of different densities. When all powders in a body have the same density (which is the case in many traditional ceramic bodies), samples of the whole body can be analyzed.  When powders in a body have different densities, however, each ingredient must be analyzed separately by sedimentation techniques. The PSD of the total body can then be calculated from individual PSDs using body composition percentages.

Centrifugal Sedimentation

Some instruments use centrifuges to perform sedimentation analyses. This increases the acceleration on particles well beyond that of gravity. This speeds the settling process, shortens analysis times, and reduces both the lower and upper particle size detection limits.  Horiba Instruments, Inc., of Irvine, CA, makes a centrifugal sedimentation instrument.

Although finer particles can be analyzed in centrifugal sedimentation instruments (compared to static sedimentation), several analyses may need to be performed to cover the finest particle size ranges. Then, results must be combined to produce a single particle size distribution covering the broader range of interest.

It is a difficult process to remove coarse particles from samples without disturbing the representative nature of the remainder of the sample. Then too, combining several different sets of PSD results from several different sample analyses into a single PSD is always tricky. Resulting distributions are frequently not smooth (continuous) at the sizes where the different analysis results have been joined. Representative sampling, in such cases, is even more critical than usual because the several different starting samples must each be equally representative of the original powder and of each other.

Overall, combining several analyses to form a single, broad particle size analysis is difficult to successfully and accurately perform – but when it must be done – it must be done!

Analysis Times

Sedimentation analyses can take from about 15 minutes to more than an hour each, depending on the analyzer, the characteristics of the powders, and the analysis size range (from several hundred micrometers down to colloidal particles, subject to the limitations discussed above.)

Detection Methods

The most common automatic sedimentation analyzers use X-ray absorption or optical light projected areas to sense particles. Some powders (such as carbon powders) are transparent to X-rays and therefore cannot be measured in instruments using X-ray absorption for particle detection. In such cases, instruments which measure projected areas of shadows cast by visible light sources must be used.

Summary

Sedimentation analysis is a commonly used method for measuring particle size distributions of ceramic raw materials.  Fundamentally, the technique measures the sedimentation rates of particles.  Its effective range includes particle sizes from about 1 micrometer to about 150 micrometers (due to analysis limitations) although automatic instruments are designed to cover from about 0.1 micrometers to about 300 micrometers.  Each suspension to be analyzed must include only a single density material.  When X-ray absorption is used with sedimentation analysis, particles must absorb X-rays.  For coal, carbonaceous and other materials which are transparent to X-rays, analyses can be performed using projected areas cast by visible light sources.

Sedimentation analysis is an excellent way to measure particle size distributions of ball clays, kaolins, and all other ceramic raw materials.

Miscellany

Suggested topics .... Please continue to send your ideas or questions for future topics.  Thanks.  Until next time ...

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