Volume 5  Number 6                            Dennis R. Dinger                                1 April 2007

Updates

"... for Ceramists" Series Books

The paperback version of Characterization Techniques for Ceramists is available on the Books and Downloads page at the web site!    Retail price is $29.95 plus shipping and handling. The book has 256 pages and it covers 34 different characterization techniques that are commonly used by ceramists.  Order your copy NOW!

The book sets on the web site have also been revised to include this new book.  A 3-book set of paperbacks, including one each of Particle Calculations for Ceramists, Rheology for Ceramists, and Characterization Techniques for Ceramists, is now available for $64.85 plus shipping and handling.  This is a $10 saving off the total retail price of the 3 paperback books.  A 3-book set of downloads is also available for $52.85.  This, too, represents a $10 saving off the total retail price of the 3 downloadable books.  

The E-Book version of Characterization Techniques for Ceramists is available for downloading at the Books and Downloads page of the website for $24.95.  The download is a 2.889 Mb self-extracting Zip® file for the Windows® environment which unzips to the 2.998 Mb book in PDF file format.  Those of you who order the downloadable book will want to know that the PDF book is formatted to print on 5.5" X 8.5" paper (i.e., 8.5" X 11" sheets cut in half.)

The other two books, Rheology for Ceramists and Particle Calculations for Ceramists, continue to be available for purchase as downloadable E-books and as paperback books at the Books and Downloads page of the web site.

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Altering Suspension PSDs to Achieve Desired Process Properties

Introduction

This subject, requested by a reader, makes an excellent topic for an article.  The discussion to follow will be a blend of theoretical/practical solutions to the problem.  Please refer to earlier e-zine articles for more details in specific areas.

Many of you have process suspensions with properties that vary from batch to batch as the particle size distribution (PSD) varies, or as the additive chemistry varies, etc.  When a second and possibly a third or fourth suspension of body or raw material needs to be mixed into the main body, how can one control it and still maintain the body properties?  There are different possible ways to proceed and we will explore some options.

First, one must determine which specific parameters need to be controlled.  In a whiteware body, one needs to keep the composition constant while controlling the packing potential of the body, the surface area of powders, the viscosity, and the rheology.  In our coal slurry project years ago, we wanted to control PSD to minimize viscosity while maximizing solids content.  In some technical ceramic applications, the porosity of the compact (which leads to control of permeability, and dry and fired shrinkages) may be the most important control parameter.  Each of you will need to decide what your specific goals are, and then you can proceed.

Trial and Error in the Laboratory

This is probably the most used method for solving most process problems.  One would hope that a lot of theory goes into preparations before lab testing takes place.  Occasionally there will be no other choice but to proceed directly to the lab.  When this is the first and only good method, don't waste any time.  Go for it.  For example, someone recently asked how to identify the best types of dispersants for use with a particular system.  The best answer is to collect all possible additives, and test them all in the lab with the body in question.  It is not a great solution, but it works.  We tested several hundred dispersants on the coal slurry project to identify a hand full that worked somewhat, and one that worked well. 

Regarding PSDs, one can make several suspensions of different PSDs to mix with the process body.  Then, mix a wide variety of compositions of test distributions with the process body and put the resulting suspensions through lab trials similar to those of the production process.  This will allow each mixture to be tested specifically for the properties determined to be important to achieve your goals.  

For example, several different PSD mixtures can be cast, dried, and fired to see how they performed.  Viscosities can be measured, behaviors with different additives and additive concentrations can be tested, casting properties and dry and fired properties can be measured, etc.

It would be better, however, if there was some theoretical guidance that could be applied first.  THEN, the testing can follow.

Purely Theoretical Work

Many properties affected by PSD changes have been discussed in earlier issues of this e-zine.  Older articles may help answer very specific questions.  But we will review some practical pointers here regarding PSD variations.  

*  Theoretical PSDs and mixtures can easily be calculated using spreadsheet programs.

*  Discrete theories of particle packing (which are frequent and common in the technical literature) are easy to use to calculate expected packing results, but their applicability to real distributions should be questioned.  These are not recommended for most real distributions.

*  Continuous theories of particle packing (such as those by Funk and Dinger, and Andreasen) and continuing research in this area are fewer and farther between, but they are more applicable to production suspensions and bodies.  Calculations are slightly more complex, but results are directly applicable to process suspensions and bodies.

*  Most real distributions are log-normal in character.  When a well-controlled distribution has been made, its histogram should be relatively linear on log-log axes, but it will still have a tail on both coarse and fine ends of the distribution.  When distributions are sufficiently narrow such that the linear central portion of the histogram disappears -- the remaining distribution will have a fine tail, followed immediately by a coarse tail.  Such distributions will appear to be log-normal.

*  An excellent suspension (packing will be reasonably good, viscosity will be good, rheology will be shear-thinning, etc.) will occur when the central, linear part of the distribution's histogram will be broad, linear on log-log axes, and with a slightly positive slope.  A slightly positive slope translates into a distribution with more particles in each successively larger size class.  The most particles (by mass or volume) will be in the largest size class of the linear region of the distribution, and the fewest particles (by mass or volume) will be in the smallest size class of the linear region of the distribution.  For theoretical packing purposes, ignore the coarse and fine tails on the distribution and concentrate on the linear central portion.  (See earlier articles on PSDs and optimum packing.)

*  Gaps (where particle size classes in the middle of the distribution contain no particles) can exist in the distribution.  If gaps exist, packing may be slightly worse, viscosity and rheology should remain similar, additive chemical requirements will differ.   

It is very easy to "play" with theoretical PSDs in computer spreadsheet programs.  If the actual PSDs of production bodies and other candidate suspensions are known, PSDs can be entered into the spreadsheet programs and mixtures of various compositions can easily be calculated.  This requires, however, that you know the PSD of the distribution you are trying to achieve.  Building PSDs without knowing what you are trying to achieve serves no purpose.  For example, if you are trying to mix new powders to duplicate an old PSD, it is relatively easy to calculate mixtures to determine whether the new PSDs can match the old one.  In this case, you can even have the spreadsheet calculate a difference value to use as a guide.  It is certainly a lot easier to mill test suspensions, measure the PSDs, and then play with mixtures in the computer than to play with mixtures in the lab.  This will quickly tell you whether you need to mill different suspensions or whether you can use the present ones to best achieve your goals.

"What If?" games are easily played in a spreadsheet program.  For example, "What if 50% of this is be added to 50% of that?  What if I make it a 40%/60% mixture?", etc.  If the PSD of the target distribution is known, trial and error can be used to calculate the best composition of mixtures to match a target distribution.  Solver® can also be used in MS Excel® to calculate it for you.  Solver® is distributed with MS Excel® but you need to specifically install it if you want to use it.  It is not automatically installed, but it resides on the distribution disk when you need it.  If a program to calculate the minimum expected porosity is available (such as the one in the DRD Add-In Functions which work with MS Excel®), a wide range of PSDs can be calculated and expected porosities can be compared. Surface areas and numbers of particles are also easy to calculate.

Do as much work in the spreadsheet as possible before going out to the lab.  If you can make a distribution in the spreadsheet, you should be able to make the same distribution in the lab -- especially if you were using real PSDs measured on a particle size analyzer.  Even if you used theoretical distributions only -- as long as they are close to the actual PSDs you can achieve with your powders, they too should provide excellent results.

                    An Extrusion Example

One student wanted to improve the extrusion characteristics of alumina powders.  He had several different calcined alumina powders that he could use.  Each of these powders measured to a PSD that was so narrow -- the histograms appeared to be log-normal distributions with no linear central portion.  He mixed these distributions in the spreadsheet program to make and vary the linear portions at the centers of the histograms of binary and ternary mixtures.  Even though each powder itself was very narrow and had no central linear region, combinations of two or three broadened the distribution to produce a short linear region in the middle of the histogram.  His initial goals were to produce broader distributions using the several ingredient alumina powders and then to vary the slope of the central linear region of the broader distributions.  

Each of the resulting mixtures were also so narrow that they still looked very much log-normal.  When viewed carefully, the histograms of the mixtures looked like volcanic peaks with different angles defining the edges of the caldera of the volcanoes.  They varied from relatively low sloping linear portions to steep linear portions.  Quick glances, however, suggested there were hardly any differences between the resulting distributions.

From the spreadsheet results, he selected the compositions he wanted to test in the lab.  This allowed him to considerably reduce the number of lab trials.  Note:  he had tested a large number of compositions in the spreadsheet.

When he then went into the lab, mixed and produced the new distributions, and extruded samples, the distributions with the shallow slopes extruded very easily (measured by tracking flow rate as a function of applied pressure in a piston extruder) and the steep slopes extruded very poorly.  Actually, there was little difference in extrusion behaviors between some of his new mixtures and the individual powders which he also tested.  The resulting changes to the histograms appeared to be relatively minor (almost non-existent), but the extrusion test results were remarkably different.  We were all surprised to learn that such 'minor' changes to the histograms produced such dramatic changes in extrusion behaviors.

                    A Superconducting Oxide Example

Several years ago, everybody was searching to identify THE new family of high temperature (i.e., room temperature) superconducting oxide materials.  Rumor had it that Nobel prizes would be in the offing to the person or group who came up with the new composition.  So everybody was searching for the new, room temperature composition.  No one ever identified this new family, by the way, but a lot of effort over several years went into the search.

During that time, one of our students was trying to tape cast thin films of superconducting oxides.  He came to me after being unsuccessful at making tapes at 60% solids.  He was using a commercial organic liquid as the suspending fluid.  His only variables were the PSD of his powders and the solids contents.  The specific problem he had was that the supplier only provided him with one powder (that is, with one PSD.)  That was it.  One!

We decided that he should ball mill that one powder to produce several different, finer distributions to be used to make a mixture.  After completing that step, he measured the PSDs of each using our particle size analyzer.  We then put the measured distribution results into the spreadsheet program and asked it to select the mixture composition that packed most densely.  With that composition in hand, he then went out to the lab and mixed his milled powders to produce that distribution.  With that distribution, he was able to successfully tape cast at 75% solids.

After further processing, he determined that he had sufficiently contaminated his powder during the ball milling, that he could not obtain the superconducting properties he  needed.  BUT, he then knew exactly whcih PSD he needed to be able to successfully tape cast his powders.  He took that information and went back to the supplier to show them the range of particle sizes he needed to successfully complete his research.

I am a firm believer in "playing" with the calculated values of distributions and mixtures of distributions in a spreadsheet program as much as possible before doing any testing in the lab.  I'm sure on the coal slurry project we calculated thousands of distributions in the lab computer to test our theories and theoretical results.  Once we knew which PSDs we wanted, then the problem became how to produce them in the lab without the necessity of mixing several individual distributions.  We wanted a one-step process:  throw the feed coal into the mill;  mill it for an hour: and dump the excellent, low viscosity slurry.  That took a lot of research as well, but we had parallel programs taking place:  (1) the theoretical, computer research told us what PSDs we needed, and (2) the milling research told us how to achieve the required PSDs. 

One-Step Milling versus Mixing Several Suspensions to Achieve Target PSDs

This is a good place to discuss one-step milling versus mixing several suspensions, each of which have been milled individually.  In the case just mentioned, we were using large batch ball mills.  They scaled up well from the lab batch ball mills used for testing.  So our goal was to make the target distribution in one step in a process similar to the one used in the smaller lab trials.  We succeeded.

Alternatively, we could have milled several different suspensions to different levels of fineness and then mixed them to achieve the target PSD.  

Upon scale-up to full production sizes, however, we necessarily had to change to a continuous ball mill plus use a stirred ball mill for fines production.  Product from the continuous ball mill was used as feed to the stirred ball mill loop.  Both streams were then metered into the final mixing tank.

Why did we change processes?  We wanted a continuous process, which the batch mills did not allow.  We also needed lots of fines, which the stirred ball mill produced efficiently but the tumbling ball mill did not.  So we chose the correct types of mills for each type of milling, and then we mixed the products to achieve our final target distributions.  

Theoretically, it makes no difference.  One-step milling versus mixing of several PSDs can produce identical distributions.  Practically, it depends how well the final mixing is performed.  Experience suggests that most mixing processes aren't performed as well as they should be.  The tendency is to stop mixing when a suspension looks mixed -- which is frequently a long way from actually achieving a homogeneous distribution.  If the mixing is performed well with the proper mixing equipment, solids content, and intensity, both ways are equivalent.

It is generally easier to achieve precise control of fine details within the target PSDs by milling several different product streams and combining them than trying to control several different features of a PSD in a one-step process.  As in the example, milling several different product streams allowed the use of different types of mills to take advantage of their efficiencies at milling different types of powders.  Tumbling ball mills mill coarse particles well and efficiently, but they do not produce fines easily.  Stirred ball mills produce sub-sieve and sub-micron fines well and efficiently.  When a PSD requires both coarse and fine powders, the use of both types of mills is advantageous.

Play With A Spreadsheet Program First -- Then Test in the Lab

This is the recommended approach.  "Play" with the spreadsheet first.  Do as much as possible -- answer as many questions as possible -- while sitting at the computer.  Then, start the tests in the lab.  The examples above discussed how we performed this type of work.  We produced many different trials in the computer first.  We even set up the computer to perform tasks automatically over our two week Christmas holiday one year.  Since it doesn't get bored or tired, we allowed it to crank 24/7 for two weeks straight.  When we returned, we had reams and reams of output to analyze, but we made good use of the computer's capabilities.  Then, when we were satisfied we knew what we wanted, we went into the lab to produce distributions with those particular PSDs.

As a computer person, I have always advocated "playing" with theoretical trials and results in a computer.  The other person on the team at that time, however, didn't really like computers.  He loved working in the lab.  So I played on the computer and he played with the laboratory research and production trials.  We combined and compared notes frequently and successfully solved our problem.

Some Final Pointers for PSD Variations

*  Narrow distributions (for example, all powders in the size range defined by two adjacent sieves) can be expected to produce (1) poor packing, and (2) dilatant rheology.  The so-called "discrete" approach to particle packing requires the use of narrow distributions.  If it is necessary to use particles with narrow size classes, as many of them as possible should be used so the resulting particle size distribution will be as broad and continuous as possible.

*  Broad distributions contain particles covering really wide ranges of particle sizes.  Refractory compositions can be extremely broad because if necessary, they can start with 1" diameter particles and continue down into the sub-micron sizes.  Electronic and other technical ceramics frequently have the narrowest size ranges.  If the coarsest particles in a distribution are 10 microns or less, the distribution by definition is narrow.  If the coarsest powder in a distribution is up in the millimeter or centimeter size range, the distribution CAN BE broad.  It can still also be narrow.

*  For lowest viscosities, one generally wants a distribution that packs most densely.  If a suspension will be dispersed with a deflocculant, the denser the packing capability, the lower the viscosity will be.  The highest viscosities will occur with very narrow distributions that pack most poorly.

*  Regarding chemical additives, flocculants can take any low viscosity suspension and increase its viscosity.  Deflocculants can take SOME high viscosity suspensions and lower their viscosities.  The limits for both of these are set by PSD considerations.  A narrow distribution that packs poorly will produce a high viscosity suspension regardless of the type and concentration of chemical additive used.  The viscosity will be high because the particles collide with one another during shear flow.  The additives used simply can't overcome high particle/particle collision rates.

*  A very broad, perfect distribution that packs really well will normally have a low viscosity using a dispersant.  Addition of flocculants, however, can cause the otherwise low viscosity body to have a high viscosity.  This is the case with many whiteware slips.  

*  The use of deflocculants will frequently allow higher solids contents to be used with similar viscosities.  If a PSD is changed slightly, or if solids contents are increased slightly, higher viscosities can usually be lowered again using deflocculants.  Similarly, when viscosities are too low, flocculants can usually be used to increase viscosities.  Just remember:  increases in deflocculant or flocculant concentrations will change the nature of the rheology as well as viscosities.  They may return process viscosities to desired levels, but deflocculants enhance dilatant character of suspensions, and flocculants render suspensions more shear-thinning.  Deflocculants enhance particle/particle collisions during shear flow.  Flocculants reduce the effects of particle/particle collisions during shear flow.  

*  Rheologies will generally be good (shear-thinning) when PSDs are broad and packing is excellent.  Even in the presence of high levels of flocculants to raise viscosities, if the PSD is broad and packing is excellent, rheologies will be good regardless of the level of viscosity.  Solids content behaves in this general direction as well.  This means that an excellent PSD in a slip will produce an excellent rheology in the slip and a good rheology in the dewatered (higher solids) cast body.  Rheologies generally get worse (they become more dilatant) as solids contents increase.  If the slip is broad with a good PSD, a dewatered cast piece from that slip will have a reasonable rheology as well.

*  Rheologies will generally be bad (tending towards dilatant) when PSDs are narrow, packing is poor, and solids contents are high.  High concentrations of deflocculant may help to decrease viscosities slightly, but a poor PSD usually controls both viscosity and rheology.  Suspensions containing especially narrow PSDs simply will not flow well, and they will tend to be dilatant -- regardless of the type or concentrations of additives used.

*  Chemical additives cannot overcome bad packing and bad PSDs.  Chemical additives can give you a broad range of properties when used with distributions that pack well and have broad PSDs.

*  To alter a PSD, without changing process properties, try to maintain or improve the fundamental packing capability of the overall PSD.  It is possible to add a second PSD to a production body which will increase its viscosity.  It is also possible to add a second PSD to a production body which will decrease its viscosity.  If the second PSD can be added without altering viscosity, that is good.  If the second PSD increases viscosity, the final body will be either more dilute or more deflocculated to achieve similar viscosity.  If the second PSD decreases viscosity, the final body can be either a higher solids content or more flocculated to achieve similar viscosity.  

*  Changes to PSD can affect solids contents, surface areas of the powders, viscosities, rheologies, and the level of flocculation/deflocculation of the body.  Controlling the PSD to alter any one of these five parameters will affect the other four as well.

*  As PSDs get fine, packing considerations become less prominent and surface areas have greater and greater effects.  Viscosities of especially fine suspensions are controlled (limited) more by the high surface areas of the powders than by the particle size distribution of the particles.  For example, a perfect PSD (from a packing standpoint) which is 100% finer than 1 micrometer will have a poor viscosity because surface/surface interactions will dominate during shear flow.  A similar perfect PSD which is between 1000 and 10 000 micrometers will hardly be affected at all by surface areas.  

This list contains many broad generalities that apply to PSD alterations and production properties of suspensions and forming bodies.  All interactions between particles become worse, i.e., more dominant, as solids contents increase.  This applies to bodies which are prepared and tuned as suspensions and are then dewatered to produce plastic forming bodies.  Particle/particle collisions will be much more dominant in the plastic forming bodies.  As particles are farther and farther apart (solids contents are low), suspension properties are more receptive to chemical additive controls.  As particles are closer and closer together (solids contents are high), suspension properties are controlled mostly by PSD and particle/particle interactions during shear flow.

These pointers are broad generalities.  With the help of computer spreadsheets, PSD variations can be calculated.  There are no programs available today, however, (to the best of my knowledge) that allow viscosities, rheologies, or effects of additives to be calculated.  Alterations to those parameters require laboratory experimentation and testing.