Volume 1 Number 3 Dennis R. Dinger 1 January 2003
An Update
Merry Christmas and Happy New Year!
Please feel free to forward this or any issue to friends and associates. If this is the first issue you've seen and you want to add your name to the mailing list, click HERE. All back issues are stored on the web site and they can be accessed from the Publications page. Questions, suggestions, and/or requests for topics to be covered in future issues of this e-zine can be sent to QuestionsandComments@DingerCeramics.com .
My new book, Rheology for Ceramists, is now available on the Books and Downloads page in PDF format as a downloadable self-extracting zip file. Adobe® Acrobat® Reader®, which is required to access the PDF file, is available as a free download using the link provided at the bottom of the Books and Downloads page. A free downloadable preview of the Rheology book is also available on the website. The preview contains a PDF version of the Table of Contents, Preface, and Chapter 3 in a self-extracting zip file.
The target audience for Rheology for Ceramists includes ceramic technicians, artists, students, engineers, managers, and anyone else who wants to know why suspensions behave the way they do. Ceramists really don't need to know all the details of the equations governing rheological phenomena. They need to understand the phenomena, why the various properties occur, and how to control them. In this book, I tried to answer the What?, Why?, and How? questions concerning rheological phenomena. As a result, the book contains only a few equations, no differential equations, and lots of explanations using common, everyday examples. After reading it, if you'd like to distribute copies to your staff, that would be great! Unlike this e-zine, which is free, the sale of books is a part of my livelihood. If you'd like to distribute copies, just purchase the appropriate number of downloads, and then make copies from your copy to distribute as you wish. I'll let you know when the paperback version will be available.
Rationale for High Intensity Dispersion
There appear to be two approaches to mixing and dispersion. The first approach is to mix suspensions as little as necessary to achieve 'homogeneity' and then to attempt to not disturb these suspensions during storage (using as little agitation intensity as possible) so properties remain constant until the slips can be used. The second approach is to use High Intensity Dispersion (HID) to mix suspensions to quickly achieve homogeneity. After HID, the intensities of applied shear during further processing are of little consequence to the constancy of slip properties. Of course in addition to these two approaches which define the extremes, there are the many ceramic process systems operated at an infinite variety of intensities between these two.
I've seen both extreme approaches in use. The first approach doesn't work. (Those who use the first approach might dispute this.) OK ... the first approach doesn't work well. A traditional casting slip may be a uniformly tan color to the human eye, but low intensity dispersion (LID) does not produce homogeneity at the particulate level. Suspensions produced using only LID typically need lots of aging time and even then, properties will continue to drift with time as the suspensions move towards equilibrium.
HID can quickly render suspensions as close to homogeneity as one can expect to achieve in ceramic process systems. Every ceramic manufacturer that uses process suspensions should find HID to be beneficial for their systems.
It seems appropriate, therefore, to devote an article to explain the rationale for HID and to mention its benefits.
HID Conditions
HID conditions are defined with respect to agitator tip speeds, but even when they are correct, if the suspensions' solids contents are not high enough, HID cannot be successfully accomplished.
Agitator Tip Speed
HID conditions occur when agitator tip speeds are 5000ft/min (1524m/min) or higher. HID agitator blades resemble carbide tipped table saw blades, with the carbide tips leaning back so they bat the particles around, rather than tipped forward to cut as on a normal saw blade.
Solids Content
This characteristic is more difficult to define than tip speed. Solids contents need to be sufficiently high so the particles are somewhat crowded. The system should not be severely dilatant, nor should it contain excess fluid. Generally speaking, HID suspensions should be about 40-50vol% solids. Typical whiteware casting slips, for example, with specific gravities ~1.8 respond well to HID.
HID Dispersion Equipment
Standard, commercial, 3-speed milkshake mixers can achieve HID conditions with 1" diameter carbide blades at both medium and high speeds. A laboratory HID disperser at Clemson University can handle 5 gallon buckets of slip with approximately 4" diameter agitator blades. HID conditions occurred at about 5000 rpm in that device. In industry, large (~6-8m3) HID blungers, with larger diameter blades, heavy refractory tank linings, and large (150hp) motors, are in use. Production sized Continuous HID (CHID) units are also in use.
Just because the mixer is capable of HID conditions, however, doesn't mean it always produces them. One engineer told me he tried HID on his production body and it didn't work. He had used a disperser/agitator combination similar to the 5 gal laboratory HID unit in the labs at Clemson, except he had run it at only ~1000rpm. Standing next to Clemson's lab unit when it's running at 1000rpm, it sounds like it's literally ripping the slip apart. It's intense! But those are not HID conditions. As bad as it sounds at 1000rpm, it sounds much worse at 5000rpm, which is where the HID conditions begin. The mere fact that you're using an "HID disperser" doesn't mean you've subjected the slip to HID conditions. Be careful about this.
Homogeneity
True HID conditions subject suspensions to such high intensities that it's doubtful the process slips will ever be exposed to any higher intensities later in processing. That's exactly what you want from HID. Flawed particles (that might break as they pass through a pump during processing) will surely break during HID. Weak agglomerates (that may break if impacted with sufficient force during aging) will break into constituent particles during HID. Book stacks of kaolinite sheets (which may or may not delaminate during processing) will be delaminated during HID. Surface impurities (which may or may not be stripped from particles during processing) will be stripped from particles during HID. The actual mixedness of a suspension will be maximized during HID. Additives and minor constituents will be well dispersed during HID. All particles, plates, agglomerate pieces, impurities, chemicals, additives, minor constituents, and ions will be well dispersed throughout the HID batch, forming what has been called the "interparticle soup."
When HID is completed and the suspension is pumped into a storage tank, all of the well-dispersed entities will move (or adsorb) to equilibrium positions. If shear imposed as the suspension passes through a pump strips some adsorbed entities from particle surfaces and returns them to the interparticle soup, they can simply return during quiescent periods to similar equilibrium positions.
Low Intensity Dispersion (LID) cannot achieve such levels of homogeneity. Slips may look homogeneous to the human eye, but down at the particle and additive molecule levels, they will not be homogeneous. When such slips are sent to aging tanks, serendipity and chance then take over. All of the phenomena mentioned above that happen during HID may happen during LID and aging if (and only if) the particles, agglomerates, book stacks, etc., are impacted perfectly at some point in time during storage or processing by agitators, tank walls, pump impellors, pump housings, pipes, or other particles. Since dispersion intensities are low during LID blunging (and even lower during storage), deagglomeration, delamination, and impurity stripping will occur randomly, by chance, and infrequently at best.
As a result, LID suspension properties tend to drift with time. If an agglomerate has a chance encounter with a pump impellor or a pipe wall, it may break to expose new, fresh surfaces to the interparticle environment. When this happens, will additive chemicals be available to adsorb onto the newly exposed surfaces? Probably not. Experience suggests that additives that are designed to adsorb onto particle surfaces will do so quickly. They won't simply hang around in the interparticle soup waiting for new surfaces to appear. They'll adsorb in thicker-than-optimum layers if fresh surfaces are not available. So when a new surface is exposed to the interparticle environment during aging, additives typically will not be there to coat them. Properties will then drift. Viscosities of suspensions in storage tanks will most likely increase daily, for example. This is a sure sign that homogeneity has not been achieved.
LID blungers in general, and storage agitators in particular, cannot achieve the high levels of mixedness possible during HID. When storage tank agitators are properly designed, they will recirculate suspensions (especially providing upward recirculation) to prevent settling of large particles. How good are storage tank agitators for mixing? Not good. Designs that produce appropriate, gentle, storage recirculation are not optimized for mixing. Sure, mixing occurs, but slowly! When suspension properties drift, into which tank are adjusting chemicals typically added? ... and mixed? Into the aging tank? How long does it take for such additives to be uniformly distributed throughout the slip in the aging tank? The time it takes to adequately mix new additives into a storage tank simply becomes another variable in the property drift problem. Will adjusting chemicals added to an aging tank actually find the appropriate particle surfaces? How long will it take them to do so? Or will they adsorb onto surfaces already coated with other additives? Or if they were added in a quick, concentrated splash into the tank (as one or two 'glugs' as some might say), will they form an over-flocculated rock before they can be dispersed, sink to the bottom of the tank, and never be adequately mixed into the suspension? Many such questions can be asked relative to low intensity agitation. Storage tanks are simply not the best place to be adjusting slips (even though this is a daily practice in most plants.)
After HID, both the levels of homogeneity and the slip properties should be far different from those that can be achieved with only LID. The questions concerning the use of storage tanks and storage impellers for adjusting slips, however, apply to both LID and HID systems. Property drift can still occur after HID mixing, but if the HID duration is adequate, property drift should be minimal.
Specific Surface Areas
HID typically does not break particles unless they are flawed and weak. HID does NOT typically increase measured Specific Surface Areas (SSA), either. One would expect that deagglomeration, delamination, and the stripping of surface impurities would increase measured SSA values. Our experience shows this does not happen.
Most of today's SSA analyzers use nitrogen adsorption techniques to measure particle surface areas. Apparently, nitrogen molecules are small enough to infiltrate kaolinite book stacks and porous agglomerates. As a result, measured SSA values routinely include the surface areas of kaolinite layers within book stacks, and of intra-agglomerate surfaces in relatively porous agglomerates. These surfaces are not exposed or available to the interparticle fluids, nor to most additives (which are much larger than nitrogen molecules). Nevertheless, SSA measurements appear to include the areas of these inner, 'hidden' surfaces.
Since HID deagglomerates, delaminates, etc., it can actually liberate these particles and expose these surfaces to the interparticle environment. Once freed, not only can they travel as individual particles, but they can also interact with additives. This particular benefit of HID should be quite valuable to most systems, because liberating these entities into the interparticle soup exposes them to the additives and allows them to perform the tasks for which they were added to the batch in the first place.
This especially applies to minor constituents, some of which are quite expensive. Not only can HID liberate them, and expose them to the interparticle environment, but once liberated and free to report as individual particles, they can then be uniformly dispersed throughout the suspension. One agglomerate (composed of 1000 small particles) at one location in a suspension will behave very differently than 1000 small particles distributed uniformly throughout the suspension. Glaze pigments are an excellent example. Experience has shown that HID can reduce the percentages of pigments required to achieve desired colors and color intensities, and it can produce more stable coloration from batch to batch. Without HID, higher pigment concentrations are frequently required to achieve less stable systems.
Energy Requirements
HID typically requires lots of power from large motors. Efficiencies of mixing should be defined relative to the power requirements needed to achieve homogeneity. Sometimes, bean counters try to define the efficiency of mixing simply by the amount of energy used. More energy used is less efficient. Less energy used is more efficient. If that's the definition of efficiency to be used, then most efficient mixing occurs when the mixing step is skipped entirely, because no energy at all will have been used (and by this definition, that would be very efficient!)
Hopefully, you're saying to yourself, "That's absurd!" That's the point! Efficiency must always be defined relative to the achievement of some goal. Efficiency of mixing isn't simply to minimize the energy used, but it is to minimize the energy used in the process of achieving a specific, desired goal. The question should be: What's the most efficient way to achieve homogeneity of mixing in ceramic process suspensions? You want to use as little energy as possible, but you want to achieve homogeneity. The definition of efficiency must be based on the amount of energy required to actually achieve homogeneity ... and that can be quite a lot.
A strong dose of high intensity, high-powered mixing, applied in one well-controlled blunger, will put a suspension much closer to true homogeneity than will several weeks of aging in low intensity storage tanks.
Motor Requirements -- Suspensions vs Simple Fluids
When sales reps are asked to size motors for a mixing tank, their guidelines typically suggest that motor sizes should increase as fluid viscosities increase. Their equations and charts are generally based on Newtonian (simple) fluids. Ceramic suspensions, however, are NOT Newtonian. Most ceramic suspensions exhibit shear-thinning rheologies and they are therefore very different from simple fluids. When performing HID, you want particles in suspension to be somewhat crowded to enhance particle/particle collisions. This brings dilatant rheologies into the picture, and those are almost certainly not covered by normal sales guidelines.
Our experience on large, production HID units used with ceramic suspensions has shown that suspension viscosities rise during HID (as expected). As new surfaces are exposed to the interparticle soup, additive coverage decreases per unit of available surface area, and viscosities tend to rise. If motor power should increase as viscosities increase, then power draws should increase in HID systems as viscosities rise with time. But just the opposite occurs (at least in the systems we've tested). As we tracked the power draw in large, production HID units, power draws decreased with time, even as viscosities increased. Apparently, particle size distributions (PSDs) were altered (improved??) during HID to those that produced improved rheological properties. The addition of deflocculants during HID to reduce viscosities had little effect on power draws. Power draws appeared to track (decrease) with improved PSDs and with the duration of HID. Fully detailed explanations for these phenomena have not yet been completely sorted out, but the results stand as described.
To add an HID blunger to a production process, use a large motor in the first unit. A 150hp motor should be adequate in a 6-8m3 blunger. The impeller diameter should be about 30% of the tank diameter, and it should be positioned approximately an impeller radius from the bottom of the tank. The tank should include baffles to prevent the suspension from spinning within the tank. Then, collect data carefully as the first unit is operated and use that information to adjust the fill depth of the tank, and to size the motor requirements for any further HID units to be installed.
HID Benefits
HID can achieve high levels of homogeneity in relatively short times. The use of HID reduces the need for long aging periods. Drift of suspension properties during aging is minimized with HID. Percentages of minor constituents, which are very well dispersed by HID systems, may be reduced while maintaining consistent properties for which they were added. Some surfaces which are accessible to nitrogen in SSA measurements, but not to interparticle fluids and additives, can be liberated by HID to report as individuals, to interact with fluids and additives, and then to be homogeneously distributed throughout the suspension.
High Intensity Dispersion should be beneficial in most ceramic process suspensions. If you are not presently using it, and have not yet considered it, or tried it ... Check it out!
Particle Shape Effects in Ceramic Processing
Most computer models use spherical particle shapes. Most ceramic particles are anything but spherical shapes. How do particle shapes affect ceramic processing phenomena? How do spherical shape assumptions affect the results of particle packing and other computer models? How do the model results relate to actual processing phenomena? These topics and questions will be addressed in this article.
Particle Packing
The simple answer to the question, 'How does particle shape affect packing?' is: It doesn't. Before you suggest that I've gone off the deep end, consider my reasoning behind this statement.
Results from our packing research from the early 1980s suggests that for broad, continuous particle size distributions classified using a fourth root of two size series (the use of all U.S. Standard Sieves produces a fourth root of two size series), densest packing occurs when each particle size class (packing from coarse to fine) fills 6.21% of the volume available to it. The coarsest size class has to fill 6.21vol% of the volume to be packed; the next smaller size class has to fill 6.21vol% of the remaining space; and so on down through the class sizes. There is a similarity condition at work here. Each size class packs similar to every other size class. So the way the first size class (the coarsest) packs will be indicative of the way all smaller size classes will pack.
Consider the case where a single, 1ft3 volume sphere is packed into a box. The sphere will be ~15" diameter ... about the size of a small beach ball, and the edge length of the cubical box will be ~30". A 15" sphere has approximately 6.21vol% of the volume of a 30" box. The box contains about 16 times the volume of the sphere. That's the requirement for dense packing of a broad, continuous distribution. The similarity condition says that each smaller particle will be required to fill 6.21vol% of proportionally smaller boxes. When this method of packing is followed precisely, there will always be enough empty smaller boxes available with the compact to accommodate the required number of smaller particles.
Back to the question: Does particle shape really matter? Couldn't a 1ft3 cube (a cube with 12" edge length) fit just as easily into a 30" edge-length box? ... or a 1ft3 octahedron? ... or a 1ft3 dodecahedron? ... or a 1ft3 hexagonal plate? This line of reasoning suggests that particle shape doesn't really affect packing. It also suggests that after many, many hours spent converting our computer models to handle non-spherical particles, and after many, many more hours of computational time, we'd achieve similar packing results for the non-spherical particles as those achieved for spheres. So I didn't write a non-spherical packing model, and following the line of reasoning just presented, my answer to this question is: Particle shape doesn't affect optimum packing potentials calculated by computer models.
Packing in Computer Models
The computer models I've written actually pack particles into a box. (Well, they packed virtual particles into a virtual box.) In such models, spheres are the shape of first choice. The results from these models allowed the calculation of packing potentials of particle size distributions. The packing potential is the densest packing factor to which a particle size distribution could pack in a perfect world. Within a computer packing model, there are no forces between particles, no particle flow, no friction between surfaces as the particles slide against one another, and no gravity. If a pore is large enough to hold a particle, one can be inserted (without any concern for a flow channel to move it from the surface of the pack to the pore -- it's simply inserted into the pore. Bingo!) It's an ideal situation.
Packing in Ceramic Systems
Packing in an actual ceramic system is not as simple as packing in a computer model. If pores exist in a compact (and many do), it's impossible to insert particles into them. In fact, once a pore exists in a compact, it's too late to do anything about it. Perfect packing in ceramic systems requires all particles in the distribution to report as individuals. It also requires perfectly homogeneous mixing, and perfectly smooth surfaces to eliminate interparticle friction. These conditions must remain at all solids contents as the system is dewatered until all particles only and finally contact at the last possible instant in the perfect, dense packing arrangement. Unfortunately, this never happens in particulate suspensions. Particles don't all report as individuals; particles aren't perfectly smooth; and suspensions are hardly ever perfectly, homogeneously mixed.
Viscous and Rheological Properties
Particle shape may not affect the calculated packing potential of a distribution, but particle shape has major effects on the viscous and rheological properties of ceramic forming bodies and suspensions. If it was possible to mix a suspension perfectly to produce a truly homogeneous distribution of particles, particles would have to move relative to one another, and slide against one another as forming and/or dewatering take place. Particle shapes definitely affect these processes. For particles to remain independent as individuals until the last possible moment, extreme levels of deflocculation are be required, and this can cause rheological problems regardless of the particle shapes. In partially flocculated bodies, which are typical in ceramic systems, particles will be loosely joined in gel structures well before dense, homogeneous packing arrangements can be achieved.
A variety of phenomena occur when non-spherical particles are present in flowing suspensions. All of these affect the viscous and rheological properties of suspensions.
Some Particles Tumble
As you all know, a football sails smoothly when thrown with a nice spiral, but it tumbles awkwardly otherwise. Most particles in suspensions and forming bodies don't spiral. They tumble. When solids contents are sufficiently low, particles can tumble without interfering with each other as they flow. Shear forces due to faster particles on one side of a particle, and slower particles on the other side, cause this. As solids contents rise, tumbling non-spherical particles interfere more and more with neighboring particles, which causes viscosities to rise and rheological properties to be more dilatant.
Some Particles Orient and Slide
At higher solids contents, for example in extrusion systems, some particles (such as hexagonal clay platelets) take preferred orientations relative to each other. Clay platelets tend to orient with their broad surfaces parallel to the surfaces of extrusion augers. When high solids clay bodies flow through extrusion dies, their plates line up parallel to the shear planes so particle surfaces slide against particle surfaces during shear flow. Particles in preferred orientations like this are not randomly, nor homogenously distributed, but some ordered packing arrangements can be relatively dense.
Some Particles Tangle With One Another
Long fibers tend to tangle and prevent mixing and flow. As I understand it, this problem held up the development of fiber reinforced cermets for a long period of time. The goal was to mix high concentrations of long fibers with fine powders, and the systems were just impossible to mix. The long fibers were the problem because they formed large, unshearable tangles.
Some Particles Change Shape During Processing
Some non-spherical particles will undergo shape changes during processing. Sharp edges can be rounded off by attrition during processing as particles in suspension collide with one another and become generally more spherical in shape. This occurs slowly in aging tanks, or more quickly in HID systems. Large, strong particles can also act as grinding media for small particles. The rule of thumb for milling media is to use balls that are 25 times the size of the feed particles. Size ratios like this certainly exist in many ceramic suspensions. When conditions are right, large particles can act as grinding media to reduce the sizes of smaller particles. So even though a body may start with non-spherical particles, it's likely that many of those particles will undergo shape changes by the time they are sent to forming operations. As particle shapes change, the viscous and rheological properties of the suspension will change as well. As particles become generally more spherical, the magnitude of dilatant interactions will decrease.
Some Particle Surfaces Are Rough
Some particles have particularly rough surfaces which hinder them from easily sliding against other particles. For any given mineral, ease of sliding decreases with particle size. As particle sizes and masses decrease, specific surface areas increase substantially. As ceramic suspensions and bodies become finer, particle mass and momentum have less effect, and surface frictional forces have more effect on the particles' capabilities to slide and to rearrange during shear. These effects hinder particles from flowing well so they can achieve their perfect, homogeneous positions within slips and bodies.
Some polymeric additives can function as lubricants to reduce surface roughnesses. The types, concentrations, and homogeneity of distribution of such additives throughout ceramic suspensions and bodies all affect surface friction between particles, which in turn affects viscous and rheological properties.
Summary
It is possible to estimate packing potentials of ceramic suspensions using computer models and spherical particle assumptions. Dense packing research results suggest that each particle must fit into a volume ~16 times its size. Most non-spherical particles can easily fit into pores that are ~16 times their size. Particle shape, therefore, appears to have little to do with packing potential.
Computer models attempt to achieve perfectly homogeneous distributions of particles throughout the perfect environments in computer volumes to be packed. This is probably the major point of difference between computer models and ceramic slips and forming bodies. If all particles in a ceramic suspension reported as individuals and were located in their perfectly distributed, homogeneous sites, the suspension results should duplicate the computer models' results. But this doesn't happen.
The main reason this doesn't happen is that homogeneity in a process suspension can only be achieved by perfect mixing. Perfect mixing is a function of the mixing process, certainly, but it's also a function of the viscous and rheological properties of the suspensions.
Particle shapes, surface properties, and sizes affect how particles flow, whether they tumble erratically or slide, whether they tangle with one another or otherwise interfere with other flowing particles to cause dilatant rheological problems, and/or whether they will change shape during mixing and storage. The state of flocculation/deflocculation in each suspension also affects the packing capabilities of suspended particles. Flocculated systems (which tend to have shear-thinning rheologies) produce relatively open (porous) structures, regardless of the packing potential of the suspended particles. Deflocculated systems (which have tendencies toward dilatant rheologies) can produce relatively dense packs depending on the particle size distribution of the particles, the smoothness of the particle surfaces, and the homogeneity of mixing of those particles.
Optimum packing efficiencies are calculated in the perfect worlds within computer models. While particle shapes don't affect optimum packing efficiencies calculated in the perfect world of computer models, they do affect the viscosities and rheologies of ceramic suspensions, which in turn affect the actual packing densities achievable during forming, as well as the dry and fired shrinkages of the ceramic compacts. This is where particle shape and particle surface properties have their greatest influences on ceramic process suspensions. As particle shapes become less and less spherical, and surfaces become more rough, suspension viscosities can be expected to increase, rheologies will become more dilatant, and actual packing densities will certainly decrease.
Miscellany
For those of you interested in the new rheology book, it's currently only available in a downloadable PDF file version. Although nobody has yet asked, I have been curious how PDF files print, so I printed the PDF file to produce a copy of the book for myself. It's formatted to fit onto half sheet sizes of paper, 5½"W X 8½"L. The security on the downloadable file prevents you from modifying the book, but it doesn't prevent you from printing it. I inserted a stack of half sheets of paper in my printer, told it I wanted a single, double-sided copy, and it produced a very nice copy of the book. I then printed extra front and back covers on heavier paper, punched and bound everything with a plastic binding, and voilà!
I know it is much nicer to read a book while sitting in a comfortable chair in the living room than to read a book at the desk from a computer screen. I wanted you to know that you can achieve this end from the PDF file.
Thanks. See you next time.
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103 Augusta Rd, Clemson, SC 29631 (864) 654-3155
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