Introduction

There are two major categories of processing problems in ceramic production companies:  those caused by chemistry and those caused by particle physics.  By chemistry, we refer to the additives in interparticle fluids that are used to adjust slip and plastic forming body viscosities and rheologies.  Many plastic forming bodies are mixed and adjusted as slips before dewatering to final processing consistencies in filter presses.  By particle physics, we refer to all physical properties of particles and their interactions (density, shape, surface area, porosity, etc.)  Degrees of non-sphericity, surface roughnesses, and interactions during flow directly relate to potential processing problems.

We learned early during our coal slurry project days (more than two decades ago) that both chemistry and particle physics had to be correct for suspension viscosities and rheologies to be good.  If either or both were bad, good suspensions could not be produced.  This is also the case within ceramic process systems -- both chemistry and particle physics must both be well-controlled to achieve desired processing properties.

In Part II of this two-part series, we will cover the major problem resulting from particle physics: dilatancy.

What Is Dilatancy?

All slips prepared by ceramic production companies fall into the general category of particle/fluid suspensions.  Most production slips consist of fine solid particles (representing a range of sizes) suspended in a carrier fluid which is typically water.  Some production suspensions use organic carrier fluids.

In both cases, whether water or organic fluids are the carrier, the solid particles must be homogeneously mixed with the fluid in a mixer and the suspension is then caused to flow to form the ware.  Some suspensions are at high solids contents (high concentrations of particles in the fluid), while some are at low solids contents (low concentrations of particles in the fluid.)  Slip casting and glaze suspensions are usually produced at high solids contents because both processes require high viscosity suspensions and particles that are quite close to one another.  Spray drying slips, however, are generally produced at relatively low viscosities because they must be atomized during the spray drying process.  For high quality atomization, particles must be far apart and viscosities must be very low as the body slip flows through the atomizer.  All ceramic suspensions consist of solid particles suspended in carrier fluids.  The distances between particles, the viscosities of the carrier fluids, the surface properties of the powders, and the applied shear rates during processing control the viscosity and rheology of each suspension and the numbers and natures of particle/particle interactions during flow and forming processes.

Dilatancy results as solid particles collide with other solid particles and with channel walls during suspension flow.  Whenever suspensions are sitting quiescent, neither particles nor fluid are flowing.  Under those circumstances, particles cannot collide with other particles.  Whenever suspensions are flowing, however, such as during mixing in blungers, stirring in holding tanks, flowing in distribution pipes, flowing through atomizers, flowing into plaster molds, and dewatering in plaster molds, particles and fluids are moving and particle/particle collisions can then occur.  Dilatancy occurs when particles are forced to move fast enough that they collide with (rather than flow around) other particles.  Dilatancy is defined as the increase of suspension viscosity as the rate of shear increases.  The fundamental cause of dilatancy is particle/particle collisions.  Whenever particles are present in a fluid, which occurs in any and all suspensions, particles can collide during flow and dilatancy can occur.  

Dilatancy can also occur in complex fluids that are not suspensions, but such occurrences are rare.  For example, the author has observed dilatancy in a heavy fuel oil as it was atomized at more than 220^oF into a combustion chamber.  This particular fuel oil consisted of a very heavy residual fuel oil (with properties similar to road tar) that was diluted with very low viscosity waste solvents.  Two waste streams (a tar and a solvent) were mixed together to make a "heavy fuel oil."  Under atomization conditions at the high temperature, the solvent fraction was vaporizing and the "oil" that was atomized was actually a foamy tar.  This is an example of a fluid under extreme conditions:  the mixture itself was extreme;  the shear rates in the atomizer were especially high;  and the temperature of the fluid was also especially high.  Such behavior by today's fuel oils is unusual -- but possible!

Dilatancy is common in ceramic suspensions and should be expected in all true suspensions -- i.e., when solid particles are suspended in a fluid.  This includes all ceramic process suspensions.  Even though most suspensions never demonstrate dilatant properties, all suspensions will go dilatant when sheared at sufficiently high shear rates.  

Newtonian Fluids

To properly define dilatancy, the two other common rheologies must also be considered.  Most common fluids are considered to be Newtonian.  All Newtonian fluids exhibit a single viscosity regardless of the applied shear rate.  Water, for example, is water, regardless of whether it is being sprayed through the garden hose nozzle, or whether it is flowing slowly down a stream.  The viscosity of water is always ~1 cP.  Vinegar has a similar viscosity.  Cooking oil has a slightly higher viscosity.  Most pure simple fluids (those which consist primarily of a single molecular type) are Newtonian and they exhibit a single viscosity regardless of applied shear.  

Because most common fluids are Newtonian, most people associate a single viscosity with each fluid.  For this reason, one can refer to the viscosity of a particular fluid and then state a single viscosity value for it.  For example, "The viscosity of water is ~1 cP."  Period!  No further explanations or qualifications need be given.  Water has a viscosity of ~1 cP.  End of story!

Most fluids encountered by the average person in the kitchen, in an auto parts store, or in daily life in general, are Newtonian.  So it is no surprise that many people don't even realize that non-Newtonian fluids exist.  

Any suspension, which by definition contains solid particles in a carrier fluid, however, is not Newtonian.  All suspensions should automatically be considered to be non-Newtonian -- never Newtonian.  The viscosities of all suspensions are affected by the interactions of particles, fluid, and shear rates during flow and they will not ever be Newtonian in behavior.

Shear-Thinning Fluids

The second most common type of fluids is shear-thinning fluids.  Many non-Newtonian fluids in the average kitchen's refrigerator are shear-thinning.  Mustard, ketchup, mayonnaise, and whipped cream are examples of common shear-thinning fluids.  Shear-thinning means that the fluids behave with lower viscosities as they are sheared at higher and higher shear rates.  Only extremely high viscosity fluids and solids can hold a spoon stationary at a normally unstable position.  But whip the fluid at a high rate (which by definition is the application of a high shear rate) with a spoon and the fluid will flow easily as if it has a very low viscosity.  Whipped cream is the best example of this.   At low shear rates, it behaves with a high viscosity;  at high shear rates, it behaves with a low viscosity.  The other examples mentioned behave similarly.

Whether or not the average person realizes that non-Newtonian shear-thinning fluids exist, most people are familiar with non-Newtonian shear-thinning fluids. 

Dilatant Fluids

Dilatancy is the opposite of shear-thinning behavior.  Dilatant fluids can also be described as shear-thickening fluids.  Because dilatant fluids are less common, many people are unaware that dilatancy exists.  The only example of a dilatant fluid that can be found in the average kitchen is a corn starch and milk (or water) mixture which is used for thickening gravy.  Some people have seen and played with corn starch suspensions, but many have not.

The author has even met some scientists who don't believe that dilatant fluids exist.  They seem to think that fluids that thicken when sheared only do so because they have been poorly mixed.  Unfortunately, this is not the case.  Dilatant suspensions thicken when sheared because (1) they contain solid particles, and (2) those solid particles collide with each other more and more violently as shear rates increase.  

All ceramists, and many chemical and process engineers who deal regularly with suspensions, do not have the luxury of denying the existence of dilatancy.  They must deal with dilatancy on a daily basis.  This especially includes all ceramic engineering students on the first day of their first ceramics lab.  Most chemical engineering students learn about rheology and non-Newtonian fluids in their advanced courses.  Many other engineers never study this subject.  Ceramists not only learn about but must deal with rheology and non-Newtonian fluids right from the very start.  

Particle/Particle Collisions

Dilatant (shear-thickening) rheologies result from particles colliding during suspension flow.  Collisions increase as more and more particles are concentrated in suspensions (as solids contents increase) and as collision intensities increase (as shear rates increase).  

Dilatancy can be minimized by reducing both the number and intensity of collisions.  The number of collisions can be reduced by lowering solids contents.  Solids contents can only be lowered so far, however.  The number and intensity of collisions can be reduced by lowering flow rates of suspensions, but this, too, has its limits.  Atomization, by its very nature, is an extremely high shear process.  If a low solids content suspension is to be atomized in a spray dryer, the suspended particles will necessarily experience extremely high shear rates and many particle/particle collisions during atomization.  If a high solids content suspension is to be blunged in a primary mixing tank, or stirred slowly in a holding tank, suspended particles will again experience particle/particle collisions.  Whenever you cause a suspension to flow, particles will collide.  Count on it.

Minimizing Dilatant Effects

All suspensions can exhibit dilatancy, but not all suspensions will.  How does one ELIMINATE dilantancy?  Dilatancy CANNOT be ELIMINATED.  How can one MINIMIZE dilatancy?  This is a proper question.  Dilatancy can be minimized by reducing both the number and intensity of collisions. 

To reduce the number of collisions, one can lower solids contents, improve the particle size distribution of the powders in suspension, and minimize all flow rates throughout the process.  To reduce collision intensities, one must minimize all suspension flow rates.  To properly address this phenomenon, there are two cases that must be considered:  (1) prepared suspensions, and (2) suspensions that are about to be prepared.

          Prepared Suspensions  

When suspensions have already been prepared, which includes all suspensions in holding tanks, in other process tanks, and in process piping, one can only minimize dilatancy by reducing shear rates.  Any suspension that has been identified as exhibiting dilatant properties can only be handled by reducing all flow rates.  If the suspension cannot be changed in any way, one can only SLOW DOWN!  This is not the direction management desires for their industrial processes because their typical goal is to proceed faster and faster.  When dilatant properties are exhibited by a suspension, the ONLY change that can be made is to reduce all shear rates.  Flow rates MUST BE reduced;  RPMs in mixers, jiggering, and roller forming operations MUST BE reduced;  velocities during tape casting MUST BE reduced;  pump volume flow rates MUST BE reduced; etc.  

ANY shear rate increases in ANY processes will only exacerbate dilatancy problems.  The author has only ever encountered one company in which dilatant rheologies were considered to be beneficial.  They considered it a desirable and beneficial property, but they could not demonstrate any place in their process in which the dilatant behaviors were actually desirable or beneficial.  In fact, they had process problems directly attributable to the dilatancy.

          Preparing Suspensions

When suspensions are being prepared, one can reduce the potential for particle/particle collisions by using lower solids contents when possible, and by improving the particle size distribution of the powders.  The most extreme cases of dilatancy will occur when all particles are the same size.  The mildest dilatancy will occur when particle sizes cover a broad range of sizes.  Another way to understand particle size distribution requirements is to understand that improved packing capabilities of powders reduces the onset and intensity of dilatancy.  Particle size distributions that can pack very densely will exhibit minimal particle/particle collisions when suspended at reasonable solids contents.  Particle size distributions that pack very poorly (all particles are the same size) will exhibit maximum particle/particle collisions when suspended even at relatively low solids contents.

One can also minimize particle/particle collisions by making sure that suspensions are partially flocculated (rather than partially or fully deflocculated).  Flocculation favors shear-thinning behavior.  Deflocculation favors dilatant behavior.  So making sure that all suspensions are at least partially flocculated will minimize dilatant effects.

Once a suspension is prepared and sent to process holding tanks, one can continue to try to tune them to more flocculated states, or to lower solids contents.  If this is not possible, the only recourse is to reduce all process shear rates.  

Is Dilatancy Ever Beneficial?

Yes!  Mild dilatancy CAN BE beneficial in one or two places.  Mild dilatancy is beneficial during high intensity mixing (HID) in which you want particles to collide with one another to improve mixing, breakup of large flocs, and breakup of some weak agglomerates.  Mild dilatancy is also beneficial during milling where, once again, you want particle/particle collisions and breakage events to occur.  

It is not necessary in either case to tune suspensions before mixing or milling to produce dilatant properties.  It is necessary, however, to HID at high solids contents to insure particle/particle collisions.  When HID is performed at low solids contents where particle/particle collisions are rare, HID does not do its job.  HID must be done at higher solids contents where particles collide frequently.  Particles should be crowded in HID suspensions.

Do not lower solids contents to try to minimize particle/particle collisions during HID or milling, because you want greater numbers and greater intensities of particle/particle collisions during those two processes.

Milling is helped when particles collide easily and frequently, although higher solids contents and crowding in mills are less important than higher solids contents during HID.  

Are there any other cases in which dilatancy is beneficial?  Not to my knowledge!

Extreme Dilatancy

When dilatancy is extreme and/or when shear rates are extremely high,  dilatant blockages can form.  As dilatancy begins, particle/particle collisions grow in number.  As the dilatant character of a suspension increases or as shear rates increase, more and more particle collisions occur.  When dilatant character of a suspension becomes extreme, or shear rates increase to extreme levels, sufficient numbers of collisions occur that a network of colliding particles can bridge out from channel walls and cause the cross-sectional area of the flow channel to be reduced.  When this happens, following particles can collide with forming bridges of particles and extend their size and strength.  If particles are flowing near the center of the channel, they may not collide with forming bridges but flow freely through the opening.  As the diameter of the central flow channel decreases, however, volume flow rates decrease, while local shear rates increase.  As local shear rates increase, dilatant problems grow:  local apparent viscosities increase and more and more particles collide with each other and with the forming bridge structures reaching out from the channel walls.  Certainly, bridging particles can form and break up and form and break up, but in continuous systems in which upstream pressures are constant, particles colliding with the forming bridge structures will have no opportunities to back up and then continue through the open passageway.  As this continues, the forming bridges of particles can reach out across the whole flow channel and totally block further flow.  Once the whole cross-sectional area of the flow channel is filled with bridging particles from the walls, the buildup is considered to be a blockage.  Under pressure from the pump, all later particles will then filter press into this blockage and fill the upstream flow channel -- possibly as far back as to the pump.  

When a dilatant blockage occurs, the pipe or flow channel will be totally blocked and effectively ruined.  The only solution at this point is to throw the blocked pipe away and replace it with another.

When using shear-thinning suspensions, it is helpful to use smaller diameter pipes to keep shear rates higher and effective viscosities lower.  In dilatant suspensions, however, it is helpful to use larger diameter pipes, which lower shear rates and minimize viscosities.  Most processes are set up for shear-thinning suspensions.  When suspensions with strongly dilatant character find their way into process piping, conditions will be favorable for dilatancy to cause lots of flow problems and especially dilatant blockages.

Dilatant blockages can occur in any and all flow pipes in the process.  When this happens, replace the blocked pipe and continue.  If all suspensions will have dilatant character, replace the blocked pipe with a larger diameter pipe so flow rates are lower in that section of pipe.  When dilatant character is unusual, unexpected, and rare, replace the blocked pipe with the same diameter, and try to insure that all suspensions fed through that point in the process will only see shear-thinning suspensions.  NOTE:  dilatant blockages will occur first at the point in the process where local conditions are most extreme.

Dilatant blockages can occur in small channels in injection molding dies.  When such blockages occur, downstream regions in the die will be blocked and the ware will exhibit unfilled and unformed regions.  

Dilatant blockages can also occur in complex extrusion dies.  In this case, regions of the die can be blocked, and the extrusion column will have unfilled channels down the length of the ware.

Eliminating Dilatancy Problems

This subject was discussed above, but it deserves repeating.  In most cases, when dilatancy causes processing problems, the immediate process solution is to reduce all process speeds.  This is necessary because the system may be filled with dilatant suspension, so the reduced speeds will minimize the dilatant behavior until the dilatant suspension is completely removed from all process piping.  The ultimate process solution, however, is to change the body to remove the dilatant character: fix the solids content; fix the particle size distribution; or fix the chemistry of the body.  Many such process problems require process engineers to retire to the lab to rework the body formulation, rather than to go out into the plant to try to work through the problem.  Some workers in the plant may not understand why the process engineer has disappeared when a nasty problem emerges, but unless the body is adjusted or the formulation changed, dilatant conditions can continue and particularly nasty process problems can continue as well.

A Particle Physics Problem

Remember, dilatancy is fundamentally a particle physics problems.  Particles collide with other particles and the effective viscosity of the suspension increases as this occurs.  Yes, chemical tuning can help to reduce dilatant character -- adjusting a suspension to be more flocculated usually helps reduce dilatancy -- but increasing the level of flocculation also increases the viscosity of the suspension (which may not be desirable).  Dilatancy is caused by particle/particle collisions, so a permanent fix must be to change the physical properties of the suspension (solids content and/or particle size distribution).

In some processes, solids contents are controlled, but particle size distribution is not.  When this occurs, it is sometimes assumed that all corrections to all suspension problems can be made with chemical additives.  After all, it is relatively easy to continue to tune suspensions after they have been blunged and pumped to holding tanks.  But that won't always work.  Dilatancy is a particle physics problem, so particle physics adjustments must necessarily be made to solve the problem.  

For example, when particle size distribution is not controlled, but solids content IS controlled, resulting process suspensions can cover a wide range of viscosities.  In such cases, target viscosities are usually achieved with chemical adjustments.  When suspension viscosities are high before chemical tuning, suspensions tuned into the target viscosity window can be highly deflocculated because the high viscosity needed to be reduced using deflocculants.  When suspension viscosities are low before chemical tuning, suspensions tuned into the target viscosity window can be highly flocculated because the low viscosity needed to be increased using flocculants.  

It is simply not possible that both highly deflocculated suspensions and highly flocculated suspensions (at a constant solids content) will perform similarly in any ceramic process.  Unless particle physics adjustments are made to fix particle physics problems like dilatancy, process suspension properties will vary all over the map -- and yields will vary all over the map as well.

How Do We Know Dilatancy Is A Particle Physics Problem?

When the author was on the faculty at Alfred University, his Ph.D. student wrote a computer model to calculate viscosities.  The student used the billiard ball approach to the problem.  The only means of energy transfer between particles in his model was due to the transfer of energy from particle/particle collisions.  The only result that the model produced was dilatancy.  It could not produce shear-thinning behavior.  The worst viscosities were for monodispersions (all particles a single size) of particles.  When a distribution of particles was tested in the model, calculated viscosities were lower than those for the monodispersions.

At that same time, all other researchers who were modelling viscosities of suspensions were calculating and predicting viscosities using attractive and repulsive fields surrounding their particles.  In those models, they would impose attractive or repulsive fields around two particles located a distance apart.  Then, they would cause the two particles to approach each other at fixed velocity.  They never allowed their particles to collide -- they had no software in their models to handle particle collisions.  The repulsive forces at the surfaces of the particles caused the particles to slow down, change direction, and move away from one another.  In those cases when their particles collided, they threw out the results and started again with lower initial approach velocities.  Their models only ever produced shear-thinning viscosities.  They never saw dilatancy.

Note that all of the surface attractive/repulsive force models, which did not allow particle collisions, they only ever predicted shear-thinning viscosities.  Our model, which totally ignored attractive/repulsive forces between particles and only paid attention to particle/particle collision energy transfers, only ever predicted dilatancy.  The results from these two fundamentally different modelling approaches were totally opposite:  In our case, particle/particle collisions only produced dilatancy; and in their case, interparticle forces only produced shear-thinning behaviors.

The two different results, however, clearly explain the whole phenomenon:  At low solids contents and/or at low shear rates where particle collisions are minimal, interparticle forces and shear-thinning rheologies dominate.  At high solids contents and/or at high shear rates where particle collisions dominate, dilatant rheologies dominate.  Over the whole range of shear rates, shear-thinning and dilatant effects are always present, counteracting one another.  Rheologies in suspensions, therefore, are the combination of these two effects which occur simultaneously.

Summary

Dilatancy is a particle physics problem.  Adjustments to suspension chemistry may produce temporary process fixes to such problems, but fundamentally, dilatancy problems must be fixed by adjustments to particle physics.  The two most common particle physics adjustments are solids content and particle size distribution.  

In the author's opinion, mild dilatancy is beneficial only during HID and milling operations.  Dilatancy is never beneficial in any other case -- especially when it occurs in process suspensions.  (I would be glad to hear exceptions to this conclusion.)

Dilatancy, in the extreme, produces dilatant blockages.  When blockages occur, wares, dies, and other process equipment can be damaged or ruined.

Dilatancy is produced by particle/particle collisions.  When dilatant problems occur, changes must be made to the body or to the process that reduce the number and/or intensity of particle/particle collisions. 

All suspensions are non-Newtonian.

All suspensions exhibit both shear-thinning and dilatant character.  Shear-thinning character usually dominates at low shear rates.  Dilatant character usually dominates at high shear rates.

At high shear rates, all suspensions will exhibit dilatancy.  

Two major ceramic process problems are syneresis and dilatancy.  Syneresis is a chemistry problem and dilatancy is a particle physics problem.  Each of these problems should be corrected by adjustments that address their specific causes.  To eliminate syneresis, suspension chemistries must be adjusted to lower levels of flocculation.  To minimize dilatancy, suspension particle physics properties and/or process shear rates must be adjusted to reduce particle/particle collisions.

Miscellany

Suggested topics for future issues of this E-zine .... Please continue to send your ideas or questions for future topics.  Thanks.  Until next time ...

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