Volume 4  Number 12                            Dennis R. Dinger                                1 October 2006

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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Dilatancy -- Fact or Fiction

Introduction

A lot has been written on the topic of dilatancy over the years in this E-zine.  Recently, when talking with a friend about this subject, I remembered that I have met some engineers and/or scientists over the years who didn't believe there were dilatant suspensions.  Whether or not dilatancy is real or myth, therefore, deserves an article.

One Example

          Rheological Measurements on Concentric-Cylinder Viscometers -- An Attempt to Show Newtonian Behavior in Suspensions

This first example chronicles an attempt to disallow yield-dilatant rheograms in favor of shear-thinning/Newtonian behaviors (that is, in favor of Bingham rheologies.)

Years ago on the coal slurry project at Alfred University, we were using a concentric cylinder viscometer to measure viscosities and rheologies.  Figure 1 below, shows a dilatant rheogram along with a shear-thinning rheogram for comparison.  It didn't matter what type of suspension we were measuring (coal slurry, ceramic slip, etc.), we always saw one of these two shapes of rheograms.

As we measured suspension viscosities at higher and higher shear rates, even shear-thinning rheograms (like the red one) would then reach a minimum viscosity, and eventually (when shear rates were high enough) the rheogram would tail up again.  We either saw yield-dilatant suspensions (like the dark blue curve) when shear rates exceeded the onset of dilatancy, or we saw shear-thinning suspensions (like the red curve) because our measurement conditions hadn't surpassed the onset of dilatancy.  [The onset of dilatancy is the shear rate at which dilatancy begins In this rheogram, it is at about 70 rpm where the dark blue rheogram hits its minimum viscosity.  At lower shear rates, the suspension is shear thinning.  At higher shear rates, the suspension is dilatant.]

These two types of rheological behavior never occur in simple fluids.  Why?  There are no particles in simple fluids to collide with one another to cause the dilatancy.  I admit, it is entirely possible that there could be dilatant fluids that are not suspensions, in which the mechanism for the dilatancy is a complex interaction phenomenon between fluid molecules.  Just like on all the TV courtroom dramas, when the prosecutor asks, "Is it possible?" I would have to answer "Yes, it is possible."  It is possible to have dilatancy without suspended particles.  We have not seen it, but it is possible.

In suspensions, in which solid particles are suspended in fluids, we know particles collide during shear.  In suspensions, therefore, dilatancy is not only possible, but it is to be expected.  We saw this kind of behavior in all of our suspensions.  When dilatancy was severe, the onset of dilatancy occurred at relatively low shear rates (at low viscometer rpms) and the rheograms dipped through a minimum and curved up at the higher shear rates.  When dilatancy was mild, we saw shear-thinning behavior throughout most of the rheogram with only a hint of dilatancy at the high shear rates.  In some suspensions, we saw only shear-thinning behavior.

One rheology we never saw was Newtonian behavior in our suspensions.  It is impossible to have Newtonian behavior in suspensions because at high shear rates, Newtonian fluids don't change their viscosities.  In suspensions at high shear rates, suspended particles will collide with one another --- and these collisions produce the dilatancy.  Newtonian behavior is a rheological characteristic of simple fluids, not of suspensions.

          A Presentation at a Technical Meeting

Our research team was working with a team of engineers from industry.  They, too, had a concentric cylinder viscometer, and they too were making suspension measurements and getting results like ours.

After giving a presentation during which we showed several rheograms of the yield-dilatant variety (the dark blue line in Figure 1), the moderator opened the floor for questions.  The first question (which was more like an argumentative comment) was, "We never see rheograms like yours in our suspensions."

Before I had a chance to answer, one of the engineers from our partner company's team stood up and announced, "We always see yield-dilatant rheograms like those in the presentation!"  The questioner and that engineer proceeded to discuss (argue??) the question for the remainder of the Q&A period.

This questioner did not see dilatancy, nor did he want to see it.  He was content with the idea that his suspensions were Newtonian at high shear rates.  He didn't question the existence of Newtonian suspensions.  He didn't want to deal with dilatant rheologies, and his rheograms supported his Newtonian contentions.

This is one type of reaction to dilatancy.  "We don't see it.  We don't have it.  We don't want it.  Our suspensions are Newtonian."

          How Could A Suspension Appear to be Newtonian?

We asked ourselves this question many times, and because of this question, we studied and carefully watched our suspensions while we were making rheological measurements.  In our viscometer, the bulk of the suspension sample was not visible, but it was possible to see some of the suspension at the top of the cylinder/cup gap.  Only a little was visible, but it was sufficient to make observations.  As we studied this, we sometimes noticed a suspension going from wet-looking to dry-looking --- in an instant.  The measured rheogram would show lots of noise and chatter at the shear rate when this happened, and it would then produce a relatively constant viscosity as shear rates further increased.  These rheograms resembled shear-thinning rheograms followed by Newtonian behavior.

Shear-thinning behavior followed by Newtonian behavior at high shear rates is also NOT possible in suspensions.  Actually, this type of behavior is known by another name -- it is known as Bingham rheology.  Bingham fluids are shear-thinning at low shear rates and Newtonian at high shear rates.  Bingham fluids are mathematically simple, but not totally realistic.  They have very simple equations and elegant rheograms, but Newtonian behavior at high shear rates suggests that one can shear such suspensions at higher and higher shear rates ad infinitum without EVER causing any particle/particle collisions and without ever producing dilatancy.  This is NOT possible.  When solid particles in suspension are sheared at higher and higher shear rates, eventually, the particles will collide and viscosities will increase.  This type of behavior is known as yield-dilatant behavior.

So why can some suspensions appear Newtonian?   When the suspension in a concentric cylinder viscometer (or other rotational viscometers) goes dilatant, it can easily produce a dilatant blockage within the gap between the measuring surfaces.  Suspensions can proceed quickly from sheared dilatant rheologies to dilatant blockages (with zero internal shear) in little more than an instant.  One instant the suspension is flowing freely, and the next instant, all particles are locked together in a dilatant blockage and no shear at all is occurring within the blockage between the measuring surfaces.  The blockage is a structure of particles bridging the gap between the measuring surfaces, and once formed, it will slide against the measuring surfaces.

When this happens, particles are not moving relative to one another.  "No shear at all," however, is not quite accurate.  When a blockage occurs in a concentric cylinder viscometer, all particles will lock together, and the whole blockage will slide against the cylinder and cup walls.  Either the blockage slides against the cylinder/cup surfaces, or the cylinder and cup lock together, stop instantly, and the viscometer breaks.  (Most good viscometers have a clutch to prevent this kind of damage.)

When a blockage forms and slides against the cylinder/cup walls, the fluid between the blockage and the walls (some of the carrier fluid) will shear, and some friction will occur due to the blockage sliding against the walls.  Both shear of the carrier fluid (which is frequently water) and sliding friction at the walls will increase proportionally as rpm increases.  This type of phenomenon will produce a rheogram that appears to be shear-thinning followed by Newtonian (or just simply Bingham.)  

Once a blockage occurs, all internal suspension shear stops, and any further measurements taken by the viscometer are meaningless.  In cases like this, when measurements continue, the rheogram will appear to be Bingham or simply Newtonian.  Such results are bogus because the suspension appears to be shearing when none is actually occurring.  

The Second and Better Example  

This second example is one in which the existence of dilatancy was actually denied by several non-ceramic engineers.

          The Erroneous Suggestion:  Dilatant-like Properties Are Indications of Poor Mixing

Years ago, one of my students and I attended an ACerS technical meeting.  That particular student had just solved a suspension flow problem for a health supply company.  They sold high density suspensions in tooth-paste-type tubes, and they wanted the tubes to be capable of being fully emptied as someone squeezed the tubes.  Frequently, only a little paste would exit the tube, the neck would clog, and further flow was not possible.  To access the paste, you then had to cut into the tube with a razor blade and scoop the paste out with a spatula.  This process was not only a mess, but inconvenient, undesirable, and prone to allowing the paste to dry out before it could be used.

The student had successfully solved this problem.  The problem was dilatancy, not poor mixing.  The blockage in the neck was a dilatant blockage, and the student's thesis showed how to control the paste so it would not produce dilatant blockages in the neck.  Clearly, this was a very high solids content paste which tended to be severely dilatant.  The shear rate produced as one squeezes paste out of a toothpaste tube is certainly not very high.  So for the paste to clog the neck with a dilatant blockage was a definite indication of extreme dilatancy conditions.  

Back to the conference ......  One of the other speakers claimed to be an extrusion/modelling expert.  Some of his data from his experimental bodies indicated dilatancy.  When it came time for Q&A, I immediately had my hand up.  I asked, "What do you do about the dilatancy?"  He asked if I had seen some indications in his data that led me to believe his body was dilatant.  I answered, "Yes."

He then proceeded to explain:  (1) He was a chemical engineer and "chemical engineers don't get hyper at the mention of the word dilatancy like ceramic engineers do";  and (2) Anything I had seen in his data that appeared to be dilatancy was just poor mixing.  

He implied that there was no such thing as dilatancy --- which is simply a construct of our warped ceramic engineering brains.  And everything that looks like dilatancy is just poor mixing.  If you see something that looks like dilatancy, just mix the body better, and the "dilatancy" will go away.

By his answer to my question, he was suggesting that the problem my student had just solved would have gone away had the student (or the paste supplier) only mixed their bodies properly.  Would that it were that simple!  

Since that meeting, I have seen several suspension piping systems which treated high solids suspensions like high viscosity Newtonian fluids.  Viscosities of molasses (high viscosity Newtonian fluids) and high solids suspensions may be similar, but their rheologies are quite different.  To design a piping system for molasses, and then use it for a high solids suspension will create lots of problems -- least of which will be the settling of solids in the pipe and worst of which will be dilatancy and dilatant blockages.

          Will Better Mixing Help?

Can dilatancy be eliminated by better mixing?  In a word:   NO.  

The only way to eliminate dilatancy is to eliminate all suspended particles.  This is not possible in suspensions.  This is certainly not possible throughout most of the ceramics industry.  We use particles all the time.  We are constantly dealing with suspensions.  You can't eliminate the solid particles.  And as long as there are suspended particles in ceramic forming bodies, high shear rates will produce particle/particle collisions, and particle/particle collisions will produce dilatancy.

Fact or Fiction?

So back we go to the original question:  Some engineers believe there is no such thing as dilatancy.  Some engineers believe their suspensions are Bingham (shear-thinning at low shear rates, and Newtonian at high shear rates.)  In both cases, the engineers are rationalizing explanations so they do not need to deal with dilatancy.  Neither is correct.  

There is an actual phenomenon known as dilatancy.  Dilatancy is caused by particle/particle collisions at high shear rates.  Dilatancy happens regularly in ceramic suspensions --- especially during high shear operations --- and sometimes during low shear rate operations.

Dilatancy can be made worse by poor mixing.  But dilatancy cannot be eliminated by great mixing.  Dilatancy is not a mixing problem.  Dilatancy is not even a mixing phenomenon. 

ALL suspensions are yield-dilatant.  Fortunately, most suspensions are processed at sufficiently low shear rates to stay well clear of the high shear regions in which dilatancy dominates.  Fortunately also, most ceramic forming takes place at suficiently low solids contents which produces conditions that are also far away from the dilatant regions.   

As ceramic and materials engineers, we need to deal with dilatancy -- we cannot ignore it nor treat it as nonexistent.  

Dilatancy is a real phenomenon that occurs frequently.  Engineers can ignore it if they want, or deny its existence, or convince themselves they are dealing with Newtonian fluids, but they jeopardize their processes when they do.